The Arab world is also the world that produced some of the greatest improvements in mathematics and in science. Even today, when a Princeton mathematician does an algorithm, he may not remember that "algorithm" derived from the name al-Khwarizmi, who is a ninth-century Arab mathematician.
Thus number may be said to rule the whole world of quantity, and the four rules of arithmetic may be regarded as the complete equipment of the mathematician.
Everybody in mathematics had given up for 100 years or 200 years the idea that you could from pictures, from looking at pictures, find new ideas. That was the case long ago in the Middle Ages, in the Renaissance, in later periods, but then mathematicians had become very abstract.
I have had my results for a long time: but I do not yet know how I am to arrive at them.
A Noah's Ark of mathematicians, their lives, loves, hard times, and madnesses, Loving and Hating Mathematics shows our community with all its warts as well as its triumphs. I especially liked the chapter on much-hated school mathematics, 'Almost All Children Left Behind.'
Sometimes a line of mathematical research extending through decades can be thought of as one long conversation in which many mathematicians take part. This is fortunately true at present.
A mathematician is a magician who converts adjectives into nouns: continuous into continuum, infinite into infinity, infinitesimal into location, 0D into point, 1D into line, curved into geodesic.
The mathematicians are the priests of the modern world.
I wanted to become a mathematician, physicist or astronomer.
The physicists defer only to mathematicians, and the mathematicians defer only to God.
Even though I am a mathematician, I look at [fetal development] with marvel: How do these instruction sets not make mistakes as they build what is us?
A jazz musician is a combination orator, dialectician, mathematician, athlete, entertainer, poet, singer, dancer, diplomat, educator, student, comedian, artist, seducer, public masturbator, and general all-round good fellow.
First rate mathematicians choose first rate people, but second rate mathematicians choose third rate people.
Rigour is to the mathematician what morality is to men.
I like words and numbers. I'm obsessed with them. You know, I think I would've been a mathematician had I kept up, but it's the stuff in your head, you know? It's like being technologically adept. You have it or you don't. You can learn it, but some people just have it. They go to sleep, wake up, and know everything. I like games, too. I love playing games.
Mathematicians practice absolute freedom.
The mathematician of to-day admits that he can neither square the circle, duplicate the cube or trisect the angle. May not our mechanicians, in like manner, be ultimately forced to admit that aerial flight is one of that great class of problems with which men can never cope... I do not claim that this is a necessary conclusion from any past experience. But I do think that success must await progress of a different kind from that of invention.
In mathematics, if a pattern occurs, we can go on to ask, Why does it occur? What does it signify? And we can find answers to these questions. In fact, for every pattern that appears, a mathematician feels he ought to know why it appears.
No mathematician should ever allow him to forget that mathematics, more than any other art or science, is a young man's game. ... Galois died at twenty-one, Abel at twenty-seven, Ramanujan at thirty-three, Riemann at forty. There have been men who have done great work later; ... [but] I do not know of a single instance of a major mathematical advance initiated by a man past fifty. ... A mathematician may still be competent enough at sixty, but it is useless to expect him to have original ideas.
If present trends continue, our country may soon find itself far behind many other nations in both science and technology nations where, if you inform strangers that you are a mathematician, they respond with admiration and not by telling you how much they hated math in school, and how they sure could use you to balance their checkbooks.
A typical mathematician does not actively try to be useful. Individual mathematicians are motivated primarily by a subtle mixture of ambition and intellectual curiosity, and not by a wish to benefit society, nevertheless, mathematics as a whole does benefit society.
By keenly confronting the enigmas that surround us, and by considering and analyzing the observations that I had made, I ended up in the domain of mathematics. Although I am absolutely without training in the exact sciences, I often seem to have more in common with mathematicians than with my fellow artists.
Let me tell you how at one time the famous mathematician Euclid became a physician. It was during a vacation, which I spent in Prague as I most always did, when I was attacked by an illness never before experienced, which manifested itself in chilliness and painful weariness of the whole body. In order to ease my condition I took up Euclid's Elements and read for the first time his doctrine of ratio, which I found treated there in a manner entirely new to me. The ingenuity displayed in Euclid's presentation filled me with such vivid pleasure, that forthwith I felt as well as ever.
If intellectual curiosity, professional pride, and ambition are the dominant incentives to research, then assuredly no one has a fairer chance of gratifying them than a mathematician.
My favourite fellow of the Royal Society is the Reverend Thomas Bayes, an obscure 18th-century Kent clergyman and a brilliant mathematician who devised a complex equation known as the Bayes theorem, which can be used to work out probability distributions. It had no practical application in his lifetime, but today, thanks to computers, is routinely used in the modelling of climate change, astrophysics and stock-market analysis.
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