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P might not be NP, reckons Norbert Blum

Norbert Blum of Universität Bonn has uploaded to the arXiv a preprint of a paper claiming to resolve the problem of whether $\mathrm{P} = \mathrm{NP}$, in the negative.

“Proofs” one way or the other turn up on the arXiv pretty much every day, but this one might actually be correct. At least, it’s not immediately obvious it isn’t.

Here’s the abstract:

Berg and Ulfberg and Amano and Maruoka have used CNF-DNF-approximators to prove exponential lower bounds for the monotone network complexity of the clique function and of Andreev’s function. We show that these approximators can be used to prove the same lower bound for their non-monotone network complexity. This implies $\mathrm{P} \neq \mathrm{NP}$.

John Baez has very quickly put together a post explaining the very basics of Blum’s argument.  Even more briefly, Blum claims to have shown that the best-case complexity of a function solving the clique decision problem is exponential, not polynomial.

Colin Wright reckons that the proof passes all of Scott Aaronson’s immediate ‘sniff tests’ for a claimed proof of a big problem, and his supplementary list for proofs to do with P versus NP. Those help you spot charlatans and Walter Mitty types, rather than looking at the actual mathematical content.

Obviously, none of us are qualified to even offer a hot take on this, so we’ll all have to wait until more experienced sorts have had a good look.

So, watch this space.

(Personally, my money is on this not quite working, purely based on my natural pessimism)

Subscript: We’re trying out a new shorter post format

We don’t have lots of time to write in-depth posts about maths news any more, what with having jobs and families to attend to, so we’ve set up this new Subscripts format for when we’ve seen a thing and want to share it but don’t have time to do any more than that.

That’s all!

Algebraic Combinatorics ditches Springer

The editorial board of the Journal of Algebraic Combinatorics have announced they’re leaving Springer and setting up a new journal called Algebraic Combinatorics. The new journal will follow the principles of Fair OA – the key points are that the journal will be free to read, fees will be low, and acceptance won’t depend on ability to pay.

Hugh Thomas, one of the editors of Algebraic Combinatorics, said of the move,

“There wasn’t a particular crisis. It has been becoming more and more clear that commercial journal publishers are charging high subscription fees and high Article Processing Charges (APCs), profiting from the volunteer labour of the academic community, and adding little value. It is getting easier and easier to automate the things that they once took care of. The actual printing and distribution of paper copies is also much less important than it has been in the past; this is something which we have decided we can do without.”

Another victory for fair and sensible maths publishing, brought about by a small group of OA advocates set up by Mark Wilson and including Timothy Gowers. There’s much more about what’s happened and why you should support the new journal on Gowers’s weblog.

Algebraic Combinatorics lives at algebraic-combinatorics.org (can you believe that was available?!)

2017 LMS prize winners announced

The London Mathematical Society has announced the winners of its various prizes and medals for this year.

Here’s a summary of the more senior prizes:

  • Alex Wilkie gets the Pólya prize for “his profound contributions to model theory and to its connections with real analytic geometry.”
  • Peter Cameron gets a Senior Whitehead prize for “his exceptional research contributions across combinatorics and group theory.” Peter has written a rare horn-tooting post on his excellent blog about winning the prize.
  • Alison Etheridge gets a Senior Anne Bennett prize “in recognition of her outstanding research on measure-valued stochastic processes and applications to population biology; and for her impressive leadership and service to the profession.”
  • John King gets a Naylor prize for “his profound contributions to the theory of nonlinear PDEs and applied mathematical modelling.”

The Berwick prize goes to Kevin Costello, and Whitehead prizes go to  Julia Gog, András Máthé, Ashley Montanaro, Oscar Randal-Williams, Jack Thorne, and Michael Wemyss.

Read the full announcement at the LMS website.

Laws of mathematics not as immutable as we thought, in Australia

Australian PM Malcolm Turnbull said, as part of a speech proposing a law to force tech companies to give the government access to encrypted messages,

“The laws of mathematics are very commendable, but the only law that applies in Australia is the law of Australia.”

The problem is that the end-to-end encryption schemes used by messaging apps make it practically impossible for the makers of the app to read messages, even if they really want to.

New Scientist writer Jacob Aron has seen the positive side of Turnbull’s comments:

The curious mathmo talks to David Roberts

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.