"The idea of natural computation has grown into a new scientific paradigm and has proved to be a rich source of new insights about nature. Many processes in nature exhibit key characteristics of computation, especially discrete units or steps and repetition according to a fixed set of rules. Although the processes may be highly complex, their regularity makes them highly amenable to simulation [...]." (David G Green & Tania Leishman, "Computing and Complexity: Networks, Nature and Virtual Worlds, Philosophy of Complex Systems, 2011)
"A genuine experience of the unexpected, in maths as much as in magic, demands of its performer at once originality of insight and a lightness of touch. Even a single step too many in a method renders ugly and clumsy the theorem or the trick." (Daniel Tammet, "Thinking in Numbers", 2012)
"Regression analysis, like all forms of statistical inference, is designed to offer us insights into the world around us. We seek patterns that will hold true for the larger population. However, our results are valid only for a population that is similar to the sample on which the analysis has been done." (Charles Wheelan, "Naked Statistics: Stripping the Dread from the Data", 2012)
"Understanding chaos requires much less advanced mathematics than other current areas of physics research such as general relativity or particle physics. Observing chaos and fractals requires no specialized equipment; chaos is seen in scores of everyday phenomena - a boiling pot of water, a dripping faucet, shifting weather patterns. And fractals are almost ubiquitous in the natural world. Thus, it is possible to teach the central ideas and insights of chaos in a rigorous, genuine, and relevant way to students with relatively little mathematics background." (David P Feldman, "Chaos and Fractals: An Elementary Introduction", 2012)
"An act of creativity is the result of an insight that arises discontinuously. Of course the insight must be preceded by something that is deeply problematic; it is so deeply problematic that a resolution may well seem impossible. This is why the resolution does not arise through systematic means but only occurs when all systematic approaches have been exhausted to no effect, that is, if you want to be creative you must sometimes be prepared to fly blind. This is not easy to do. Creativity involves living for protracted periods with the kind of tension that arises in situations of cognitive dissonance." (William Byers, "Deep Thinking: What Mathematics Can Teach Us About the Mind", 2015)
"Mathematical modeling is the modern version of both applied mathematics and theoretical physics. In earlier times, one proposed not a model but a theory. By talking today of a model rather than a theory, one acknowledges that the way one studies the phenomenon is not unique; it could also be studied other ways. One's model need not claim to be unique or final. It merits consideration if it provides an insight that isn't better provided by some other model." (Reuben Hersh, "Mathematics as an Empirical Phenomenon, Subject to Modeling", 2017)
"Sometimes mathematical advances happen by just looking at something in a slightly different way, which doesn’t mean building something new or going somewhere different, it just means changing your perspective and opening up huge new possibilities as a result. This particular insight leads to calculus and hence the understanding of anything curved, anything in motion, anything fluid or continuously changing."
"Artificial intelligence is defined as the branch of science and technology that is concerned with the study of software and hardware to provide machines the ability to learn insights from data and the environment, and the ability to adapt in changing situations with high precision, accuracy and speed." (Amit Ray, "Compassionate Artificial Intelligence", 2018)
"The goal of data science is to improve decision making by basing decisions on insights extracted from large data sets. As a field of activity, data science encompasses a set of principles, problem definitions, algorithms, and processes for extracting nonobvious and useful patterns from large data sets. It is closely related to the fields of data mining and machine learning, but it is broader in scope." (John D Kelleher & Brendan Tierney, "Data Science", 2018)
"The patterns that we extract using data science are useful only if they give us insight into the problem that enables us to do something to help solve the problem." (John D Kelleher & Brendan Tierney, "Data Science", 2018)
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