What Is Mathematics?

Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. "Immortality" may be a silly word, but probably a mathematician has the best chance of whatever it may mean.

- G. H. Hardy, A Mathematician's Apology

Podcast of the Day

Melvyn Bragg and guests discuss the way perceptions of the importance of mathematics have fluctuated in the 20th century, the nature of mathematical ability, and what mathematics can show us about how life began, and how it might continue. Galileo wrote “this grand book the universe… is written in the language of mathematics”. It was said before Galileo and has been said since and in the last decades of the 20th century it is being said again, most emphatically. How important is maths in relation to other sciences at the end of the twentieth century - will it ever be made redundant, or is it increasingly crucial to our understanding of the world and ourselves? What insight can it give us into the origins of life, and the functioning of our brains, and what does it mean to say that maths has become more ‘visual’?

Listen to Melvyn Bragg and guests discuss Mathematics on the In Our Time podcast

Video of the Day

Short Article of the Day

Mathematics is often praised (or ignored) on the grounds that it is far removed from the lives of ordinary people, but that assessment of the subject is utterly mistaken. As G. H. Hardy observed in A Mathematician’s Apology:

Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune; and there are probably more people really interested in mathematics than in music. Appearances suggest the contrary, but there are easy explanations. Music can be used to stimulate mass emotion, while mathematics cannot; and musical incapacity is recognized (no doubt rightly) as mildly discreditable, whereas most people are so frightened of the name of mathematics that they are ready, quite unaffectedly, to exaggerate their own mathematical stupidity.

Continue reading Luke Heaton's article: In Defense of Mathematics

Further Reading

The applicability of mathematics can lie anywhere on a spectrum from the completely trivial to the utterly mysterious. At the one extreme, mathematics is used outside of mathematics in cases which range from everyday calculations like the attempt to balance one’s checkbook through the most demanding abstract modeling of subatomic particles. The techniques underlying these applications are perfectly clear to those who have mastered them, and there seems to be little for the philosopher to say about such cases. At the other extreme, scientists and philosophers have often mentioned the remarkable power that mathematics provides to the scientist, especially in the formulation of new scientific theories. Most famously, Wigner claimed that “The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve." And according to Kant, “In any special doctrine of nature there can be only as much proper science as there is mathematics therein." Many agree that the problem of understanding the significant tie between mathematics and modern science is an interesting and significant challenge for the philosopher of mathematics...

Continue reading the Internet Encyclopedia of Philosophy article on The Applicability of Mathematics

Related Topics

 Game Theory | Logic | Philosophy

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