# Carnival of Mathematics 149

The next issue of the Carnival of Mathematics, rounding up blog posts from the month of August, and compiled by Mel, is now online at Just Maths.

The Carnival rounds up maths blog posts from all over the internet, including some from our own Aperiodical. See our Carnival of Mathematics page for more information.

# Scenes at a maths conference

We’re all trying to combat the stereotypes of mathematicians: we try our best to make our work accessible to the public; we wear clean clothes and make eye contact; some of us even had the good sense to be female. But sometimes, the woolly-headed mathematician of legend materialises in his pure form.

Here, in his own words, are a few things that happened at a conference recently attended by one of my friends.

# 919444¹⁰⁴⁸⁵⁷⁶ + 1 is prime

Distributed internet prime number search PrimeGrid has found a new largest generalised Fermat prime.

The discovery was made on 29th August, and was double-checked before being announced on 2nd September. PrimeGrid uses a distributed computing approach and uses spare computer time donated by volunteer computers connected to their network.

A generalised Fermat prime is a prime number of the form $a^{2^n} + 1$, with $a \gt 0$. It’s called ‘generalised’ because ‘Fermat prime’ is the name for the particular case $a=2$.

Much like Mersenne primes, there are special tests which make it much easier to check if a number of this form is prime than for a general number. For this reason, they’re a good place to look for new large primes.

Until now only 392 generalised Fermat primes had been found: this new discovery makes 393. At 6,253,210 digits long, it’s now the 12th largest of all known primes, and the second-largest known non-Mersenne prime.

PrimeGrid have put out an announcement in PDF format giving some more details about the search, and credits for the many people involved writing algorithms and providing computers to run them on.

The PrimeGrid homepage has more information about the many different prime number searches they run, and how to join in the search with your own PC.

# Maths at the British Science Festival

The British Science Festival is organised annually by the British Science Association, and this year it’s hosted by the University of Brighton and the University of Sussex from Tuesday 5 to Saturday 9 September. For more details and full listings, see the main British Science Festival website.

We’ve pulled out some of the mathematics-related events in the main programme – from theatre reproductions to puzzle workshops and plenty of talks and lectures, there’s something for everyone!

# London Mathematical Society launches Mathematical Sciences Directory

The London Mathematical Society yesterday launched its Mathematical Sciences Directory (LMS MSDirectory), a directory of mathematical scientists in the UK. Entries include some personal information, academic networks and social media, current employment and information on education/qualifications. Yes, it’s yet another place to list all this information.

The LMS website suggests a set of benefits for being on the list, including networking with others in UK mathematical sciences and the opportunity to contribute data anonymously to projects such as the Mathematical Sciences People Pipeline, which are used “to make representation to national policy-makers regarding the mathematical sciences”.

Those eligible to be listed include people with a maths degree from a UK institution, those currently working in mathematical sciences in the UK with or without a maths degree, and current students. You don’t have to be an LMS member to be on the list. The FAQ suggests the list was initially populated with data from “over 5,000 mathematicians” (though some may have opted-out before launch – they first emailed me in March asking me to check my data or opt-out) and people can opt to join.

# New YouTube videos by me and James Grime

I’ve been at it again, making videos for that YouTube – this time, a collabo with James Grime. We have each posted a video on the topic of a mathematical game, as we both had things we wanted to make videos about but nobody to play with, so we met up after school and made some YouTubes.

My video features two games which *SPOILER* turn out to have maths in them. I’m also doing a bit of a giveaway on Twitter, where you can win the actual cards used in the video (I will post them out in the IRL post mail), so reply to this tweet if you want a chance to win:

James has also posted his video, which is about a different game:

# 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)