Quotes About Mathematics

The fact that simultaneous discovery occurs in mathematics, as well as the sciences, points toward some objective element within their subject matter that is independent of the psyche of the investigator.

The ease with which collaboration occurs in mathematical research and the essential similarity of the fruits of such collaboration to that of individual work points suggestively towards a powerful objective element behind the scenes that is discovered rather than invented.

Most scientists and mathematicians operate as if Platonism is true regardless of whether they believe that it is. That is, they work as though there were an unknown realm of truth to be discovered.

I tell you, with complex numbers you can do anything.

Mathematicians call it "the arithmetic of congruences." You can think of it as clock arithmetic. Temporarily replace the 12 on a clock face with 0. The 12 hours of the clock now read 0, 1, 2, 3, … up to 11. If the time is eight o'clock, and you add 9 hours, what do you get? Well, you get five o'clock. So in this arithmetic, 8 + 9 = 5; or, as mathematicians say, 8 + 9 ? 5 (mod 12), pronounced "eight plus nine is congruent to five, modulo twelve.

It was in 1742 that Christian Goldbach put forward his famous conjecture that every even number greater than 2 can be expressed as the sum of two primes.

which has inspired at least one novel, Apostolos Doxiadis's Uncle Petros and Goldbach's Conjecture29).

If you're not thinking about numbers, you're probably not thinking.

Bernhard Riemann was a very pure case of the intuitive mathematician. This needs some explaining. The mathematical personality has two large components, the logical and the intuitive. Both are present in any good mathematician, but often one or the other is strongly dominant.

Let us say, in a word, that the correlation between the laws of mathematics and of physics is the evidence of the rational character of nature. Nature may be reduced to motions; and motions can be understood only as force, activity. But the laws which connect motions are fundamentally mathematical laws,- laws of reason. Hence force, activity, can be understood only as rational, as spiritual. Nature is thus seen to mean Activity, and Activity is seen to mean Intelligence

Mathematics is often cited as an example of purely normative thinking dependent upon a priori canons and supra-empirical material. But it is hard to see how the student who approaches the matter historically can avoid the conclusion that the status of mathematics is as empirical as metallurgy.

I am a mathematician, sir. I never permit myself to think.

Now I feel as if I should succeed in doing something in mathematics, although I cannot see why it is so very important. . . The knowledge doesn't make life any sweeter or happier, does it?

Had my life increased, or merely added to itself? There had been addition and subtraction in my life, but how much multiplication?

Throughout his life Newton must have devoted at least as much attention to chemistry and theology as to mathematics.

The more reasonable a student was in mathematics, the more unreasonable she was in the affairs of real life, concerning which fewtrustworthy postulates have yet been ascertained.

Of Belief Human mathematics, so to speak, like the length of life, are subject to the doctrine of chances.

But I simply can't stand a view limited to this earth, I feel life is so small unless it has windows into other worlds...I like mathematics largely because it is not human.

It's your life story if you're a mathematician: every time you discover something neat, you discover that Gauss or Newton knew it in his crib.

Mathematics, even in its present and most abstract state, is not detached from life. It is just the ideal handling of the problems of life.

its very nature, scientific investigation takes for granted such assumptions as that: there is a physical world existing independently of our minds; this world is characterized by various objective patterns and regularities; our senses are at least partially reliable sources of information about this world; there are objective laws of logic and mathematics that apply to the objective world outside our minds;

What is the epistemology of the philosophy of nature itself? Is it an a priori discipline the way that mathematics and metaphysics are often claimed to be? Or are its claims subject to empirical falsification the way that those of natural science typically are? These

Second, the intellect abstracts from even the common sensible features of things and considers only their quantitative features. Mathematics is the field of inquiry corresponding to this degree of abstraction.

The mathematics are distinguished by a particular privilege, that is, in the course of ages, they may always advance and can never recede.