Pierre de Fermat

I have discovered a method for solving all problems of history by means of algebra, which is more general than that of Herodotus.

It is impossible for a cube to be written as a sum of two cubes or a fourth power to be written as a sum of two fourth powers, or, in general, for any number which is a power greater than the second to be written as a sum of two like powers.

And perhaps, posterity will be grateful to me for having shown that the Ancients did not know everything.

The nature of the problem is such that, while its proof is hidden, its truth is accepted.

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

There is scarcely any one who states purely arithmetical questions, scarcely any one who understands them. Is this not because arithmetic has been treated up to this time geometrically rather than arithmetically?

Every prime number of the form 4n+1 is uniquely expressible as the sum of two squares.

I was the first to discover the most beautiful property of numbers of the form 2^(2^n) + 1, from which I drew many consequences.

The method by which I demonstrate the truth of my propositions is truly my own, and I do not owe it to any author.

I would send you the proof, if I did not fear it being too long.

It is knowledge that makes the difference between man and beast, and between man and man.

In my opinion, all of the sciences are interconnected; a single chain links them.

The ultimate goal of the mathematical sciences is nothing but the honor of the human spirit.

I have been occupied with the discovery of the most perfect numbers and with many other subtle matters in arithmetic.

To find a perfect number, it is necessary to find a prime number of the form 2^n - 1.

The theory of numbers is the queen of mathematics.

I have considered the problem of dividing a number into two squares in an infinity of ways.

My reasoning is based on a method which I call 'descent', infinite or indefinite.

It is easy to multiply numbers, but difficult to factor them.

I am almost convinced that all numbers are sums of three triangular numbers.