Everything has mathematics at its heart. When everything is stripped away all that remains is the code. ibid.
They’re ruling our lives: algorithms. Algorithms are everywhere. These bite-sized chunks of maths have become essential to our daily lives. Marcus du Sautoy, The Secret Rules of Modern Living: Algorithms, BBC 2015
They are strangely beautiful, tapping into the mathematical order that underpins how the universe works. ibid.
A series of step by step instructions. ibid.
Algorithms are extremely old. ibid.
Spinoza got everybody all stirred up with stuff about how mathematics is the only truth and how everybody should have absolute freedom to speak and think how they choose. James Burke: Connections s2e10: New Harmony, BBC 1994
‘Mathematics is even the basis for music.’ Inside the Mind of Leonardo starring Peter Capaldi, Sky Arts 2013
Let no man who is not a mathematician read the elements of my work. Leonardo da Vinci
It has been my experience that competency in mathematics, both in numerical manipulations and in understanding its conceptual foundations, enhances a person's ability to handle the more ambiguous and qualitative relationships that dominate our day-to-day financial decision-making. Alan Greenspan
Some advice: keep the flame of curiosity and wonderment alive, even when studying for boring exams. That is the well from which we scientists draw our nourishment and energy. And also, learn the math. Math is the language of nature, so we have to learn this language. Michio Kaku
Srinivasa Ramanujan was the strangest man in all of mathematics, probably in the entire history of science. He has been compared to a bursting supernova, illuminating the darkest, most profound corners of mathematics, before being tragically struck down by tuberculosis at the age of 33 ... Working in total isolation from the main currents of his field, he was able to re-derive 100 years’ worth of Western mathematics on his own. The tragedy of his life is that much of his work was wasted rediscovering known mathematics. Michio Kaku
It is actually unreasonable how mathematics works. Why should the world behave according to mathematical laws?
It is not only that it becomes easier to describe with mathematics. As you got deeper and deeper into reality mathematics becomes the only way to describe reality. Professor Lenny Susskind
From the intrinsic evidence of his creation, the Great Architect of the Universe now begins to appear as a pure mathematician. James Jeans, The Mysterious Universe, 1930
Goldbach Conjecture: All Even Numbers Can Be Written as the Sum of Two Primes. Christian Goldbach, 1690-1764
cf.
Mertens Conjecture 1897: Verified to Ten Billion: Despite the apparently overwhelming evidence in favour, it has recently been discovered that the Mertens Conjecture is false. Nature Magazine
That happens all the time. You know. Well, people make errors or jump at conclusions. You see, it’s so painful to write down all the details of a proof that at times you say, All right, this is obvious, and you go on. Usually that’s where the error lies ... I have been guilty of that myself and I think everybody else had been at times. Jean DieuDonne
A mathematician really wants to understand things. Jean DieuDonne
They will always remain abstract. So from about 1840 on mathematicians had to deal with objects which were not susceptible of being a visual approach. So that’s why mathematics had become more and more abstract – Abstractions pile upon abstractions. And there doesn’t seem to be any end of it. Jean DieuDonne
If we didn’t have infinity there would be no mathematics at this time ... Infinity for us has become formal. Jean DieuDonne
In mathematics you don’t understand them. You just get used to them. John von Neumann
Mathematical ideas originate in empirics ... But, once they are so conceived, the subject begins to live a peculiar life of its own and is better compared to a creative one, governed almost entirely by aesthetical motivations ... As a mathematical discipline travels, or after much ‘abstract’ inbreeding, [it] is in danger of degeneration. John von Naumann
Economic problems are not formulated clearly and are often stated in such vague terms as to make mathematical treatment a priori appear hopeless because it is quite uncertain what the problems really are. John von Neumann & Oskar Morgenstern
Imagine that all of you and in Hades and I am the devil. I make the following proposition, I say: I’ve written down on a positive integer on a slip of paper, a whole number ... Every day you’re allowed one guess as to what that number is … Raymond Smullyan
The last decade has seen a steady increase in the application of concepts from the theory of games to the study of evolution. Fields as diverse as sex ratio theory, animal distribution, contest behaviour and reciprocal altruism have contributed to what is now emerging as a universal way of thinking about phenotypic evolution. John Maynard Smith, Evolution and the Theory of Games 1973 p7
The equilibrium which is used is what I do is perfectly adjusted in relation to what you’re doing, and what you’re doing or what any other person is doing is perfectly adjusted to what I’m doing or what all other people are doing. They are seeking separate optimisation. Just like poker players. John Nash, mathematician
Game theory works in terms of self-interest. Some Game Theory concepts could be unsound. There’s over-dependence on rationality. That is my enlightenment. John Nash
A German mathematical genius, David Hilbert, had unleashed a revolution in mathematics. Hilbert set out a famous program in 1900 of which the goal was nothing less than the ‘axiomatization of all mathematics so that it could be mechanized and solved in a routine manner’ ... The Hilbert program emerged at the turn of the century as a response to a perceived crisis in mathematics. Sylvia Nasar, A Beautiful Mind
Melvin Hausner recalled: ‘He was always buried in thought. He’d sit in the common room by himself. He could easily walk by you and not see you. He was always muttering to himself. Always whistling. Nash was always thinking ... If he was lying on a table, it was because he was thinking. Just thinking. You see could see he was thinking.’
He seemed to be enjoying himself immensely. A profound dislike for merely absorbing knowledge and a strong compulsion to learn by doing is one of the most reliable signs of genius. He was obsessed with learning from scratch. Milnor recalled, ‘It was as if he wanted to rediscover; for himself, three hundred years of mathematics.’ ibid.
He was always on the lookout for problems. ‘He was very much aware of unsolved problems,’ said Milnor. ‘He really cross-examined people on what were the important problems.’ ibid.
John von Neumann was the very brightest star in Princeton’s mathematical firmament and the apostle of the new mathematical era ... A giant among pure mathematicians by the time he was 30 years old, he had become in turn physicist, economist, weapons expert, and computer visionary. Of his 150 published papers, 60 were in pure mathematics, 20 in physics, and 60 in applied mathematics, including statistics and game theory. ibid.
[John] von Neumann could divide two eight-digit numbers in his head. ibid.
The Theory of Games and Economic Behaviour [Von Neumann and Morgenstern] was in every way a revolutionary book. In line with Morgenstern’s agenda the book was a ‘blistering attack’ on the prevailing paradigm in economics and Olympian Keynesian perspective, in which individual incentives and individual behaviour were often subsumed, as well as an attempt to ground the theory in individual psychology. ibid.
Nash wrote his first paper, one of the great classics of modern economics, during his second term in Princeton. The Bargaining Problem is a remarkably down-to-earth work for a mathematician, especially a young mathematician ... behaviour that economics had long considered part of human psychology, and therefore beyond the reach of economic reasoning, was, in fact, amenable to systematic analysis. ibid.
The entire edifice of game theory rests on two theorems: Von Neumann’s min-max theorem of 1928 and Nash’s equilibrium theorem of 1950 ... Nash introduced the distinction between cooperative and non-cooperative games ... By broadening the concept to include games that involved a mix of cooperation and competition, Nash succeeded in opening the door in applications of game theory to economics, political science, sociology, and, ultimately, evolutionary biology. ibid.