Michi’s blog » Blog Archive » On purity and essence of mathematics

On purity and essence of mathematics

June 15th, 2008

I seem, lately, to be so densely planned that all I can do for my blog is to react on blog posts from Ben Webster at the Secret Blogging Seminar.

He has, recently, written a post inspired by the xkcd comic on purity in the sciences. The comic is funny, and rings true, but Ben brings up a severe criticism of the premises of the comic that rings back to my own years as a hotheaded undergraduate.

You should read all of Ben’s post, but if you don’t, you should at least read the following:

And I think one of the key points here is this: mathematics is not science. Mathematics is often lumped in with science, and is often used by scientists. Mathematicians often know more science than normal people, and certainly scientists know more mathematics. But mathematics and science are fundamentally different activities, as different as making a gun and fighting in a battle. I mean, no one would claim there are no links between those occupations, or that gun-makers don’t pay a lot of attention to how guns are used, but not even a child would mistake one for the other. Putting mathematics on a continuum of purity with sciences is like putting it on a continuum with disciplines of art ordered by “highbrow-ness” (actually, I would argue that the latter captures the nature of mathematics better).

The critique here is pretty close to my own age-old hobby horse: the epistemology of mathematics is fundamentally different from the epistemology of the sciences. I used to use this as an argument for transferring the Department of Mathematics at Stockholm University from the Faculty of Sciences to the Faculty of Humanities. Nobody really took me serious back then. However, the basic ideas underlying it all reoccurs: both in Ben’s post, and in Pozorvlak’s excellent shot at classifying academic disciplines by their epistemology. Pozorvlak expands on his treatment of it all, but if we restrict it to the case Ben discusses, his point is basically this:
Mathematics deals with statements that can be proven.
Science deals with statements that cannot be proven, but can be falsified.

These two types of statements lead pretty immediately to different ideas of what truth is – and what knowledge is and all sorts of deep philosophical (as in cannot be proven, cannot be falsified, cannot even find circumstantial evidence for) questions dealing with the meta-level of academic research.

Nowadays, my University has the Mathematics department placed in the Faculty for Mathematics and Computer Science – and I have much less objections to this state of affairs.

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about: Michi is a recent PhD working in homological algebra and applied algebraic topology. This blog is his outlet for texts with some manner of thought put into them. Over at his LiveJournal intimate details and streams of consciousness might be found.
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