A mathematical point is the most indivisble and unique thing which art can present.
You can not apply mathematics as long as words still becloud reality.
Mathematics: silent harmonies. Music: sounding numbers.
The history of mathematics, lacking the guidance of philosophy, [is] blind, while the philosophy of mathematics, turning its back on the most intriguing phenomena in the history of mathematics, is empty.
André Weil always looked like that, not only when he talked about the devil.
I studied mathematics which is the madness of reason.
If I feel unhappy, I do mathematics to become happy. If I am happy, I do mathematics to keep happy.
The sky is where mathematics and magic become one.
The "seriousness" of a mathematical theorem lies, not in its practical consequences, which are usually negligible, but in the significance of the mathematical ideas which it connects.
[Mathematics] is security. Certainty. Truth. Beauty. Insight. Structure. Architecture. I see mathematics, the part of human knowledge that I call mathematics, as one thing-one great, glorious thing. Whether it is differential topology, or functional analysis, or homological algebra, it is all one thing. . . . They are intimately interconnected, they are all facets of the same thing. That interconnection, that architecture, is secure truth and is beauty. That's what mathematics is to me.
Medicine makes people ill, mathematics make them sad and theology makes them sinful.
Algebraic geometry seems to have acquired the reputation of being esoteric, exclusive, and very abstract, with adherents who are secretly plotting to take over all the rest of mathematics. In one respect this last point is accurate.
Mathematics may be compared to a mill of exquisite workmanship, which grinds you stuff of any degree of fineness; but, nevertheless, what you get out depends upon what you put in; and as the grandest mill in the world will not extract wheat-flour from peascods, so pages of formulae will not get a definite result out of loose data.
Mathematics is like childhood diseases. The younger you get it, the better.
If I were again beginning my studies, I would follow the advice of Plato and start with mathematics.
Mathematics is the only true metaphysics.
In my own professional work I have touched on a variety of different fields. I've done work in mathematical linguistics, for example, without any professional credentials in mathematics; in this subject I am completely self-taught, and not very well taught.
Contradiction is not a sign of falsity, nor the lack of contradiction a sign of truth.
Here is something Category-Theorists like: it is trivial, but not trivially trivial.
The problem is that no ethical system has ever achieved consensus. Ethical systems are completely unlike mathematics or science. This is a source of concern.