Math Quotes - Page 3

The kind of knowledge which is supported only by observations and is not yet proved must be carefully distinguished from the truth; it is gained by induction, as we usually say. Yet we have seen cases in which mere induction led to error. Therefore, we should take great care not to accept as true such properties of the numbers which we have discovered by observation and which are supported by induction alone. Indeed, we should use such a discovery as an opportunity to investigate more exactly the properties discovered and to prove or disprove them; in both cases we may learn something useful.

A line is length without breadth.

To divide a cube into two other cubes, a fourth power, or in general any power whatever into two powers of the same denomination above the second is impossible, and I have assuredly found an admirable proof of this, but the margin is too narrow to contain it.

I never got a pass mark in math ... Just imagine - mathematicians now use my prints to illustrate their books.

There are two versions of math in the lives of many Americans: the strange and boring subject that they encountered in classrooms and an interesting set of ideas that is the math of the world, and is curiously different and surprisingly engaging. Our task is to introduce this second version to today's students, get them excited about math, and prepare them for the future.

All models are wrong, but some are useful.

In [great mathematics] there is a very high degree of unexpectedness, combined with inevitability and economy.

If there is a 50-50 chance that something can go wrong, then 9 times out of ten it will.

It will be another million years, at least, before we understand the primes.

My freshman year of high school I joined the chess and math clubs.

I do not believe in the gifted. If [the students] have ganas, I can make them do it.

As long as algebra is taught in school, there will be prayer in school.

It is better to solve one problem five different ways, than to solve five problems one way.

You know that I write slowly. This is chiefly because I am never satisfied until I have said as much as possible in a few words, and writing briefly takes far more time than writing at length.

There is no smallest among the small and no largest among the large, but always something still smaller and something still larger.

Do the math: You never settle for less than the whole if you knew the half.

Mathematics is written for mathematicians.

It is by logic that we prove, but by intuition that we discover. To know how to criticize is good, to know how to create is better.

In order to solve this differential equation you look at it until a solution occurs to you.

Now I will have less distraction.

Geometry is the foundation of all painting.

Perfect numbers like perfect men are very rare.

Symmetry, as wide or as narrow as you may define its meaning, is one idea by which man through the ages has tried to comprehend and create order, beauty and perfection.

Since you are now studying geometry and trigonometry, I will give you a problem. A ship sails the ocean. It left Boston with a cargo of wool. It grosses 200 tons. It is bound for Le Havre. The mainmast is broken, the cabin boy is on deck, there are 12 passengers aboard, the wind is blowing East-North-East, the clock points to a quarter past three in the afternoon. It is the month of May. How old is the captain?

Mathematics is a game played according to certain simple rules with meaningless marks on paper.