John Edensor Littlewood Quotes

Try a hard problem. You may not solve it, but you will prove something else.

I read in the proof sheets of Hardy on Ramanujan: "As someone said, each of the positive integers was one of his personal friends." My reaction was, "I wonder who said that; I wish I had." In the next proof-sheets I read (what now stands), "It was Littlewood who said ... "

I recall once saying that when I had given the same lecture several times I couldn't help feeling that they really ought to know it by now.

A good mathematical joke is better, and better mathematics, than a dozen mediocre papers.

Before creation, God did just pure mathematics. Then He thought it would be a pleasant change to do some applied.

The higher mental activities are pretty tough and resilient, but it is a devastating experience if the drive does stop. Some people lose it in their forties and can only stop. In England they are a source of Vice-Chancellors.

A linguist would be shocked to learn that if a set is not closed this does not mean that it is open, or again that "E is dense in E" does not mean the same thing as "E is dense in itself".

The theory of numbers is particularly liable to the accusation that some of its problems are the wrong sort of questions to ask. I do not myself think the danger is serious; either a reasonable amount of concentration leads to new ideas or methods of obvious interest, or else one just leaves the problem alone. "Perfect numbers" certainly never did any good, but then they never did any particular harm.

The infinitely competent can be uncreative.

The first test of potential in mathematics is whether you can get anything out of geometry.

In presenting a mathematical argument the great thing is to give the educated reader the chance to catch on at once to the momentary point and take details for granted: two trivialities omitted can add up to an impasse). The unpractised writer, even after the dawn of a conscience, gives him no such chance; before he can spot the point he has to tease his way through a maze of symbols of which not the tiniest suffix can be skipped.

I've been giving this lecture to first-year classes for over twenty-five years. You'd think they would begin to understand it by now.

I listen only to Bach, Beethoven or Mozart. Life is too short to waste on other composers.

The first lecture of each new year renews for most people a light stage fright.

It is possible for a mathematician to be "too strong" for a given occasion. He forces through, where another might be driven to a different, and possible more fruitful, approach. (So a rock climber might force a dreadful crack, instead of finding a subtle and delicate route.)