David Hilbert Quotes

Some infinities are bigger than other infinities.

[On Cantor's work:] The finest product of mathematical genius and one of the supreme achievements of purely intellectual human activity.

Euclid avoids it [the treatment of the infinite]; in modern mathematics it is systematically introduced, for only then is generality obtained.

We must say that there are as many squares as there are numbers.

One of the most amazing things about mathematics is the people who do math aren't usually interested in application, because mathematics itself is truly a beautiful art form. It's structures and patterns, and that's what we love, and that's what we get off on.

When I dealt with set theory, I could never make it be the music that I wanted.

Mathematicians didn't invent infinity until 1877. So they thought it was impossible that Africans could be using fractal geometry.

Mathematics has beauty and romance. It's not a boring place to be, the mathematical world. It's an extraordinary place; it's worth spending time there.

I have found a very great number of exceedingly beautiful theorems.

It's such a diversion to be constantly thinking of better ways I can teach people math that my hunger is for that really, for new ways of translating the beauty of it.

Pure mathematics is, in its way, the poetry of logical ideas.

My interest in science started quite early. My earliest school recollection, from age 6, is actually of mathematics, realizing that one could fill an entire page with digits and never come to the largest possible number, so I saw what was meant by infinity.

Nature never uses prime numbers. But mathematicians do.

I can see that, without being excited, mathematics can look pointless and cold.

Modern mathematics, that most astounding of intellectual creations, has projected the mind's eye through infinite time and the mind's hand into boundless space.

Set theory in sheep's clothing.

There are infinite numbers between 0 and 1.

Math is the only place where truth and beauty mean the same thing.

I’m so tired... I was up all night trying to round off infinity.

There are things which seem incredible to most men who have not studied Mathematics.

Mathematics has been called the science of the infinite. Indeed, the mathematician invents finite constructions by which questions are decided that by their very nature refer to the infinite. This is his glory.

A googolplex is precisely as far from infinity as is the number 1... no matter what number you have in mind, infinity is larger still.

It is almost as hard to define mathematics as it is to define economics, and one is tempted to fall back on the famous old definition attributed to Jacob Viner, "Economics is what economists do," and say that mathematics is what mathematicians do. A large part of mathematics deals with the formal relations of quantities or numbers.

Euclid alone Has looked on Beauty bare. Fortunate they Who, though once only and then but far away, Have heard her massive sandal set on stone.

Mathematics is really an art, not a science.