A Quote by Albert Einstein
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.
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Programming is one of the most difficult branches of applied mathematics; the poorer mathematicians had better remain pure mathematicians.
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.
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.
Poincaré [was] the last man to take practically all mathematics, pure and applied, as his province. ... Few mathematicians have had the breadth of philosophic vision that Poincaré had, and none in his superior in the gift of clear exposition.
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.
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.
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.
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.
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.
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.
Democracy can't work. Mathematicians, peasants, and animals, that's all there is - so democracy, a theory based on the assumption that mathematicians and peasants are equal, can never work. Wisdom is not additive; its maximum is that of the wisest man in a given group.
The inner circle of pure mathematicians will respond to the book with delight.
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.
... there are those who believe that mathematics can sustain itself and grow without any further contact with anything outside itself, and those who believe that nature is still and always will be one of the main (if not the main) sources of mathematical inspiration. The first group is identified as "pure mathematicians" (though "purist" would be more adequate) while the second is, with equal inadequacy, referred to as "applied".
It appears that the solution of the problem of time and space is reserved to philosophers who, like Leibniz, are mathematicians, or to mathematicians who, like Einstein, are philosophers.
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.
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