Subrahmanyan Chandrasekhar - Collected Quotes

"All of us are sensitive to nature's beauty. It is not unreasonable that some aspects of this beauty are shared by the natural sciences." (Subrahmanyan Chandrasekhar, "Beauty and the Quest for Beauty in Science", Physics Today Vol. 32 (7), [lecture] 1979)

"It is, indeed an incredible fact that what the human mind, at its deepest and most profound, perceives as beautiful finds its realization in external nature.[...] What is intelligible is also beautiful." (Subrahmanyan Chandrasekhar, "Beauty and the Quest for Beauty in Science", Physics Today Vol. 32 (7), [lecture] 1979)

"The black holes of nature are the most perfect macroscopic objects there are in the universe: the only elements in their construction are our concepts of space and time." (Subrahmanyan Chandrasekhar, "The Mathematical Theory of Black Holes", 1983)

"A black hole partitions the three-dimensional space into two regions: an inner region which is bounded by a smooth two-dimensional surface called the event horizon; and an outer region, external to the event horizon, which is asymptotically flat; and it is required (as a part of the definition) that no point in the inner region can communicate with any point of the outer region. This incommunicability is guaranteed by the impossibility of any light signal, originating in the inner region, crossing the event horizon. The requirement of asymptotic flatness of the outer region is equivalent to the requirement that the black hole is isolated in space and that far from the event horizon the space-time approaches the customary space-time of terrestrial physics." (Subrahmanyan Chandrasekhar, "On Stars, Their Evolution, and Their Stability",[Nobel lecture] 1983)

"The mathematical theory of black holes is a subject of immense complexity; but its study has convinced me of the basic truth of the ancient mottoes 'The simple is the seal of the true' and 'beauty is the splendor of truth.'" (Subrahmanyan Chandrasekhar, "On Stars, Their Evolution, and Their Stability",[Nobel lecture] 1983)

"Turning to the physical properties of the black holes, we can study them best by examining their reaction to external perturbations such as the incidence of waves of different sorts. Such studies reveal an analytic richness of the Kerr space-time which one could hardly have expected. This is not the occasion to elaborate on these technical matters. Let it suffice to say that contrary to every prior expectation, all the standard equations of mathematical physics can be solved exactly in the Kerr space-time. And the solutions predict a variety and range of physical phenomena which black holes must exhibit in their interaction with the world outside." (Subrahmanyan Chandrasekhar, "On Stars, Their Evolution, and Their Stability",[Nobel lecture] 1983)

"In some strange way, any new fact or insight that I may have found has not seemed to me as a 'discovery' of mine, but rather something that had always been there and that I had chanced to pick up." (Subrahmanyan Chandrasekhar, "Truth and Beauty: Aesthetics and Motivations in Science", 1987)

"The pursuit of science has often been compared to the scaling of mountains, high and not so high. But who amongst us can hope, even in imagination, to scale the Everest and reach its summit when the sky is blue and the air is still, and in the stillness of the air survey the entire Himalayan range in the dazzling white of the snow stretching to infinity? None of us can hope for a comparable vision of nature and of the universe around us. But there is nothing mean or lowly in standing in the valley below and awaiting the sun to rise over Kinchinjunga." (Subrahmanyan Chandrasekhar, "Truth and Beauty: Aesthetics and Motivations in Science, 1987)

"When a supremely great creative mind is kindled, it leaves a blazing trail that remains a beacon for centuries." (Subrahmanyan Chandrasekhar, "Newton and Michelangelo", Current Science Vol. 67 (7), 1994)

"This 'shuddering before the beautiful', this incredible fact that a discovery motivated by a search after the beautiful in mathematics should find its exact replica in Nature, persuades me to say that beauty is that to which the human mind responds at its deepest and most profound." (Subrahmanyan Chandrasekhar)

Sheldon L Glashow - Collected Quotes

"Tapestries are made by many artisans working together. The contributions of separate workers cannot be discerned in the completed work, and the loose and false threads have been covered over. So it is in our picture of particle physics." (Sheldon L Glashow, "Towards a Unified Theory - Threads in a Tapestry", [Nobel lecture] 1979)

"The confusion of the past [in particle physics] is now replaced by a simple and elegant synthesis. [This] standard theory may survive as a part of the ultimate theory, or it may turn out to be fundamentally wrong. In either case, it will have been an important way-station, and the next theory will have to be better." (Sheldon L Glashow, "Towards a Unified Theory - Threads in a Tapestry", [Nobel lecture] 1979)

"Contemplation of superstrings may evolve into an activity as remote from conventional particle physics as particle physics is from chemistry, to be conducted at schools of divinity by future equivalents of medieval theologians. For the first time since the Dark Ages, we can see how our noble search may end, with faith replacing science once again." (Sheldon L Glashow, "Desperately Seeking Superstrings?", Physics Today, 1986)

"In lieu of the traditional confrontation between theory and experiment, superstring theorists pursue an inner harmony where elegance, uniqueness and beauty define truth. The theory depends for its existence upon magical coincidences, miraculous cancellations and relations among seemingly unrelated (and possibly undiscovered) fields of mathematics." (Sheldon L Glashow, "Desperately Seeking Superstrings?", Physics Today, 1986)

"The theory of everything may come in its time, but not until we are certain that Nature has exhausted her bag of performable tricks." (Sheldon L Glashow, "Desperately Seeking Superstrings?", Physics Today, 1986)

"No matter how compelling or elegant it is, a theory of physics must be subjected to experimental verification or it differs little from medieval theology." (Sheldon L Glashow, "Interactions: A Journey Through the Mind of a Particle Physicist and, the Matter of This World", 1988)

"I don't have the hubris to imagine a theory of everything. I think that we scientists are seeking an understanding of the natural world. We come in various types - chemists and physicists and biologists and such - and we all have the same goal. We are making progress. The theories we have today of life and chemistry and physics are much better than they were ten years ago. And ten years from now they will be better still." (Sheldon Lee Glashow, [interview] 2003)

"String theory has had a long and wonderful history. It originated as a technique to try to understand the strong force. It was a calculational mechanism, a way of approaching a mathematical problem that was too difficult, and it was a promising way, but it was only a technique. It was a mathematical technique rather than a theory in itself." (Sheldon Lee Glashow, [interview] 2003)

"What the string theorists do is arguably physics. It deals with the physical world. They're attempting to make a consistent theory that explains the interactions we see among particles and gravity as well. That's certainly physics, but it's a kind of physics that is not yet testable. It does not make predictions that have anything to do with experiments that can be done in the laboratory or with observations that could be made in space or from telescopes." (Sheldon Lee Glashow, [interview] 2003)

Frederick Soddy - Collected Quotes

"Physical science enjoys the distinction of being the most fundamental of the experimental sciences, and its laws are obeyed universally, so far as is known, not merely by inanimate things, but also by living organisms, in their minutest parts, as single individuals, and also as whole communities. It results from this that, however complicated a series of phenomena may be and however many other sciences may enter into its complete presentation, the purely physical aspect, or the application of the known laws of matter and energy, can always be legitimately separated from the other aspects." (Frederick Soddy, "Matter and Energy", 1912)

"The laws expressing the relations between energy and matter are, however, not solely of importance in pure science. They necessarily come first in order [...] in the whole record of human experience, and they control, in the last resort, the rise or fall of political systems, the freedom or bondage of nations, the movements of commerce and industry, the origin of wealth and poverty, and the general physical welfare of the race." (Frederick Soddy, "Matter and Energy", 1912)

"The real value of science is in the getting, and those who have tasted the pleasure of discovery alone know what science is. A problem solved is dead. A world without problems to be solved would be devoid of science." (Frederick Soddy, "Matter and Energy", 1912)

"For a modern ruler the laws of conservation and transformation of energy, when the vivifing stream takes its source, the ways it wends its course in nature, and how, under wisdom and knowledge, it may be intertwined with human destiny, instead of careering headlong to the ocean, are a study at least as pregnant with consequences to life as any lesson taught by the long unscientific history of man." (Frederick Soddy, "Science and Life", 1920)

"One of the main duties of science is the correlation of phenomena, apparently disconnected and even contradictory." (Frederick Soddy, "Structure of the Atom", 1920)

"Radioactivity is a new primary science owing allegiance neither to physics nor chemistry, as these sciences were understood before its advent, because it is concerned with a knowledge of the elementary atoms themselves of a character so fundamental and intimate that the old laws of physics and chemistry, concerned almost wholly with external relationships, do not suffice." (Frederick Soddy, "Structure of the Atom", 1920)

"The history of man is dominated by, and reflects, the amount of available energy." (Frederick Soddy, "Science and Life", 1920)

"As scientific men we have all, no doubt, felt that our fellow men have become more and more satisfying as fish have taken up their work which has been put often to base uses, which must lead to disaster. But what sin is to the moralist and crime to the jurist so to the scientific man is ignorance. On our plane, knowledge and ignorance are the immemorial adversaries. Scientific men can hardly escape the charge of ignorance with regard to the precise effect of the impact of modern science upon the mode of living of the people and upon their civilisation. For them, such a charge is worse than that of crime." (Frederick Soddy, [Nobel prize speech] 1922)

"Chemistry has been termed by the physicist as the messy part of physics, but that is no reason why the physicists should be permitted to make a mess of chemistry when they invade it." (Frederick Soddy [attributed])

Chen-Ning Yang - Collected Quotes

"It is common knowledge today that in general a symmetry principle (or equivalently an invariance principle) generates a conservation law. For example, the invariance of physical laws under space displacement has as a consequence the conservation of momentum, the invariance under space rotation has as a consequence the conservation of angular momentum." (Chen-Ning Yang, "The Law of Parity Conservation and Other Symmetry Laws of Physics", [Nobel lecture] 1957)

"Nature possesses an order that one may aspire to comprehend." (Chen-Ning Yang, "The Law of Parity Conservation and Other Symmetry Laws of Physics", [Nobel lecture] 1957)

"[...] nature seems to take advantage of the simple mathematical representations of the symmetry laws. When one pauses to consider the elegance and the beautiful perfection of the mathematical reasoning involved and contrast it with the complex and far-reaching physical consequences, a deep sense of respect for the power of the symmetry laws never fails to develop." (Chen-Ning Yang, "The Law of Parity Conservation and Other Symmetry Laws of Physics", [Nobel lecture] 1957)

"The quantum numbers that designate the states of a system are often identical with those that represent the symmetries of the system." (Chen-Ning Yang, "The Law of Parity Conservation and Other Symmetry Laws of Physics", [Nobel lecture] 1957)

"Whereas the continuous symmetries always lead to conservation laws in classical mechanics, a discrete symmetry does not. With the introduction of quantum mechanics, however, this difference between the discrete and continuous symmetries disappears. The law of right-left symmetry then leads also to a conservation law: the conservation of parity." (Chen-Ning Yang, "The Law of Parity Conservation and Other Symmetry Laws of Physics", [Nobel lecture] 1957) 

"With the advent of special and general relativity, the symmetry laws gained new importance. Their connection with the dynamic laws of physics takes on a much more integrated and interdependent relationship than in classical mechanics, where logically the symmetry laws were only consequences of the dynamical laws that by chance possess the symmetries. Also in the relativity theories the realm of the symmetry laws was greatly enriched to include invariances that were by no means apparent from daily experience. Their validity rather was deduced from, or was later confirmed by complicated experimentation. Let me emphasize that the conceptual simplicity and intrinsic beauty of the symmetries that so evolve from complex experiments are for the physicists great sources of encouragement. One learns to hope that Nature possesses an order that one may aspire to comprehend." (Chen-Ning Yang, "The Law of Parity Conservation and Other Symmetry Laws of Physics", [Nobel lecture] 1957)

Jacques Monod - Collected Quotes

"There are living systems; there is no living 'matter'. No substance, no single molecule, extracted and isolated from a living being possess, of its own, the aforementioned paradoxical properties. They are present in living systems only; that is to say, nowhere below the level of the cell." (Jacques Monod, "From Biology to Ethics", 1969)

"A totally blind process can by definition lead to anything; it can even lead to vision itself." (Jacques Monod, "Chance and Necessity: An Essay on the Natural Philosophy of Modern Biology", 1970)

"Among all the occurrences possible in the universe the a priori probability of any particular one of them verges upon zero. Yet the universe exists; particular events must take place in it, the probability of which (before the event) was infinitesimal. At the present time we have no legitimate grounds for either asserting or denying that life got off to but a single start on earth, and that, as a consequence, before it appeared its chances of occurring were next to nil. [...] Destiny is written concurrently with the event, not prior to it." (Jacques Monod, "Chance and Necessity: An Essay on the Natural Philosophy of Modern Biology", 1970)

"Even today a good many distinguished minds seem unable to accept or even to understand that from a source of noise natural selection alone and unaided could have drawn all the music of the biosphere. In effect natural selection operates upon the products of chance and can feed nowhere else; but it operates in a domain of very demanding conditions, and from this domain chance is barred. It is not to chance but to these conditions that evolution owes its generally progressive course, its successive conquests, and the impression it gives of a smooth and steady unfolding." (Jacques Monod, "Chance and Necessity: An Essay on the Natural Philosophy of Modern Biology", 1970)

"Every living being is also a fossil. Within it, all the way down to the microscopic structure of its proteins, it bears the traces if not the stigmata of its ancestry." (Jacques Monod, "Chance and Necessity: An Essay on the Natural Philosophy of Modern Biology", 1970)

"Evolution in the biosphere is therefore a necessarily irreversible process defining a direction in time; a direction which is the same as that enjoined by the law of increasing entropy, that is to say, the second law of thermodynamics. This is far more than a mere comparison: the second law is founded upon considerations identical to those which establish the irreversibility of evolution. Indeed, it is legitimate to view the irreversibility of evolution as an expression of the second law in the biosphere." (Jacques Monod, "Chance and Necessity: An Essay on the Natural Philosophy of Modern Biology", 1970)

"A curious aspect of the theory of evolution is that everybody thinks he understands it." (Jacques Monod, "On the Molecular Theory of Evolution", 1974)

"One of the great problems of philosophy, is the relationship between the realm of knowledge and the realm of values. Knowledge is what is; values are what ought to be. I would say that all traditional philosophies up to and including Marxism have tried to derive the “ought” from the “is.” My point of view is that this is impossible, this is a farce." (Jacques Monod)

"The scientific attitude implies the postulate of objectivity - that is to say, the fundamental postulate that there is no plan; that there is no intention in the universe." (Jacques Monod)

Hermann Bondi - Collected Quotes

"On the most usual assumption, the universe is homogeneous on the large scale, i. e. down to regions containing each an appreciable number of nebulae. The homogeneity assumption may then be put in the form: An observer situated in a nebula and moving with the nebula will observe the same properties of the universe as any other similarly situated observer at any time." (Sir Hermann Bondi, "Review of Cosmology," Monthly Notices of the Royal Astronomical Society, 1948)

"The human mind is conservative, and the scientist makes no exception from this rule. He will accept a new theory only if it stands the trial of many experimental tests." (Hermann Bondi, [Nobel lecture] 1955)

"A quantity like time, or any other physical measurement, does not exist in a completely abstract way. We find no sense in talking about something unless we specify how we measure it. It is the definition by the method of measuring a quantity that is the one sure way of avoiding talking nonsense [...]" (Sir Hermann Bondi, "Relativity and Common Sense: A New Approach to Einstein", 1964)

"Throughout science there is a constant alternation between periods when a particular subject is in a state of order, with all known data falling neatly into their places, and a state of puzzlement and confusion, when new observations throw all neatly arranged ideas into disarray." (Sir Hermann Bondi, "Astronomy and the Physical Sciences", 1966)

"A theory is scientific only if it can be disproved. But the moment you try to cover absolutely everything the chances are that you cover nothing." (Sir Hermann Bondi, "Assumption and Myth in Physical Theory", 1967)

"All science is full of statements where you put the best face on your ignorance, where you say: true enough, we know awfully little about this, but more or less irrespective of the stuff we don't know about, we can make certain useful deductions." (Sir Hermann Bondi, "Assumption and Myth in Physical Theory", 1967)

"Science is driven forward by unexpected and surprising results emerging from new experiments or by the appearance of contradictions between theories previously thought compatible. Solving such problems as they arise is of the essence of our work. Thus science is not something strange and odd but the most human of pursuits." (Sir Hermann Bondi, "The Philosopher of Science", Nature Vol.358 (6385), 1992)

"Time must never be thought of as pre-existing in any sense; it is a manufactured quantity." (Sir Hermann Bondi)

"To the nonscientist it must seem strange that, while the history of science appears to be a brilliant success story, from a logical point of view the stress is always on disproof and hence on the failure rather than on the confirmation of theories." (Sir Hermann Bondi)

Lars P Hansen - Collected Quotes

"Part of a meaningful quantitative analysis is to look at models and try to figure out their deficiencies and the ways in which they can be improved. A more subtle challenge for statistical methods is to explore systematically potential modeling errors in order to assess the quality of the model predictions. This kind of uncertainty about the adequacy of a model or model family is not only relevant for econometricians outside the model but potentially also for agents inside the models." (Lars P Hansen, "Uncertainty Outside and Inside Economic Models", [Nobel lecture] 2013)

"Uncertainty, generally conceived, is not often embraced in public discussions of economic policy. When uncertainty includes incomplete knowledge of dynamic responses, we might well be led away from arguments that 'complicated problems require complicated solutions'. When complexity, even formulated probabilistically, is not fully understood by policy makers, perhaps it is the simpler policies that are more prudent. This could well apply to the design of monetary policy, environmental policy and financial market oversight. Enriching our toolkit to address formally such challenges will improve the guidance that economists give when applying models to policy analysis." (Lars P Hansen, "Uncertainty Outside and Inside Economic Models", [Nobel lecture] 2013)

"Using random processes in our models allows economists to capture the variability of time series data, but it also poses challenges to model builders. As model builders, we must understand the uncertainty from two different perspectives. Consider first that of the econometrician, standing outside an economic model, who must assess its congruence with reality, inclusive of its random perturbations. An econometrician’s role is to choose among different parameters that together describe a family of possible models to best mimic measured real world time series and to test the implications of these models. I refer to this as outside uncertainty. Second, agents inside our model, be it consumers, entrepreneurs, or policy makers, must also confront uncertainty as they make decisions. I refer to this as inside uncertainty, as it pertains to the decision-makers within the model. What do these agents know? From what information can they learn? With how much confidence do they forecast the future? The modeler’s choice regarding insiders’ perspectives on an uncertain future can have significant consequences for each model’s equilibrium outcomes." (Lars P Hansen, "Uncertainty Outside and Inside Economic Models", [Nobel lecture] 2013)

"When confronted with multiple models, I find it revealing to pose the resulting uncertainty as a two-stage lottery. For the purposes of my discussion, there is no reason to distinguish unknown models from unknown parameters of a given model. I will view each parameter configuration as a distinct model. Thus a model, inclusive of its parameter values, assigns probabilities to all events or outcomes within the model’s domain. The probabilities are often expressed by shocks with known distributions and outcomes are functions of these shocks. This assignment of probabilities is what I will call risk. By contrast there may be many such potential models. Consider a two-stage lottery where in stage one we select a model and in stage two we draw an outcome using the model probabilities. Call stage one model ambiguity and stage two risk that is internal to a model." (Lars P Hansen, "Uncertainty Outside and Inside Economic Models", [Nobel lecture] 2013)

"When there is a reference to a decision problem, an analysis with multiple priors can deduce bounds on the expected utility consequences of alternative decisions, and more generally a mapping from alternative priors into alternative expected outcomes." (Lars P Hansen, "Uncertainty Outside and Inside Economic Models", [Nobel lecture] 2013)

"Why is it fruitful to consider model misspecification? In economics and as in other disciplines, models are intended to be revealing simplifications, and thus deliberately are not exact characterizations of reality; it is therefore specious to criticize economic models merely for being wrong. The important criticisms are whether our models are wrong in having missed something essential to the questions under consideration." (Lars P Hansen, "Uncertainty Outside and Inside Economic Models", [Nobel lecture] 2013)

"For us, a model is a stochastic process, that is, a probability distribution over a sequence of random variables, perhaps indexed by a vector of parameters. For us, model uncertainty includes a suspicion that a model is incorrect." (Lars P Hansen & Thomas J Sargent, "Uncertainty within Economic Models", 2015)

"I view the work I've done related to statistics and economics as roughly speaking, how to do something without having to do everything. So economic models - how any model by definition isn't right. When someone just says, 'Oh, your model is wrong.' That's not much of an insight. What you want to know is, is wrong in important ways or wrong in ways that are less relevant? And you want to know what does the data really say about the model?" (Lars P Hansen)

Leon M Lederman - Collected Quotes

"A physical system is said to possess a symmetry if one can make a change in the system such that, after the change, the system is exactly the same as it was before. We call the change we are making to the system a symmetry operation or a symmetry transformation. If a system stays the same when we do a transformation to it, we say that the system is invariant under the transformation." (Leon M Lederman & Christopher T Hill, "Symmetry and the Beautiful Universe", 2004)

"Although nature suggests a pathway to a mathematical description of everything, it has thus far eluded a final or complete grand mathematical synthesis. […] Mathematics is therefore inspired by nature. But it does not have to conduct experimental observations to proceed. The worlds of mathematics and theoretical physics are therefore distinct - they have different 'mission statements'. Whereas theoretical physics maps the properties of the nature we experience, mathematics builds a map of all possible 'natures' that logic permits to exist." (Leon M Lederman & Christopher T Hill, "Symmetry and the Beautiful Universe", 2004)

"Art imitates nature through the incorporation of discrete symmetries, and indeed, reflection symmetry can be found throughout nature." (Leon M Lederman & Christopher T Hill, "Symmetry and the Beautiful Universe", 2004)

"Eternal constancy of the laws of physics is a symmetry. What we see as we look back in time, or we peer through telescopes out into space, or we look through our powerful microscopes (particle accelerators), is the same system of laws of physics governing the whole universe at all times and at all places. These are the basic symmetries of the structure of our universe and its contents and, at a deeper level, the symmetries of the laws that govern the universe themselves. Indeed, the symmetries we uncover are the basic principles that define our laws of nature and the laws of physics, hence those that control our universe." (Leon M Lederman & Christopher T Hill, "Symmetry and the Beautiful Universe", 2004)

"General relativity explains gravitation as a curvature, or bending, or warping, of the geometry of space-time, produced by the presence of matter. Free fall in a space shuttle around Earth, where space is warped, produces weightlessness, and is equivalent from the observer's point of view to freely moving in empty space where there is no large massive body producing curvature. In free fall we move along a 'geodesic' in the curved space-time, which is essentially a straight-line motion over small distances. But it becomes a curved trajectory when viewed at large distances. This is what produces the closed elliptical orbits of planets, with tiny corrections that have been correctly predicted and measured. Planets in orbits are actually in free fall in a curved space-time!" (Leon M Lederman & Christopher T Hill, "Symmetry and the Beautiful Universe", 2004)

"In the physics of complex systems we can introduce a statistical concept, a measure of randomness, called entropy. In a quiet equilibrium, like hot onion soup sitting in a thermos bottle with no escaping heat, the entropy remains constant in time. However, in violent nonequilibrium processes, like shattering glass or explosions, the entropy always increases. Essentially, entropy, as a measure of randomness, will always increase when a very ordered initial condition leads to a very disordered final state through the normal laws of physics. The fact that entropy at best stays the same in equilibrium, or increases in all other processes, is called the second law of thermodynamics." (Leon M Lederman & Christopher T Hill, "Symmetry and the Beautiful Universe", 2004) 

"Mathematicians have evolved a systematic way of thinking about symmetries that is fairly easy to grasp at the outset and a lot of fun to play with. This almost magical subject is known as group theory. […] Group theory is the mathematical language of symmetry, and it is so important that it seems to play a fundamental role in the very structure of nature. It governs the forces we see and is believed to be the organizing principle underlying all of the dynamics of elementary particles. Indeed, in modem physics the concept of symmetry serves as perhaps the most crucial concept of all. Symmetry principles are now known to dictate the basic laws of physics, to control the structure and dynamics of matter, and to define the fundamental forces in nature. Nature, at its most fundamental level, is defined by symmetry." (Leon M Lederman & Christopher T Hill, "Symmetry and the Beautiful Universe", 2004)

"Quantum-mechanical effects appear in physical systems that are exceedingly small. A small system means very tiny objects with very tiny amounts of energy, moving around over very short time intervals. Quantum effects show up dramatically once we arrive at length scales the size of the atom, about one ten-thousandth of a millionth of a meter. In fact, we simply cannot understand an atom without quantum mechanics. This is not to say that nature itself suddenly 'switches off'' classical mechanics and 'switches on' quantum mechanics when we enter this new submicroscopic realm. Quantum mechanics is always valid and always holds true at all scales of nature. Rather, quantum effects gradually become more and more pronounced as we descend into the world of atoms. Quantum mechanics is the ultimate set of rules, as far as we know, that governs how nature works" (Leon M Lederman & Christopher T Hill, "Symmetry and the Beautiful Universe", 2004)

"So, a scientist's definition of symmetry would be something like this: symmetry is an invariance of an object or system to a transformation. The invariance is the sameness or constancy of the system in form, appearance, composition, arrangement, and so on, and a transformation is the abstract action we apply to the system that takes it from one state into another, equivalent, one. There are often numerous transformations we can apply on a given system that take it into an equivalent state." (Leon M Lederman & Christopher T Hill, "Symmetry and the Beautiful Universe", 2004)

"Suppose that while flipping a coin, a small black hole passed by and ate the coin. As long as we got to see the coin, the probabilities of heads and tails would add to one, but the possibility of a coin disappearing altogether into a black hole would have to be included. Once the coin crosses the event horizon of the black hole, it simply does not meaningfully exist in our universe anymore. Can we simply adjust our probabilistic interpretation to accommodate this outcome? Will we ever encounter negative probabilities?" (Leon M Lederman & Christopher T Hill, "Symmetry and the Beautiful Universe", 2004)

"Symmetry is ubiquitous. Symmetry has myriad incarnations in the innumerable patterns designed by nature. It is a key element, often the central or defining theme, in art, music, dance, poetry, or architecture. Symmetry permeates all of science, occupying a prominent place in chemistry, biology, physiology, and astronomy. Symmetry pervades the inner world of the structure of matter, the outer world of the cosmos, and the abstract world of mathematics itself. The basic laws of physics, the most fundamental statements we can make about nature, are founded upon symmetry." (Leon M Lederman & Christopher T Hill, "Symmetry and the Beautiful Universe", 2004)

"The space and time of the universe that we humans inhabit contain symmetries. These are almost obvious yet subtle, even mysterious. Space and time form the stage upon which the dynamics - that is, the motion and interactions of the physical systems, atoms, atomic nuclei, protozoa, and people - are played out. The symmetries of space and time control the dynamics of the physical interactions of matter." (Leon M Lederman & Christopher T Hill, "Symmetry and the Beautiful Universe", 2004)

"The subject of mathematics has its own identity, on the other hand, and, in contrast to physicists, mathematicians attempt to create a roadmap of all possible logical systems that could consistently exist, whether they ultimately have anything to do with nature or not. Yet nature provides the basis of abstraction that gives birth to mathematics. " (Leon M Lederman & Christopher T Hill, "Symmetry and the Beautiful Universe", 2004)

"The symmetries that we sense and observe in the world around us affirm the notion of the existence of a perfect order and harmony underlying everything in the universe. Through symmetry we sense an apparent logic at work in the universe, external to, yet resonant with, our own minds. [...] Symmetry gives wings to our creativity. It provides organizing principles for our artistic impulses and our thinking, and it is a source of hypotheses that we can make to understand the physical world." (Leon M Lederman & Christopher T Hill, "Symmetry and the Beautiful Universe", 2004)

"Theoretical physics borrows from mathematics (or, if there's none to borrow, they invent new mathematics) in order to create a mathematical roadmap of things that can happen in the real world, in nature. It strives to explain all of the many different phenomena observed in the universe, perhaps ultimately seeking one elegant and economical logical system. However, physicists usually settle for lesser triumphs, in which many physical systems with common and comprehensible behaviors are successfully described. This description is always created in the abstract language of mathematics." (Leon M Lederman & Christopher T Hill, "Symmetry and the Beautiful Universe", 2004)

"We have come, in our time, to systematize our understanding of the rules of nature. We say that these rules are the laws of physics. The language of the laws of nature is mathematics. We acknowledge that our understanding of the laws is still incomplete, yet we know how to proceed to enlarge our understanding by means of the 'scientific method' - a logical process of observation and reason that distills the empirically true statements we can make about nature." (Leon M Lederman & Christopher T Hill, "Symmetry and the Beautiful Universe", 2004)

"We often wonder why the more complex systems seem to indicate a preferred direction of time, or an arrow of time, whereas their elementary counterparts do not. […] This has to do with the if-then nature of physics questions. Anything we observe involves laws of motion but also particular initial conditions. […] The initial conditions are what make a situation look peculiar when we time reverse it." (Leon M Lederman & Christopher T Hill, "Symmetry and the Beautiful Universe", 2004)

Jean-Baptiste Perrin - Collected Quotes

"Allow us now a hypothesis that is arbitrary but not self-contradictory. One might encounter instances where using a function without a derivative would be simpler than using one that can be differentiated. When this happens, the mathematical study of irregular continua will prove its practical value." (Jean-Baptiste Perrin, 1906)

"Consider, for instance, one of the white flakes that are obtained by salting a solution of soap. At a distance its contour may appear sharply defined, but as we draw nearer its sharpness disappears. The eye can no longer draw a tangent at any point. A line that at first sight would seem to be satisfactory appears on close scrutiny to be perpendicular or oblique. The use of a magnifying glass or microscope leaves us just as uncertain, for fresh irregularities appear every time we increase the magnification, and we never succeed in getting a sharp, smooth impression, as given, for example, by a steel ball. So, if we accept the latter as illustrating the classical form of continuity, our flake could just as logically suggest the more general notion of a continuous function without a derivative." (Jean-Baptiste Perrin, 1906)

"If, to go further, we [...] attribute to matter the infinitely granular structure that is in the spirit of atomic theory, our power to apply to reality the rigorous mathematical concept of continuity will greatly decrease." (Jean-Baptiste Perrin, 1906)

"It must be borne in mind that, although closer observation of any object generally leads to the discovery of a highly irregular structure, we often can with advantage approximate its properties by continuous functions. Although wood may be indefinitely porous, it is useful to speak of a beam that has been sawed and planed as having a finite area. In other words, at certain scales and for certain methods of investigation, many phenomena may be represented by regular continuous functions, somewhat in the same way that a sheet of tinfoil may be wrapped round a sponge without following accurately the latter's complicated contour." (Jean-Baptiste Perrin, 1906)

"Mathematicians, however, are well aware that it is childish to try to show by drawing curves that every continuous function has a derivative. Though differentiable functions are the simplest and the easiest to deal with, they are exceptional. Using geometrical language, curves that have no tangents are the rule, and regular curves, such as the circle, are interesting but quite special." (Jean-Baptiste Perrin, 1906)

"The fundamental laws of chemistry which are well known to you and which are laws of discontinuity (discontinuity between chemical species, and discontinuous variation according to the 'multiple proportions' in the composition of species made from the same simple bodies) then become immediately clear: they are imposed solely by the condition that the molecule constituting a compound contains a necessarily whole number of atoms of each of the simple bodies combined in this compound." (Jean-Baptiste Perrin, "Discontinuous Structure of Matter", [Nobel lecture] 1926)

"We are, finally, forced to think that each grain only follows the portion of liquid surrounding it, in the same way that an indicating buoy indicates and analyses the movement all the better if it is smaller: a float follows the movement of the sea more faithfully than a battleship. We obtain from this an essential property of what is called a liquid in equilibrium: its repose is only an illusion due to the imperfection of our senses, and what we call equilibrium is a certain well-defined permanent system of a perfectly irregular agitation. This is an experimental fact in which no hypothesis plays any part." ("Discontinuous Structure of Matter", [Nobel lecture] 1926)

"It is thus that statistics reveals more and more the inconstancy and the irregularity of much social phenomena, when in lieu of applying it to a great nation altogether, one descends to a province, a town, a village." (Jean-Baptiste Perrin)

Ragnar A K Frisch - Collected Quotes

"I believe that economic theory has arrived at a point in its development where the appeal to quantitative empirical data has become more necessary than ever. At the same time its analyses have reached a degree of complexity that require the application of a more refined scientific method than that employed by the classical economists." (Ragnar Frisch, 1926)

"Intermediate between mathematics, statistics, and economics, we find a new discipline which, for lack of a better name, may be called econometrics. Econometrics has as its aim to subject abstract laws of theoretical political economy or 'pure' economics to experimental and numerical verification, and thus to turn pure economics, as far as possible, into a science in the strict sense of the word." (Ragnar Frisch, "On a Problem in Pure Eco­nomics", 1926)

"Certain exterior impulses hit the economic mechanism and thereby initiate more or less regular oscillations." (Ragnar Frisch, "Propagation problems and impulse problems in dynamic economics", 1933)

"In reality the cycles we have the occasion to observe are generally not damped. How can the maintenance of the swings be explained? Have theses dynamic laws deduced from theory and showing damped oscillations no value in explaining the real phenomena, or in what respect do the dynamic laws need to be completed in order to explain the real happenings? They (dynamic laws) only form one element of the explanation: they solve the propagation problem. But the impulse problem remains." (Ragnar Frisch, "Propagation problems and impulse problems in dynamic economics", 1933)

"[...] the length of the cycles and the tendency towards dampening are determined by the intrinsic structure of the swinging system, while the intensity (the amplitude) of the fluctuations is determined primarily by the exterior impulse. An important consequence of this is that a more or less regular fluctuation may be be produced by a cause which operates irregularly." (Ragnar Frisch, "Propagation problems and impulse problems in dynamic economics", 1933)

"The majority of the economic oscillations which we encounter seem to be explained most plausibly as free oscillations." (Ragnar Frisch, "Propagation problems and impulse problems in dynamic economics", 1933)

"The propagation problem is the problem of explaining by the structural properties of the swinging system what the character of the swings would be in case the system was started in some initial situation." (Ragnar Frisch, "Propagation problems and impulse problems in dynamic economics", 1933)

"When we approach the study of business cycle with the intention of carrying through an analysis that is truly dynamic and determinate in the above sense, we are naturally led to distinguish between two types of analyses: the micro-dynamic and the macro-dynamic types. The micro-dynamic analysis is an analysis by which we try to explain in some detail the behaviour of a certain section of the huge economic mechanism, taking for granted that certain general parameters are given. Obviously it may well be that we obtain more or less cyclical fluctuations in such sub-systems, even though the general parameters are given. The essence of this type of analysis is to show the details of the evolution of a given specific market, the behaviour of a given type of consumers, and so on." (Ragnar Frisch, "Propagation problems and impulse problems in dynamic economics", 1933)

"As long as economic theory still works on a purely qualitative basis without attempting to measure the numerical importance of the various factors, practically any 'conclusion' can be drawn and defended." (Ragnar Frisch, "From Utopian Theory to Practical Applications", [Nobel lecture] 1970)

"Deep in the human nature there is an almost irresistible tendency to concentrate physical and mental energy on attempts at solving problems that seem to be unsolvable." (Ragnar Frisch, "From Utopian Theory to Practical Applications", [Nobel lecture] 1970)

Maurice Allais - Collected Quotes

"All science is based on models, and every scientific model comprises three distinct stages: statement of well-defined hypotheses; deduction of all the consequences of these hypotheses, and nothing but these consequences; confrontation of these consequences with observed data." (Maurice Allais, "An Outline of My Main Contributions to Economic Science", [Noble lecture] 1988)

"However, mathematics is not and cannot be anything more than a tool, and all my work rests on the conviction that, in its use, the only two really fruitful stages in the scientific approach are, firstly, a thorough examination of the initial hypotheses; and secondly, a discussion of the meaning and empirical relevance of the results obtained. What remains is but tautological calculation, which is of interest only to the mathematician, and the mathematical rigour of the reasoning can never justify a theory based on postulates if these postulates do not correspond to the true nature of the observed phenomena." (Maurice Allais, "An Outline of My Main Contributions to Economic Science", [Noble lecture] 1988)

"My approach has never been to start from theories to arrive at facts, but on the contrary, to try to bring out from the facts the explanatory thread without which they appear incomprehensible and elude effective action." (Maurice Allais, "An Outline of My Main Contributions to Economic Science", [Noble lecture] 1988)

"The mathematical theories generally called 'mathematical theories of chance' actually ignore chance, uncertainty and probability. The models they consider are purely deterministic, and the quantities they study are, in the final analysis, no more than the mathematical frequencies of particular configurations, among all equally possible configurations, the calculation of which is based on combinatorial analysis. In reality, no axiomatic definition of chance is conceivable." (Maurice Allais, "An Outline of My Main Contributions to Economic Science", [Noble lecture] 1988)

"The model and the theory it represents must be accepted, at least temporarily, or rejected, depending on the agreement or disagreement between observed data and the hypotheses and implications of the model. When neither the hypotheses nor the implications of a theory can be confronted with the real world, that theory is devoid of any scientific interest. Mere logical, even mathematical, deduction remains worthless in terms of the understanding of reality if it is not closely linked to that reality." (Maurice Allais, "An Outline of My Main Contributions to Economic Science", [Noble lecture] 1988)

"The use of even the most sophisticated forms of mathematics can never be considered as a guarantee of quality. Mathematics is, and can only be, a means of expression and reasoning. The real substance on which the economist works remains economic and social. Indeed, one must avoid the development of a complex mathematical apparatus whenever it is not strictly indispensable. Genuine progress never consists in a purely formal exposition, but always in the discovery of the guiding ideas which underlie any proof. It is these basic ideas which must be explicitly stated and discussed." (Maurice Allais, "An Outline of My Main Contributions to Economic Science", [Noble lecture] 1988)

"The submission to observed or experimental data is the golden rule which dominates any scientific discipline. Any theory whatever, if it is not verified by empirical evidence, has no scientific value and should be rejected. This is true, for example, of the contemporary theories of general economic equilibrium." (Maurice Allais, "An Outline of My Main Contributions to Economic Science", [Noble lecture] 1988)

"Submission to the experimental data is the golden rule that dominates any scientific discipline." (Maurice Allais, [speech] 1993)

"A theory is only as good as its assumptions. If the premises are false, the theory has no real scientific value. The only scientific criterion for judging the validity of a scientific theory is a confrontation with the data of experience." (Maurice Allais, "L'anisotropie de l'espace", 1997)

"Any author who uses mathematics should always express in ordinary language the meaning of the assumptions he admits, as well as the significance of the results obtained. The more abstract his theory, the more imperative this obligation. In fact, mathematics are and can only be a tool to explore reality. In this exploration, mathematics do not constitute an end in itself, they are and can only be a means." (Maurice Allais, "La formation scientifique" 1997)

"Too many theorists have a tendency to ignore facts that contradict their convictions." (Maurice Allais, "L'anisotropie de l'espace", 1997)

Leonid V Kantorovich - Collected Quotes

"The method of successive approximations is often applied to proving existence of solutions to various classes of functional equations; moreover, the proof of convergence of these approximations leans on the fact that the equation under study may be majorised by another equation of a simple kind. Similar proofs may be encountered in the theory of infinitely many simultaneous linear equations and in the theory of integral and differential equations. Consideration of semiordered spaces and operations between them enables us to easily develop a complete theory of such functional equations in abstract form." (Leonid V Kantorovich, "On one class of functional equations", 1936)

"I discovered that a whole range of problems of the most diverse character relating to the scientific organization of production (questions of the optimum distribution of the work of machines and mechanisms, the minimization of scrap, the best utilization of raw materials and local materials, fuel, transportation, and so on) lead to the formulation of a single group of mathematical problems (extremal problems). These problems are not directly comparable to problems considered in mathematical analysis. It is more correct to say that they are formally similar, and even turn out to be formally very simple, but the process of solving them with which one is faced [i. e., by mathematical analysis] is practically completely unusable, since it requires the solution of tens of thousands or even millions of systems of equations for completion." (Leonid V Kantorovich, "Mathematical Methods of Organizing and Planning Production", Management Science 6(4), 1960)

"A solution of newly appearing economic problems, and in particular those connected with the scientific-technical revolution often cannot be based on existing methods but needs new ideas and approaches. Such one is the problem of the protection of nature. The problem of economic valuation of technical innovations efficiency and rates of their spreading cannot be solved only by the long-term estimation of direct outcomes and results without accounting peculiarities of new industrial technology, its total contribution to technical progress." (Leonid V Kantorovich, "Mathematics in Economics: Achievements, Difficulties, Perspectives", [Nobel lecture]1975)

"In our time mathematics has penetrated into economics so solidly, widely and variously, and the chosen theme is connected with such a variety of facts and problems that it brings us to cite the words of Kozma Prutkov which are very popular in our country: 'One can not embrace the unembraceable'. The appropriateness of this wise sentence is not diminished by the fact that the great thinker is only a pen-name." (Leonid V Kantorovich, "Mathematics in Economics: Achievements, Difficulties, Perspectives", [Nobel lecture]1975) [lead paragraph]

"In planning the idea of decentralization must be connected with routines of linking plans of rather autonomous parts of the whole system. Here one can use a conditional separation of the system by means of fixing values of flows and parameters transmitted from one part to another. One can use an idea of sequential recomputation of the parameters, which was successfully developed by many authors for the scheme of Dantzig-Wolfe and for aggregative linear models." (Leonid V Kantorovich, "Mathematics in Economics: Achievements, Difficulties, Perspectives," 1975)

"In spite of its universality and good precision the linear model is very elementary in its means which are mainly those of linear algebra, so even people with very modest mathematical training can understand and master it. The last is very important for a creative and non-routine use of the analytical means which are given by the model." (Leonid V Kantorovich, "Mathematics in Economics: Achievements, Difficulties, Perspectives," 1975)

"The hard thing in a model realization is to receive and often to construct necessary data which in many cases have considerable errors and sometimes are completely absent, since none needed them previously. Difficulties of principle lie in the future prediction data and in the estimation of industry development variants." (Leonid V Kantorovich, "Mathematics in Economics: Achievements, Difficulties, Perspectives", [Nobel lecture] 1975)

"The treatment of the economy as a single system, to be controlled toward a consistent goal, allowed the efficient systematization of enormous information material, its deep analysis for valid decision-making. It is interesting that many inferences remain valid even in cases when this consistent goal could not be formulated, either for the reason that it was not quite clear or for the reason that it was made up of multiple goals, each of which to be taken into account." (Leonid V Kantorovich, "Mathematics in Economics: Achievements, Difficulties, Perspectives", [Nobel lecture] 1975)

"The accounting methods based on mathematical models, the use of computers for computations and information data processing make up only one part of the control mechanism, another part is the control structure." (Leonid V Kantorovich, "Mathematics in Economics: Achievements, Difficulties, Perspectives", [Nobel lecture]1975)

"One aspect of reality was temporarily omitted in the development of the theory of function spaces. Of great importance is the relation of comparison between practical objects, alongside algebraic and other relations between them." (Leonid V Kantorovich, "Functional analysis: Basic Ideas)", Siberian Mathematical Journal 28 (1), 1987)

Max Born - Collected Quotes

"The difficulty involved in the proper and adequate means of describing changes in continuous deformable bodies is the method of differential equations. […] They express mathematically the physical concept of contiguous action." (Max Born, "Einstein's Theory of Relativity", 1920)

"It is natural that a man should consider the work of his hands or his brain to be useful and important. Therefore nobody will object to an ardent experimentalist boasting of his measurements and rather looking down on the 'paper and ink' physics of his theoretical friend, who on his part is proud of his lofty ideas and despises the dirty fingers of the other." (Max Born, " Experiment and Theory in Physics", 1943)

"The conception of chance enters in the very first steps of scientific activity in virtue of the fact that no observation is absolutely correct. I think chance is a more fundamental conception that causality; for whether in a concrete case, a cause-effect relation holds or not can only be judged by applying the laws of chance to the observation." (Max Born, 1949)

"When a scientific theory is firmly established and confirmed, it changes its character and becomes a part of the metaphysical background of the age: a doctrine is transformed into a dogma." (Max Born, "Natural Philosophy of Cause and Chance", 1949)

"All great discoveries in experimental physics have been due to the intuition of men who made free use of models, which were for them not products of the imagination, but representatives of real things." (Max Born, "Physical Reality", Philosophical Quarterly Vol. 3 (11),1953)

"Every object that we perceive appears in innumerable aspects. The concept of the object is the invariant of all these aspects. From this point of view, the present universally used system of concepts in which particles and waves appear simultaneously, can be completely justified. The latest research on nuclei and elementary particles has led us, however, to limits beyond which this system of concepts itself does not appear to suffice. The lesson to be learned from what I have told of the origin of quantum mechanics is that probable refinements of mathematical methods will not suffice to produce a satisfactory theory, but that somewhere in our doctrine is hidden a concept, unjustified by experience, which we must eliminate to open up the road." (Max Born, "The Statistical Interpretations of Quantum Mechanics", [Nobel lecture] 1954)

"[...] if we can never actually determine more than one of the two properties (possession of a definite position and of a definite momentum), and if when one is determined we-can make no assertion at all about the other property for the same moment, so far as our experiment goes, then we are not justified in concluding that the 'thing' under examination can actually be described as a particle in the usual sense of the term." (Max Born, "Atomic Physics", 1957)

"Physics is in the nature of the case indeterminate, and therefore the affair of statistics." (Max Born, "Atomic Physics", 1957)

"The ultimate origin of the difficulty lies in the fact (or philosophical principle) that we are compelled to use words of common language when we wish to describe a phenomenon, not by logical or mathematical analysis, but by a picture appealing to the imagination. Common language has grown by everyday experience and can never surpass these limits. Classical physics has restricted itself to the use of concepts of this kind by analyzing visible motions it has developed two ways of representing them by elementary processes moving particles and waves. There is no other wav of giving a pictorial description of motions - we have to apply it even in the region of atomic process, where classical physics break down." (Max Born, "Atomic Physics", 1957)

"[...] the whole course of events is determined by the laws of probability; to a state in space there corresponds a definite probability, which is given by the de Brogile wave associated with the state." (Max Born, "Atomic Physics", 1957)

"The belief that there is only one truth and that oneself is in possession of it, seems to me the deepest root of all that is evil in the world." (Max Born, "Natural Philosophy of Cause and Chance", 1964)

"There are metaphysical problems, which cannot be disposed of by declaring them meaningless. For, as I have repeatedly said, they are ‘beyond physics’ indeed and demand an act of faith. We have to accept this fact to be honest. There are two objectionable types of believers: those who believe the incredible and those who believe that ‘belief’ must be discarded and replaced by "the scientific method." (Max Born, "Natural Philosophy of Cause and Chance", 1964)

"Science is not formal logic - it needs the free play of the mind in as great a degree as any other creative art. It is true that this is a gift which can hardly be taught, but its growth can be encouraged in those who already possess it." (Max Born)

Eugene P Wigner - Collected Quotes

"The regularities in the phenomena which physical science endeavors to uncover are called the laws of nature. The name is actually very appropriate. Just as legal laws regulate actions and behavior under certain conditions but do not try to regulate all action and behavior, the laws of physics also determine the behavior of its objects of interest only under certain well-defined conditions but leave much freedom otherwise." (Eugene P Wigner, "Events, Laws of Nature, and Invariance principles", [Nobel lecture] 1914)

"The simplicities of natural laws arise through the complexities of the languages we use for their expression." (Eugene P Wigner, 1959)

"Nothing in our experience suggests the introduction of [complex numbers]. Indeed, if a mathematician is asked to justify his interest in complex numbers, he will point, with some indignation, to the many beautiful theorems in the theory of equations, of power series, and of analytic functions in general, which owe their origin to the introduction of complex numbers. The mathematician is not willing to give up his interest in these most beautiful accomplishments of his genius." (Eugene P Wigner, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences", Communications in Pure and Applied Mathematics 13 (1), 1960)

"Somebody once said that philosophy is the misuse a terminology which was invented just for this purpose. In the same vein, I would say that mathematics is the science of skillful operations with concepts and rules invented just for this purpose."  (Eugene Wigner, "The of Mathematics in the Natural Sciences," Communications on Pure Applied Mathematics 13 (2), 1960)

"The enormous usefulness of mathematics in natural sciences is something bordering on the mysterious, and there is no rational explanation for it. It is not at all natural that ‘laws of nature’ exist, much less that man is able to discover them. The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning." (Eugene P Wigner, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences," 1960)

"The mathematical formulation of the physicist’s often crude experience leads in an uncanny number of cases to an amazingly accurate description of a large class of phenomena. This shows that the mathematical language has more to commend it than being the only language which we can speak; it shows that it is, in a very real sense, the correct language." (Eugene P Wigner, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences", Communications in Pure and Applied Mathematics 13 (1), 1960)

"[…] mathematics is the science of skillful operations with concepts and rules invented just for this purpose." (Eugene P Wigner, 'The Unreasonable Effectiveness of Mathematics in the Natural Sciences," 1960)

"The mathematician is not willing to give up his interest in these most beautiful accomplishments of his genius." (Eugene P Wigner, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences", Communications in Pure and Applied Mathematics 13 (1), 1960)

"Physics does not endeavour to explain nature. In fact, the great success of physics is due to a restriction of its objectives: it only endeavours to explain the regularities in the behavior of objects." (Eugene P Wigner, "Events, Laws of Nature, and Invariance Principles", [Nobel Lecture], 1963)

"We have ceased to expect from physics an explanation of all events, even of the gross structure of the universe, and we aim only at the discovery of the laws of nature, that is the regularities, of the events." (Eugene P Wigner, "Events, Laws of Nature, and Invariance Principles", [Nobel Lecture], 1963)

"We know many laws of nature and we hope and expect to discover more. Nobody can foresee the next such law that will be discovered. Nevertheless, there is a structure in laws of nature which we call the laws of invariance. This structure is so far-reaching in some cases that laws of nature were guessed on the basis of the postulate that they fit into the invariance structure." (Eugene P Wigner, "The Role of Invariance Principles in Natural Philosophy", 1963)

“Physics can teach us only what the laws of nature are today. It is only Astronomy that can teach us what the initial conditions for these laws are.” (Eugene P Wigner, “The Case for Astronomy”, Proceedings of the American Philosophical Society Vol. 8 (1), 1964)

"It is now natural for us to try to derive the laws of nature and to test their validity by means of the laws of invariance, rather than to derive the laws of invariance from what we believe to be the laws of nature." (Eugene P Wigner, "Symmetries and Reflections: Scientific Essays", 1967)

"I believe that the present laws of physics are at least incomplete without a translation into terms of mental phenomena." (Eugene P Wigner, "Physics and the Explanation of Life", 1970)

"In science, it is not speed that is the most important. It is the dedication, the commitment, the interest and the will to know something and to understand it - these are the things that come first." (Eugene P Wigner, [interview by István Kardos] 1978)

"Part of the art and skill of the engineer and of the experimental physicist is to create conditions in which certain events are sure to occur." (Eugene P Wigner, "Symmetries and Reflections", 1979)

"Physics is becoming so unbelievably complex that it is taking longer and longer to train a physicist. It is taking so long, in fact, to train a physicist to the place where he understands the nature of physical problems that he is already too old to solve them." (Eugene P Wigner) 

"The enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and there is no rational explanation of it." (Eugene P Wigner) 

 

"With thermodynamics, one can calculate almost everything crudely; with kinetic theory, one can calculate fewer things, but more accurately; and with statistical mechanics, one can calculate almost nothing exactly." (Eugene P Wigner) 

Steven Weinberg - Collected Quotes

"Nothing in physics seems so hopeful to as the idea that it is possible for a theory to have a high degree of symmetry was hidden from us in everyday life. The physicist's task is to find this deeper symmetry." (Steven Weinberg, American Scientist, 1977)

"Our mistake is not that we take our theories too seriously, but that we do not take them seriously enough. It is always hard to realize that these numbers and equations we play with at our desks have something to do with the real world." (Steven Weinberg, "The First Three Minutes", 1977)

"A physicist who says that a theory is beautiful does not mean quite the same thing that would be meant in saying that a particular painting or a piece of music or poetry is beautiful. It is not merely a personal expression of aesthetic pleasure; it is much closer to what a horse-trainer means when he looks at a racehorse and says that it is a beautiful horse. The horse-trainer is of course expressing a personal opinion, but it is an opinion about an objective fact: that, on the basis of judgements that the trainer could not easily put into words, this is the kind of horse that wins races [...] The physicist’s sense of beauty is also supposed to serve a purpose –it is supposed to help the physicist select ideas that help us to explain nature." (Steven Weinberg, "Dreams of a Final Theory", 1992)

"How surprising it is that the laws of nature and the initial conditions of the universe should allow for the existence of beings who could observe it. Life as we know it would be impossible if any one of several physical quantities had slightly different values." (Steven Weinberg, "Life in the Quantum Universe", Scientific American, 1995)

 "It seems that scientists are often attracted to beautiful theories in the way that insects are attracted to flowers - not by logical deduction, but by something like a sense of smell." (Steven Weinberg, "Physics Today", 2005)

"The progress of science has been largely a matter of discovering what questions should be asked." (Steven Weinberg, "To Explain the World: The Discovery of Modern Science", 2015)

"Mathematics is the means by which we deduce the consequences of physical principles. More than that, it is the indispensable language in which the principles of physical science are expressed." (Steven Weinberg, "To Explain the World: The Discovery of Modern Science", 2015)

"The distinction between mathematics and science is pretty well settled. It remains mysterious to us why mathematics that is invented for reasons having nothing to do with nature often turns out to be useful in physical theories." (Steven Weinberg, "To Explain the World: The Discovery of Modern Science", 2015)

"The proper measure of a philosophical system or a scientific theory is not the degree to which it anticipated modern thought, but its degree of success in treating the philosophical and scientific problems of its own day." (Steven Weinberg, "To Explain the World: The Discovery of Modern Science", 2015)

"There is a beauty in these laws that mirrors something that is built into the structure of the universe at a very deep level" (Steven Weinberg, "To Explain the World: The Discovery of Modern Science", 2015)

"The universe is an enormous direct product of representations of symmetry groups." (Steven Weinberg)

Max Planck - Collected Quotes

“Nature prefers the more probable states to the less probable because in nature processes take place in the direction of greater probability. Heat goes from a body at higher temperature to a body at lower temperature because the state of equal temperature distribution is more probable than a state of unequal temperature distribution.” (Max Planck, “The Atomic Theory of Matter”, 1909)

"An indispensable hypothesis, even though still far from being a guarantee of success, is however the pursuit of a specific aim, whose lighted beacon, even by initial failures, is not betrayed." (Max Planck, [Nobel lecture] 1918) 

"If one wishes to obtain a definite answer from Nature one must attack the question from a more general and less selfish point of view." (Max Planck, “A Survey of Physics”, 1925)

"In all cases, the quantum hypothesis has given rise to the idea, that in Nature, changes occur which are not continuous, but of an explosive nature." (Max Planck, “A Survey of Physics”, 1925)

“Nothing is more interesting to the true theorist than a fact which directly contradicts a theory generally accepted up to that time, for this is his particular work.” (Max Planck, “A Survey of Physics”, 1925)

"The chief law of physics, the pinnacle of the whole system is, in my opinion, the principle of least action." (Max Planck, “A Survey of Physics”, 1925)

"The measure of the value of a new hypothesis in physics is not its obviousness but its utility."  (Max Planck, “A Survey of Physics”, 1925)

"Modern Physics impresses us particularly with the truth of the old doctrine which teaches that there are realities existing apart from our sense-perceptions, and that there are problems and conflicts where these realities are of greater value for us than the richest treasures of the world of experience." (Max Planck, "The Universe in the Light of Modern Physics", 1931)

"Physics would occupy an exceptional position among all the other sciences if it did not recognize the rule that the most far-reaching and valuable results of investigation can only be obtained by following a road leading to a goal which is theoretically unobtainable. This goal is the apprehension of true reality." (Max Planck, "The Universe in the Light of Modern Physics", 1931)

"We have no right to assume that any physical laws exist, or if they have existed up until now, that they will continue to exist in a similar manner in the future." (Max Planck, "The Universe in the Light of Modern Physics", 1931)

"Axioms are instruments which are used in every department of science, and in every department there are purists who are inclined to oppose with all their might any expansion of the accepted axioms beyond the boundary of their logical application." (Max Planck,"Where is Science Going?", 1932) 

"Every measurement first acquires its meaning for physical science through the significance which a theory gives it." (Max Planck,"Where is Science Going?", 1932)

"It goes without saying that the laws of nature are in themselves independent of the properties of the instruments with which they are measured. Therefore in every observation of natural phenomena we must remember the principle that the reliability of the measuring apparatus must always play an important role." (Max Planck,"Where is Science Going?", 1932)

"It is not the possession of truth, but the success which attends the seeking after it, that enriches the seeker and brings happiness to him." (Max Planck, "Where is Science Going?", 1932)

"No doctrinal system in physical science, or indeed perhaps in any science, will alter its content of its own accord. Here we always need the pressure of outer circumstances. Indeed the more intelligible and comprehensive a theoretical system is the more obstinately it will resist all attempts at reconstruction or expansion."  (Max Planck, "Where is Science Going?", 1932)

"Scientific discovery and scientific knowledge have been achieved only by those who have gone in pursuit of them without any practical purpose whatsoever in view." (Max Planck, “Where is Science Going?”, 1932)

"There is scarcely a scientific axiom that is not nowadays denied by somebody. And at the same time almost any nonsensical theory that may be put forward in the name of science would be almost sure to find believers and disciples."  (Max Planck, “Where is Science Going?”, 1932) 

"We are in a position similar to that of a mountaineer who is wandering over uncharted spaces, and never knows whether behind the peak which he sees in front of him and which he tries to scale there may not be another peak still beyond and higher up." (Max Planck, “Where is Science Going?”, 1932)

"It is impossible to make a clear cut between science, religion, and art. The whole is never equal simply to the sum of its various parts." (Max Planck, "The Philosophy of Physics", 1936) 

"Physics is an exact Science and hence depends upon measurement, while all measurement itself requires sense-perception. Consequently all the ideas employed in Physics are derived from the world of sense-perception." (Max Planck, "The Universe in the Light of Modern Physics", 1937) 

"A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it." (Max Planck, "A Scientific Autobiography", 1949) 

"It is never possible to predict a physical occurrence with unlimited precision." (Max Planck, "A Scientific Autobiography", 1949)  

"Science is not contemplative repose amidst knowledge already gained, but is indefatigable work and an ever progressive development." (Max Planck, "A Scientific Autobiography", 1949) 

"Since the real world, in the absolute sense of the word, is independent of individual personalities, and in fact of all human intelligence, every discovery made by an individual acquires a completely universal significance. This gives the inquirer, wrestling with his problem in quiet seclusion, the assurance that every discovery will win the unhesitating recognition of all experts throughout the entire world, and in this feeling of the importance of his work lies his happiness. It compensates him fully for many a sacrifice which he must make in his daily life." (Max Planck, "The Meaning and Limits of Exact Science", 1949)

"The outside world is something independent from man, something absolute, and the quest for the laws which apply to this absolute appeared to me as the most sublime scientific pursuit in life." (Max Planck, "A Scientific Autobiography", 1949)  

"[...] when the pioneer in science sends for the groping feelers of his thoughts, he must have a vivid intuitive imagination, for new ideas are not generated by deduction, but by an artistically creative imagination. Nevertheless, the worth of a new idea is invariably determined, not by the degree of its intuitiveness - which, incidentally, is to a major extent a matter of experience and habit - but by the scope and accuracy of the individual laws to the discovery of which it eventually leads. (Max Planck, The Meaning and Limits of Exact Science, Science Vol. 110 (2857), 1949)

“Science does not mean an idle resting upon a body of certain knowledge; it means unresting endeavor and continually progressing development toward an end which the poetic intuition may apprehend, but which the intellect can never fully grasp.” (Max Planck, “The New Science”, 1959)

"Science does not mean an idle resting upon a body of certain knowledge; it means unresting endeavor and continually progressing development toward an end which the poetic intuition may apprehend, but which the intellect can never fully grasp." (Max Planck, “The New Science”, 1959)

“This other world is the so-called physical world image; it is merely an intellectual structure. To a certain extent it is arbitrary. It is a kind of model or idealization created in order to avoid the inaccuracy inherent in every measurement and to facilitate exact definition.” (Max Planck, “The Philosophy of Physics”, 1963)

"Experiments are the only means of knowledge at our disposal. The rest is poetry, imagination." (Max Planck)