Mathematical Discovery Quotes

Math research is more like a marathon.

The greatest mathematicians, as Archimedes, Newton, and Gauss, always united theory and applications in equal measure.

Thus, in a sense, mathematics has been most advanced by those who distinguished themselves by intuition rather than by rigorous proofs.

A lot of the math that I do, it's not sort of premeditated. I talk online or with a colleague, and I get interested, and I just follow where it leads.

The Good Lord made all the integers; the rest is man's doing.

I remember having this vague idea that what mathematicians did was that some authority, someone, gave them problems to solve, and they just sort of solved them.

About Thomas Hobbes: He was 40 years old before he looked on geometry; which happened accidentally. Being in a gentleman's library, Euclid's Elements lay open, and "twas the 47 El. libri I" [Pythagoras' Theorem]. He read the proposition "By God", sayd he, "this is impossible:" So he reads the demonstration of it, which referred him back to such a proposition; which proposition he read. That referred him back to another, which he also read. Et sic deinceps, that at last he was demonstratively convinced of that truth. This made him in love with geometry.

I enjoyed like nothing else working in pure math, discovering new formulas.

I am interested in mathematics only as a creative art.

Rarely in the history of science has an abstract mathematical idea been received more enthusiastically by the entire scientific community than the invention of logarithms.

We are on the verge: Today our program proved Fermat's next-to-last theorem.

For scholars and laymen alike it is not philosophy but active experience in mathematics itself that can alone answer the question: What is mathematics?

The mathematics is not there till we put it there.

Even the greatest mathematicians, the ones that we would put into our mythology of great mathematicians, had to do a great deal of leg work in order to get to the solution in the end.

I entertain no doubts as to the truths of the tranfinites, which I recognized with God's help and which, in their diversity, I have studied for more than twenty years; every year, and almost every day brings me further in this science.

Mathematical discoveries, small or great are never born of spontaneous generation.

There might be a hidden structure in pi that we simply haven't discovered.

Over the centuries, monumental upheavals in science have emerged time and again from following the leads set out by mathematics.

I believe that numbers and functions of Analysis are not the arbitrary result of our minds; I think that they exist outside of us, with the same character of necessity as the things of objective reality, and we meet them or discover them, and study them, as do the physicists, the chemists and the zoologists.

God made the integers, man made the rest.

The method of Fluxions is the general key by help whereof the modern mathematicians unlock the secrets of Geometry, and consequently of Nature.

Mathematics is not a contemplative but a creative subject.

I hope that seeing the excitement of solving this problem will make young mathematicians realize that there are lots and lots of other problems in mathematics which are going to be just as challenging in the future.

Creating a body of mathematics is about intellectual labor, not some kind of transcendental revelation. There are plenty of important components of European fractal geometry that are missing from the African version.

The best that Gauss has given us was likewise an exclusive production. If he had not created his geometry of surfaces, which served Riemann as a basis, it is scarcely conceivable that anyone else would have discovered it. I do not hesitate to confess that to a certain extent a similar pleasure may be found by absorbing ourselves in questions of pure geometry.