Explore Quotes on Mathematics

The only reason that we like complex numbers is that we don't like real numbers.

log log log x goes to infinity with great dignity.

A felicitous but unproved conjecture may be of much more consequence for mathematics than the proof of many a respectable theorem.

A beautiful problem is no joke!

Sometimes a good idea comes to you when you are not looking for it. Through an improbable combination of coincidence, naivete and lucky mistakes.

I like to think of mathematicians as forming a nation of our own without distinctions of geographical origin, race, creed, sex, age or even time... all dedicated to the most beautiful of the arts and sciences.

... and it is probably that there is some secret here which remains to be discovered.

But as Nature is the best guide, teaching must be the development of natural inclinations, for which purpose the teacher must watch his pupil and listen to him, not continually bawl words into his ears as if pouring water into a funnel. Good teaching will come from a mind well made rather than well filled.

A heavy warning used to be given that pictures are not rigorous; this has never had its bluff called and has permanently frightened its victims into playing for safety.

Mathematics is persistent intellectual honesty.

Mathematical study and research are very suggestive of mountaineering. Whymper made several efforts before he climbed the Matterhorn in the 1860's and even then it cost the life of four of his party. Now, however, any tourist can be hauled up for a small cost, and perhaps does not appreciate the difficulty of the original ascent. So in mathematics, it may be found hard to realise the great initial difficulty of making a little step which now seems so natural and obvious, and it may not be surprising if such a step has been found and lost again.

Everyone else would climb a peak by looking for a path somewhere in the mountain. Nash would climb another mountain altogether and from that distant peak would shine a searchlight back onto the first peak.

The greatest reward for a student is not a good grade. It is the willingness of his teacher to listen to him.

Mathematics is, in many ways, the most precious response that the human spirit has made to the call of the infinite.

Every dimension is special.

Inspiration is constantly in the air. It's up to us to develop the sensitivity to pick up on it.

Mathematics is an activity governed by the same rules imposed upon the symphonies of Beethoven, the paintings of DaVinci, and the poetry of Homer.

If you had done something twice, you are likely to do it again.

When I give this talk to a physics audience, I remove the quotes from my 'Theorem'.

Counting pairs is the oldest trick in combinatorics... Every time we count pairs, we learn something from it.

Mathematicians care no more for logic than logicians for mathematics.