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All odd integers greater than 7 are the sum of three odd primes!

By Christian Lawson-Perfect. Posted May 14, 2013

It seems that big mathematical advances are like buses – you wait ages for one, and then two come along at once. Also revealed yesterday was a proof of the odd Goldbach conjecture: that all odd numbers greater than 7 can be written as the sum of exactly three odd primes. The proof is contained in Major arcs for Goldbach’s theorem, a paper submitted to the arXiv by Harald Helfgott, who’s a mathematician at the École Normale Supérieure in Paris. This new paper completes the work started in Helfgott’s previous paper, Minor arcs for Golbach’s problem, published last year.

The strong Goldbach conjecture states that every even number can be written as the sum of two primes. This is still unproven, and remains one of the long-standing unproven results in number theory. Sadly, it’s the opinion of Terence Tao, among others, that the method used to prove the weak conjecture probably won’t work on the strong conjecture.

The paper: Major arcs for Goldbach’s theorem by Harald Helfgott

via Terry Tao on Google+

Primes really do stick together

By Christian Lawson-Perfect. Posted May 14, 2013



“The author has succeeded to prove a landmark theorem in the distribution of prime numbers. … We are very happy to strongly recommend acceptance of the paper for publication in the Annals.”

According to the Nature News blog, at yesterday’s seminar given by Yitang Zhang it was revealed that his proof that there are infinitely many pairs of primes less than seventy million apart has already been refereed for the Annals of Mathematics; that’s a quote from the referee’s report above.

It seems the proof doesn’t use any unconventional machinery (in contrast to Mochizuki’s Proof from Planet 9 of the abc conjecture) and is fairly uncontroversial. How pleasant! Of course, someone might find a problem with it once it’s publicly available, but that’s the way for all things.

Source: First proof that infinitely many prime numbers come in pairs at Nature News

Primes gotta stick together

By Christian Lawson-Perfect and Peter Rowlett. Posted May 13, 2013

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.

All Squared, Number 5: Favourite maths books (part 1)

By Christian Lawson-Perfect and Katie Steckles. Posted May 11, 2013



Good maths books are simultaneously plentiful and rare. While there are a few classics almost everyone knows about and has copies of (Gardner, Hardy, etc.), the trade in lesser-known maths books is considerably less well-organised. Very few bookshops have well-stocked maths sections, and insipid pop maths books dominate. Unless you hear about a good maths book through word of mouth, you’ll often only encounter it once it’s ended up in a second-hand bookshop, usually a refugee from an emptied maths department library.

But books, more than anything else, are where the beauty of maths really manifests itself. It’s where ideas are presented most clearly, after they’ve had time to percolate through a few more brains. We talked to David Singmaster, professor of maths and metagrobologist, about his favourite maths books.



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Random walks on slides

By Christian Lawson-Perfect. Posted May 10, 2013

Some grad students at Carnegie Mellon had a fun idea: what if each slide in a presentation was made by a different person, based only on the previous slide?

Being grad students and thus having nothing better to be getting on with, they did just that, and nominated one of their number to deliver the resulting presentation without having seen any of the slides in advance.

Watch the video below. Prepare to hear lots of nerdy giggling.

[youtube url=https://www.youtube.com/watch?v=XIz1XcPpcx4]

via Haggis the Sheep on Twitter

abc: the story so far

By Christian Lawson-Perfect. Posted May 10, 2013

You should take some time to read this very well-written piece about Shin Mochizuki’s claimed proof of the abc conjecture: “The Paradox of the Proof”, by Caroline Chen.

It covers the story from all angles: a biog of Mochizuki, a clear, non-nonsense description of the conjecture, the tale of the mathematical community’s attempts to understand it, and some insightful rumination on the nature of proof.

via Marcus du Sautoy on Twitter, among others

(TL;DR – still nobody knows whether the proof is correct or not)

Art for a maths department

By Christian Lawson-Perfect. Posted April 29, 2013



I don’t think the university maths department I work in has enough art in it. I have gazed covetously upon the walls of other departments I visit, covered with beautiful mathematically-inspired paintings and inspirational posters, serving as a backdrop to cabinets full of geometrical curiosities. I recently suggested to our Head of School that we could buy some art, and he said “That’s a good idea. Send me some suggestions.”

I was pretty delighted with that response, so I spent an enjoyable hour trawling the internet for art that would inspire and enrich our students and staff. We don’t really have anywhere obvious to put sculptures, so I wanted something you can hang on a wall. I had no idea how much money the Head of School was thinking of spending, so I assumed the worst and tried to stick to cheap posters and prints as a starting point. I wasn’t just looking for art – anything to decorate the walls, even if it ends up teaching the students something, is desirable.

My first port of call was my Arty Maths blog. I’ve been collecting nice bits of art that invoke or involve maths (and not art created purely to represent maths) for almost two years now. Unfortunately, it turns out I’ve almost exclusively been collecting sculptures and video works. That meant I had to do some googling!

Because I found some nice things, and in case anyone else is tasked with decorating a maths department and needs ideas, here’s what I found: