Where do different fields of mathematics intersect? - MathOverflow [closed]

Where do different fields of mathematics intersect?

2011-05-01T20:04:41Z

Here is the problem: Two mathematicians meet at a bar. They like each other and tend to collaborate. But it is not so clear what problems could be of common interest to both of them. Of course, the traditional way is they keep describing they work or their field in general so that hopefully they catch something at the end. But is there any reference, graph, table or whatever that they can use to help them? This, of course, makes sense only when such a reference keeps updated based on the continuous production in mathematics.

Answer by quid for Where do different fields of mathematics intersect?

2011-05-01T22:44:52Z

First, I have to agree that in principle this is too broad a question. Many fields are closely related, some are vaguely related, and some are at first sight unrelated (but one never knows). And, Mariano Suárez-Alvarez suggestion how to find out about frequent interactions of fields is a very good one.

Second, André Henriques says the graph is the complete graph. And, yes I guess if one looks carefully enough this is indeed true. A place where something along these lines is in my opinion argued very convincingly, and one of my favorite mathematical talks, is "The Importance of Mathematics. A Lecture by Timothy Gowers" available on video, e.g., here but I assume elsewhere too.

From the description of the video:

His theme underscores the unity of different apparently diverse sub-fields of mathematics. His exposition is exceptionally clear and easy to follow, making mathematics accessible to non-experts. This lecture is a treasure trove of mathematical intuition and insight into the relationship between mathematics and its applications. Using historical and present-day examples, the speaker makes a convincing argument that mathematics plays a crucial role in the advancement of science.

For example it shows (if I remember correctly) how to arrive in a very natural way from questions on PDEs to questions of (combinatorial) number theory. My memeory is a bit vague, so this might not be exact but something along these lines, which also reminds me that I should rewatch the video some time soon.

Sorry, to those who think this question should not be answered, or think my answer is not precise enough. But, I like this talk a lot and did not want to miss this (in my opinion) fitting opportunity to mention it.

Answer by Yemon Choi for Where do different fields of mathematics intersect?

2011-05-01T22:50:24Z

If I understand your question correctly: I think that dialogue is a far better way to settle on possible directions for collaboration than looking up MSC codes or tables saying how many times the phrases "noncommutative geometry" or "mirror symmetry" are mentioned in a given article. So I think your question is starting from a dubious premise.