Abstract Mathematics Quotes

If indeed, as Hilbert asserted, mathematics is a meaningless game played with meaningless marks on paper, the only mathematical experience to which we can refer is the making of marks on paper.

In 1975, ... [speaking with Shiing Shen Chern], I told him I had finally learned ... the beauty of fiber-bundle theory and the profound Chern-Weil theorem. I said I found it amazing that gauge fields are exactly connections on fiber bundles, which the mathematicians developed without reference to the physical world. I added, "this is both thrilling and puzzling, since you mathematicians dreamed up these concepts out of nowhere." He immediately protested: "No, no. These concepts were not dreamed up. They were natural and real."

Carnal embrace is sexual congress, which is the insertion of the male genital organ into the female genital organ for purposes of procreation and pleasure. Fermat’s last theorem, by contrast, asserts that when x, y and z are whole numbers each raised to power of n, the sum of the first two can never equal the third when n is greater than 2.

Mathematics is entirely free in its development, and its concepts are only linked by the necessity of being consistent, and are co-ordinated with concepts introduced previously by means of precise definitions.

Everybody in mathematics had given up for 100 years or 200 years the idea that you could from pictures, from looking at pictures, find new ideas. That was the case long ago in the Middle Ages, in the Renaissance, in later periods, but then mathematicians had become very abstract.

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.

In abstract mathematics, of course operations alter those particular relations which are involved in the considerations of number and space, and the results of operations are those peculiar results which correspond to the nature of the subjects of operation.

The only thing that might have annoyed some mathematicians was the presumption of assuming that maybe the axiom of choice could fail, and that we should look into contrary assumptions.

The Theory of Groups is a branch of mathematics in which one does something to something and then compares the result with the result obtained from doing the same thing to something else, or something else to the same thing.

The most important resource of counties of the future will be the number of math trained brains.

No one has yet discovered any warlike purpose to be served by the theory of numbers or relativity, and it seems unlikely that anyone will do so for many years.

I confess that Fermat's Theorem as an isolated proposition has very little interest for me, because I could easily lay down a multitude of such propositions, which one could neither prove nor dispose of.

To choose one sock from each of infinitely many pairs of socks requires the Axiom of Choice, but for shoes the Axiom is not needed.

There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world