What is mathematics for? Posted on 19 November 2012 by John “What is mathematics for? To delight the mind and help us understand the world.” From the back cover of Calculus Gems.
10 thoughts on “What is mathematics for?”
I would quibble slightly with the second half of that, depending on exactly what you mean by “understand”. I think math is a fabulous tool for modeling reality; I don’t think it is necessarily a description of reality. I feel the same way about physics — it’s a system for making better and better predictions, but not necessarily (at any given point in time) an accurate description of the fundamental nature of the universe(s).
But then, I read Kuhn for the first time recently, which probably explains some of that.
Hello, I fully agree with you about math. I’m 16, I’m in high school. I think math and physic are very RELEVANT FOR life everyday and all we need to do in any field.
So, Good bye. :-)
For quite some time I’ve been saying that mathematics is a collection of related multi-player social/creative games, the most popular sub-collection of which is called ZFC. Each player can choose from one or more goals: forming conjectures others find interesting, proving theorems others find useful or interesting, or disproving conjectures that have attracted some interest. From time to time, a scientific model of the world may happen to correspond to something in the game, at which point the professional mathematicians collectively find renewed faith in their funding.
How dare anyone suggest mathematics is related to the real world! My math is PURE! :)
Jacobi, in a letter to Legendre : “Fourier avait l’opinion que le but principal des mathématiques était l’utilité publique et l’explication des phénomènes naturels ; mais un philosophe comme lui aurait dû savoir que le but unique de la science, c’est l’honneur de l’esprit humain, et que sous ce titre, une question de nombres vaut autant qu’une question du système du monde”.
“It is true that Mr. Fourier had the opinion that the principal purpose of mathematics was the benefit of the society and the explanation of phenomena of nature; but a philosopher like he should know that the sole purpose of science is the honor of the human mind, and under this title, a question about numbers is as valuable as a question about the system of the world.”
I tend to agree with David Tate. I would choose for “help us to get a grip on the world”. It helps to create models of the world that can be of practical use, even if they are not completly accurate. The delight from the first part can help to create the illusion we can truly understand and control reality!
I’m not sure if ‘delight’ is the right word, for the first part. I think that it is not actually possible for a mind to be delighted, since, after all, it consists only of neurons firing in response to stimulation.
Nevertheless, we sometimes have experiences that we interpret as delight, and mathematics can trigger these experiences.
I think that we can substantially improve the back of Mr Simmons book by replacing his statement with the following:
“What is mathematics for? To cause experiences often interpreted as delight, and to provide models that, at times, coincide usefully with the world”
I’m sure that Mr. Simmons will be quite thankful for our work in improving on his errors.
So please can you try to explain to me Eric how I can feel delighted by the subtle touch of irony in your contributions? If it’s not my mind then what other part of me is it? And what is more real, the sensation of delight or the idea that we can reduce our mind to ‘just’ a bunch of firing neurons?
Eric’s irony was deliberate. I believe he was taking a swipe at reductionism.
On the Internet, no one can tell if your dog is being ironic.