A Quote by William Thurston
Mathematicians can and do fill in gaps, correct errors, and supply more detail and more careful scholarship when they are called on or motivated to do so. Our system is quite good at producing reliable theorems that can be solidly backed up. It's just that the reliability does not primarily come from mathematicians formally checking formal arguments; it comes from mathematicians thinking carefully and critically about mathematical ideas.
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As for mathematicians themselves: don't expect too much help. Most of them are too far removed in their ivory towers to take up such challenges. And anyway, they are not competent. After all, they are just mathematicians-what we need is paramathematicians, like you... It is you who can be the welding force, between mathematicians and stories, in order to achieve the synthesis.
Relations between pure and applied mathematicians are based on trust and understanding.
Namely, pure mathematicians do not trust applied mathematicians, and applied mathematicians do not understand pure mathematicians.
Mathematicians have been hiding and writing messages in the genetic code for a long time, but it's clear they were mathematicians and not biologists because, if you write long messages with the code that the mathematicians developed, it would more than likely lead to new proteins being synthesized with unknown functions.
The mathematical fraternity is a little like a self-perpetuating priesthood. The mathematicians of today teach the mathematicians of tomorrow and, in effect, decide whom to admit to the priesthood.
It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done. Statesmen despise publicists, painters despise art-critics, and physiologists, physicists, or mathematicians have usually similar feelings: there is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain. Exposition, criticism, appreciation, is work for second-rate minds.
Whenever I want to represent or depict the official version, I will refer to them as 'mathematicians' or 'mathematical physicists' or idiots or something like that. There are no physicists in mainstream 'Physics.' From Newton to Einstein to Hawking, they are all just mathematicians as far as Science and Physics are concerned.
When I told my son that I had to give a talk about my work to non-mathematicians, he warned me that regular people don't think like mathematicians.
We decided that 'trivial' means 'proved'. So we joked with the mathematicians: We have a new theorem- that mathematicians can prove only trivial theorems, because every theorem that's proved is trivial.
I am obliged to interpolate some remarks on a very difficult subject: proof and its importance in mathematics. All physicists, and a good many quite respectable mathematicians, are contemptuous about proof. I have heard Professor Eddington, for example, maintain that proof, as pure mathematicians understand it, is really quite uninteresting and unimportant, and that no one who is really certain that he has found something good should waste his time looking for proof.
Programming is one of the most difficult branches of applied mathematics; the poorer mathematicians had better remain pure mathematicians.
The mathematicians have been very much absorbed with finding the general solution of algebraic equations, and several of them have tried to prove the impossibility of it. However, if I am not mistaken, they have not as yet succeeded. I therefore dare hope that the mathematicians will receive this memoir with good will, for its purpose is to fill this gap in the theory of algebraic equations.
Now, as Mandelbrot points out, ... Nature has played a joke on the mathematicians. The 19th-century mathematicians may not have been lacking in imagination, but Nature was not. The same pathological structures that the mathematicians invented to break loose from 19th-century naturalism turn out to be inherent in familiar objects all around us.
Even the greatest mathematicians, the ones that we would put into our mythology of great mathematicians, had to do a great deal of leg work in order to get to the solution in the end.
Philosophers and psychiatrists should explain why it is that we mathematicians are in the habit of systematically erasing our footsteps. Scientists have always looked askance at this strange habit of mathematicians, which has changed little from Pythagoras to our day.
I knew a lot of black scientists, engineers, and mathematicians, and female mathematicians and engineers, women of all backgrounds. So this idea that anyone could be an engineer, a mathematician, or whatever, was something that I had grown up with and thought was really normal.
Outside observers often assume that the more complicted a piece of mathematics is, the more mathematicians admire it. Nothing could be further from the truth. Mathematicians admire elegance and simplicity above all else, and the ultimate goal in solving a problem is to find the method that does the job in the most efficient manner. Though the major accolades are given to the individual who solves a particular problem first, credit (and gratitude) always goes to those who subsequently find a simpler solution.
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