Seeing there is nothing that is so troublesome to mathematical practice, nor that doth more molest and hinder calculators, than the multiplications, divisions, square and cubical extractions of great numbers.... I began therefore to consider in my mind by what certain and ready art I might remove those hindrances.
He went on to develop and invent logarithms and caluclating devices and the precursor to the slide rule.
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.
In mathematics we have long since drawn the rein, and given over a hopeless race.
I'm a mathematician, basically. What I do is look around for problems where I can find useful applications for mathematics. All I do, really, is the math, and other people have the ideas.
To every problem there is already a solution, whether you know it or not. To every sum in there is already a correct answer, whether the mathematician has found it or not.
Abel has left mathematicians enough to keep them busy for 500 years.
There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world
In math, you're either right or you're wrong.
The definition of a good mathematical problem is the mathematics it generates rather than the problem itself.
The mathematician, carried along on his flood of symbols, dealing apparently with purely formal truths, may still reach results of endless importance for our description of the physical universe.
It seems that if one is working from the point of view of getting beauty in one's equations, and if one has really a sound insight, one is on a sure line of progress.
The fundamental laws necessary for the mathematical treatment of a large part of physics and the whole of chemistry are thus completely known, and the difficulty lies only in the fact that application of these laws leads to equations that are too complex to be solved.
What affected me most profoundly was the realization that the sciences of cryptography and mathematics are very elegant, pure sciences. I found that the ends for which these pure sciences are used are less elegant.