On Mind (Unsourced)

"A fact is not novel if it has an analogue which could have some interest. A fact which does not fit in with a series of known facts is a fact which deserves particular attention. If the mind had to retain all individual facts, it could not manage and science would not exist; but when these facts can be connected by general laws and by theories, when a large number of these facts can be represented by a single one, one can remember them more easily, one can generalise one’s ideas, one can compare one general fact with another general fact and discoveries can succeed each other. It is only when laws can be introduced into a science that it assumes the true character of science." (Joseph L Gay-Lussac)

"Besides language and music, mathematics is one of the primary manifestations of the free creative power of the human mind." (Hermann Weyl)

"By observation, facts are distinctly and minutely impressed in the mind; by analogy, similar facts are connected ; by experiment, new facts are discovered ; and, in the progression of knowledge, observation, guided by analogy, leads to experiment, and analogy, confirmed by experiment, becomes scientific truth." (Sir Humphry Davy)

"Cognitive psychology has shown that the mind best understands facts when they are woven into a conceptual fabric, such as a narrative, mental map, or intuitive theory. Disconnected facts in the mind are like unlinked pages on the Web: They might as well not exist." (Steven Pinker)

"Disclaimer: Even if the below quotes are translations that reflect maybe a more or less modern language used to interpret them, their importance as first attempts to define the inner workings of the mind remains.

"Do not train a child to learn by force or harshness; but direct them to it by what amuses their minds, so that you may be better able to discover with accuracy the peculiar bent of the genius of each." (Plato)

"Does there truly exist an insuperable contradiction between religion and science? Can religion be superseded by science? The answers to these questions have, for centuries, given rise to considerable dispute and, indeed, bitter fighting. Yet, in my own mind there can be no doubt that in both cases a dispassionate consideration can only lead to a negative answer. What complicates the solution, however, is the fact that while most people readily agree on what is meant by ‘science,’ they are likely to differ on the meaning of ‘religion’." (Albert Einstein)

"Educating the mind without educating the heart is no education at all." (Aristotle)

"Education is not learning, but the training of the mind that it may learn." (Sir William W Gull)

"Education's purpose is to replace an empty mind with an open one." (Malcolm S Forbes)

"Either mathematics is too big for the human mind, or the human mind is more than a machine." (Kurt Gödel)

"Human beings suffer from a 'centralized mindset'; they would like to assign the coordination of activities to a central command. But the way social insects form highways and other amazing structures such as bridges, chains, nests (by the way, African fungus-growing termites have invented air conditioning) and can perform complex tasks (nest building, defense, cleaning, brood care, foraging, etc) is very different: they self-organize through direct and indirect interactions." (Eric Bonabeau)

"I will simply express my strong belief, that that point of self-education which consists in teaching the mind to resist its desires and inclinations, until they are proved to be right, is the most important of all, not only in things of natural philosophy, but in every department of daily life." (Michael Faraday)

"Imaginary numbers have an intuitive explanation: they 'rotate' numbers, just like negatives make a 'mirror image' of a number. […] Seeing imaginary numbers as rotations gives us a new mindset to approach problems; the 'plug and chug' formulas can make intuitive sense, even for a strange topic like complex numbers." (Kalid Azal, Math, Better Explained)

"Imagination, as well as reason, is necessary to perfection in the philosophical mind. A rapidity of combination, a power of perceiving analogies, and of comparing them by facts, is the creative source of discovery." (Sir Humphry Davy)

"Indeed, when in the course of a mathematical investigation we encounter a problem or conjecture a theorem, our minds will not rest until the problem is exhaustively solved and the theorem rigorously proved; or else, until we have found the reasons which made success impossible and, hence, failure unavoidable. Thus, the proofs of the impossibility of certain solutions plays a predominant role in modern mathematics; the search for an answer to such questions has often led to the discovery of newer and more fruitful fields of endeavour." (David Hilbert)

"Intuition is the conception of an attentive mind, so clear, so distinct, and so effortless that we cannot doubt what we have so conceived." (René Descartes)

"[…] it is only through Mathematics that we can thoroughly understand what true science is. Here alone can we find in the highest degree simplicity and severity of scientific law, and such abstraction as the human mind can attain." (Auguste Comte)

"It is the mark of an educated mind to rest satisfied with the degree of precision which the nature of the subject admits and not to seek exactness where only an approximation is possible." (Aristotle)

"It is very helpful to represent these things in this fashion since nothing enters the mind more readily than geometric figures." (René Descartes)

"It stands to the everlasting credit of science that by acting on the human mind it has overcome man's insecurity before himself and before nature." (Albert Einstein)

"Learn just enough of the subject [metaphysics] to enable your mind to get rid of it." (Benjamin Jowett)

"Mathematical inquiry lifts the human mind into closer proximity with the divine than is attainable through any other medium." (Hermann Weyl)

"Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the mind will never penetrate." (Leonhard Euler)

"Mathematics began to seem too much like puzzle solving. Physics is puzzle solving, too, but of puzzles created by nature, not by the mind of man." (Maria Goeppert-Mayer)

"Mathematics is a spirit of rationality. It is this spirit that challenges, simulates, invigorates and drives human minds to exercise themselves to the fullest. It is this spirit that seeks to influence decisively the physical, normal and social life of man, that seeks to answer the problems posed by our very existence, that strives to understand and control nature and that exerts itself to explore and establish the deepest and utmost implications of knowledge already obtained." (Morris Kline)

"Mathematics is music for the mind; Music is mathematics for the soul." (Stanley Gudder)

"Mathematics is the science that yields the best opportunity to observe the working of the mind. Its study is the best training of our abilities as it develops both the power and the precision of our thinking. Mathematics is valuable on account of the number and variety of its applications. And it is equally valuable in another respect: By cultivating it, we acquire the habit of a method of reasoning which can be applied afterwards to the study of any subject and can guide us in life's great and little problems." (Nicolas de Condorcet)

"Mathematics originates in the mind of an individual, as it doubtless originated historically in the collective life of mankind, with the recognition of certain recurrent abstract features in common experience, and the development of processes of counting, measuring, and calculating, by which order can be brought into the manipulations of these features. It originated in this manner, indeed; but already at a very early stage it begins to transcend the practical sphere and its character undergoes a corresponding change. Intellectual curiosity progressively takes charge, despite the fact that practical considerations may for long continue to be the main source of interest and may indeed never cease to stimulate the creation of new concepts and new methods. As mathematics breaks from its early dependence on practical utility, its ‘immediate’ significance is at the same time lost and the goal is to discover what it is that makes 'emancipated' mathematics valid. (Geoffrey T Kneebone)

"Metaphysics, in whatever latitude the term be taken, is a science or complement of sciences exclusively occupied with mind." (Sir William Hamilton)

"Nothing has afforded me so convincing a proof of the unity of the Deity as these purely mental conceptions of numerical and mathematical science which have been by slow degrees vouchsafed to man, and are still granted in these latter times by the Differential Calculus, now superseded by the Higher Algebra, all of which must have existed in that sublimely omniscient Mind from eternity." (Mary Somerville)

"Nothing stimulates great minds to work on enriching knowledge with such force as the posing of difficult but simultaneously interesting problems." (John Bernoulli)

"Our minds are finite, and yet even in those circumstances of finitude, we are surrounded by possibilities that are infinite, and the purpose of human life is to grasp as much as we can out of that infinitude." (Alfred N Whitehead)

"Science is the labor and handicraft of the mind; poetry can only be considered its recreation." (Sir Francis Bacon)

"Show all these fanatics a little geometry, and they learn it quite easily. But, strangely enough, their minds are not thereby rectified. They perceive the truths of geometry, but it does not teach them to weighp robabilities. Their minds have set hard. They will reason in a topsy-turvy wall all their lives, and I am sorry for it." (Voltaire)

"The aim of education should be to convert the mind into a living fountain not a reservoir." (John Mason)

"The business of education is not to make the young perfect in any one of the sciences, but so to open their minds as may best make them capable of any, when they shall apply themselves to it." (John Locke)

"The essence of engineering consists not so much in the mere construction of the spectacular layouts or developments, but in the invention required - the analysis of the problem, the design, the solution by the mind which directs it all." (William Hood)

"The idea of a universal mind or Logos would be, I think, a fairly plausible inference from the present state of scientific theory." (Arthur Eddington)

"The laws of thought, and especially of number, must hold good in heaven, whether it is a place or a state of mind; for they are independent of any particular sphere of existence, essential to Being itself, to God’s being as well as ours, laws of His mind before we learned them. The multiplication table will hold good in heaven […]" (Hilda P Hudson)

"The man of science will acts as if this world were an absolute whole controlled by laws independent of his own thoughts or act; but whenever he discovers a law of striking simplicity or one of sweeping universality or one which points to a perfect harmony in the cosmos, he will be wise to wonder what role his mind has played in the discovery, and whether the beautiful image he sees in the pool of eternity reveals the nature of this eternity, or is but a reflection of his own mind." (Tobias Dantzig)

"[…] the notion of the infinite […] forces itself upon our mind and yet is incomprehensible. When this notion takes possession of the understanding we have only to bow before it." (Louis Pasteur)

"The sole aim of science is the honor of the human mind, and from this point of view a question about numbers is as important as a question about the system of the world." (Carl Gustav Jacobi)

"The teacher, if indeed wise, does not bid you to enter the house of their wisdom, but leads you to the threshold of your own mind." (Kahil Gibran)

"The truth of a theory is in your mind, not in your eyes." (Albert Einstein)

"There is a great difference between the spirit of Mathematics and the spirit of Observation. In the former, the principles are palpable, but remote from common use; so that from want of custom it is not easy to turn our head in that direction; but if it be thus turned ever so little, the principles are seen fully confessed, and it would argue a mind incorrigibly false to reason inconsequentially on principles so obtrusive that it is hardly possible to overlook them." (Blaise Pascal)

"This, therefore, is mathematics: she reminds you of the invisible form of the soul; she gives to her own discoveries; she awakens the mind and purifies the intellect; she brings light to our intrinsic ideas; she abolishes oblivion and ignorance which are ours by birth." (Proclus Lycaeus, cca 5th century)

"‘Tis of singular use, rightly to understand, and carefully to distinguish from hypotheses or mere suppositions, the true and certain consequences of experimental and mathematical philosophy; which do, with wonderful strength and advantage, to all such as are capable of apprehending them, confirm, establish, and vindicate against all objections, those great and fundamental truths of natural religion, which the wisdom of providence has at the same time universally implanted, in some degree, in the minds of persons even of the meanest capacities, not qualified to examine demonstrative proofs." (Samuel Clarke)

"To educate a man in mind and not in morals is to educate a menace to society." (Theodore Roosevelt)

"What else can the human mind hold besides numbers and magnitudes? These alone we apprehend correctly, and if piety permits to say so, our comprehension is in this case of the same kind as God’s, at least insofar as we are able to understand it in this mortal life." (Johannes Kepler)

"What, after all, is mathematics but the poetry of the mind, and what is poetry but the mathematics of the heart?" (David E Smith)

"You know how the divine Simplicity enfolds all things. Mind is the image of this enfolding Simplicity. If, then, you called this divine Simplicity infinite Mind, it will be the exemplar of our mind. If you called the divine mind the totality of the truth of things, you will call our mind the totality of the assimilation of things, so that it may be a totality of ideas. In the divine Mind conception is the production of things; in our mind conception is the knowledge of things. If the divine Mind is absolute Being, then its conception is the creation of beings; and conception in the human mind is the assimilation of beings." (Nicholas of Cusa)