A Quote by Steven G. Krantz

A mathematician experiments, amasses information, makes a conjecture, finds out that it does not work, gets confused and then tries to recover. A good mathematician eventually does so - and proves a theorem.
A mathematician is an? individual who calls himself a 'physicist' and does 'physics' and physical experiments with abstract concepts.
If a mathematician wishes to disparage the work of one of his colleagues, say, A, the most effective method he finds for doing this is to ask where the results can be applied. The hard pressed man, with his back against the wall, finally unearths the researches of another mathematician B as the locus of the application of his own results. If next B is plagued with a similar question, he will refer to another mathematician C. After a few steps of this kind we find ourselves referred back to the researches of A, and in this way the chain closes.
I think you can fan the flames, but I think in the same way that a mathematician is a mathematician - He's not taught to be a mathematician. He either has a feeling for equations and an understanding and delight in it, not only in the purity of it, but in its beauty as well.
That's my mathematician who examines problems which I put before him and checks their validity. You see, I am not myself a good mathematician.
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.
The desire to explore thus marks out the mathematician. This is one of the forces making for the growth of mathematics. The mathematician enjoys what he already knows; he is eager for more knowledge.
A mathematician is a person who can find analogies between theorems; a better mathematician is one who can see analogies between proofs and the best mathematician can notice analogies between theories.
You don't have to be a genius mathematician to have a career in cyber security, but it certainly helps to be a strong mathematician.
As a poet and as a mathematician, he would reason well; as a mere mathematician, he could not have reasoned at all.
A mathematician who is not also something of a poet will never be a complete mathematician.
I was a mathematician by nature, and still am - I just knew I didn't want to be a mathematician. So I decided not to take any mathematics courses.
Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means. The geometer might be replaced by the "logic piano" imagined by Stanley Jevons; or, if you choose, a machine might be imagined where the assumptions were put in at one end, while the theorems came out at the other, like the legendary Chicago machine where the pigs go in alive and come out transformed into hams and sausages. No more than these machines need the mathematician know what he does.
Neither you nor I nor anybody else knows what makes a mathematician tick. It is not a question of cleverness. I know many mathematicians who are far abler than I am, but they have not been so lucky. An illustration may be given by considering two miners. One may be an expert geologist, but he does not find the golden nuggets that the ignorant miner does.
The scientist has to take 95 per cent of his subject on trust. He has to because he can't possibly do all the experiments, therefore he has to take on trust the experiments all his colleagues and predecessors have done. Whereas a mathematician doesn't have to take anything on trust. Any theorem that's proved, he doesn't believe it, really, until he goes through the proof himself, and therefore he knows his whole subject from scratch. He's absolutely 100 per cent certain of it. And that gives him an extraordinary conviction of certainty, and an arrogance that scientists don't have.
The whole thing that makes a mathematician’s life worthwhile is that he gets the grudging admiration of three or four colleagues.
No more than these machines need the mathematician know what he does.
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