Way back at the end of last year I put out a call to mathematicians I know: hop on Skype and chat to me for a while about the work you’re doing at the moment. The first person to answer was David Roberts, a pure mathematician from Adelaide.
We had a fascinating talk about one thread of David’s current work, which involves all sorts of objects I know no more about than their names. I had intended to release this as a podcast, but the quality of my recording was very poor and it turns out I’m terrible at audio editing, so instead here’s a transcription. Assume all mistakes are mine, not David’s.
If you’ve ever wanted to know what it’s like to work in the far reaches of really abstract maths, this is an excellent glimpse of it.
DR: I’m David Roberts, I’m a pure mathematician, currently between jobs. I work – as far as research goes – generally on geometry and category theory, and the interplay between those two. And also a little bit of logic stuff, which I thought I’d talk about.
Update 14/05/2013: The seminar was successful: Zhang announced that his proof has already been refereed for the Annals, and everyone seems happy with it.
Hard Maths news now: there’s a rumour going round that Yitang (Tom) Zhang of the University of New Hampshire reckons he can prove that there are infinitely many different pairs of primes at most 70,000,000 apart.
Interesting, non-mathematically-unaware data visualisations on the blog Ideas Illustrated, including the origins of English words, the distributions of LEGO bricks, and how Wisconsin voters ended up on Null Island.
(via David Roberts on Google+)
On Google+ (sadly in a post with limited visibility, so I can’t link directly to it), Rongmin Lu (via David Roberts) highlights a case of “american whispers”, where a piece of research is helped along by press releases and media paraphrasing to become a completely different result.
Here’s how American whispers works:
1. You publish a paper, say on a new approximation to the discrete Fourier transform. To show the relevance of your work, you then say something like your new algorithm “improve[s] over the Fast Fourier Transform”.
2. Next, your institution’s press office issues a press release. To make it sound fun, they come up with a snazzy title “Faster-than-fast Fourier transform”. Pretty neat, huh?
3. Finally, some news website picks it up and then, suddenly, it’s all about “a new way of calculating Fast Fourier Transforms”. Ta-da!
I think you’d all agree that it’s way better than Chinese whispers.
Sergey Ten commented, saying that the press release in question wasn’t too bad, and mentions the idea that “random” data from real-world measurements is usually spread around a manifold of lower dimension than the sample space, which I think is the idea behind the paper Barcodes: the persistent topology of data, which I linked to in my last Interesting Esoterica summation.
On a similar note, Nalini Joshi points out that it isn’t news when centuries-old maths is used to solve a new problem: http://www.physorg.com/news/2012-03-combining-centuries-old-mathematical-theorems-efficient.html
Update: Rongmin’s original post is hidden to the public, so I’ve pasted it in here. I hope the limited visibility was a side-effect of the way Google+ works and not a deliberate decision to restrict the post’s audience.