mathematical investigation Quotes

I believe that numbers and functions of Analysis are not the arbitrary result of our minds; I think that they exist outside of us, with the same character of necessity as the things of objective reality, and we meet them or discover them, and study them, as do the physicists, the chemists and the zoologists.

Regarding the fundamental investigations of mathematics, there is no final ending ... no first beginning.

All results of the profoundest mathematical investigation must ultimately be expressible in the simple form of properties of the integers.

I do my precalc homework, and then when I'm done I actually sit with the textbook for like three hours and try to understand what I just did. That's the kind of weekend it is--the kind where you have so much time you go past the answers and start looking into the ideas.

He that gives a portion of his time and talent to the investigation of mathematical truth, will come to all other questions with a decided advantage over his opponents.

Archimedes to Eratosthenes greeting. ... certain things first became clear to me by a mechanical method, although they had to be demonstrated by geometry afterwards because their investigation by the said method did not furnish an actual demonstration. But it is of course easier, when we have previously acquired by the method, some knowledge of the questions, to supply the proof than it is to find it without any previous knowledge.

The investigation of mathematical truths accustoms the mind to method and correctness in reasoning, and is an employment peculiarly worthy of rational beings.

The study of mathematics is, if an unprofitable, a perfectly harmless and innocent occupation.

I didn't feel comfortable at first with pure mathematics, or as a professor of pure mathematics. I wanted to do a little bit of everything and explore the world.

A great deal of my work is just playing with equations and seeing what they give.