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.
One can imagine that the ultimate mathematician is one who can see analogies between analogies.
Good mathematicians see analogies. Great mathematicians see analogies between analogies.
Mathematics is the study of analogies between analogies. All science is. Scientists want to show that things that don't look alike are really the same. That is one of their innermost Freudian motivations. In fact, that is what we mean by understanding.
An axiomatic system establishes a reverberating relationship between what a mathematician assumes (the axioms) and what he or she can derive (the theorems). In the best of circumstances, the relationship is clear enough so that the mathematician can submit his or her reasoning to an informal checklist, passing from step to step with the easy confidence the steps are small enough so that he cannot be embarrassed nor she tripped up.
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.
We lay down a fundamental principle of generalization by abstraction: The existence of analogies between central features of various theories implies the existence of a general theory which underlies the particular theories and unifies them with respect to those central features.
Kanye [West] just says the funniest analogies that are so random. I should start keeping a book - in 20 years, I'll have a big book of analogies.They always make me laugh.
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.
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.
If genius has any common denominator, I would propose breadth of interest and the ability to construct fruitful analogies between fields.
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.
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.
The computer was, to the best of my feelings about the subject, not thinking like a mathematician, and it was much more successful, because it was thinking not like a mathematician.
I think, in a lot of ways, directing is puppeteering. I guess I see a lot of analogies between what puppeteers and filmmakers do. There's something about creating life out of things that have no life.