Marcus du Sautoy has this week presented to the world the physics of Eric Weinstein. ‘Geometric Unity’, apparently, argues “that the seemingly baroque features of the standard model of particle physics are in fact inexorable and geometrically natural when generalizations of the Yang-Mills and Dirac theories are unified with one of general relativity”.
Apparently, du Sautoy and Weinstein were postdocs together in the 1990s. Weinstein is a mathematical physicist turned economist who has been working on his these ideas privately for 20 years. Two years ago, he started to explain his thoughts to Marcus in a bar in New York.
Harald Helfgott has announced a proof of the odd Goldbach conjecture (also known as the ternary or weak Goldbach conjecture). This is big news. Like a good maths newshound, Christian Perfect promptly wrote this up for The Aperiodical as “All odd integers greater than 7 are the sum of three odd primes!”
Wait, though, there’s a problem. As Relinde Jurrius pointed out on Twitter, the formulation used in the paper abstract was not quite the same.
The ternary Goldbach conjecture, or three-primes problem, asserts that every odd integer $N$ greater than $5$ is the sum of three primes. The present paper proves this conjecture.
The version Christian used makes the assertion using odd primes, whereas the paper abstract only claims “the sum of three primes”. The latter version includes $7$ because $7$ can be written as the sum of three primes, but not odd ones ($7 = 3+2+2$). Certainly, you can see both statements of the weak Goldbach conjecture used (for example, here’s the $\gt 5$ version and here’s the $\gt 7$ version). Are they equivalent?
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.
I have a new toy. ‘Ox Blocks’ box promises “Noughts and Crosses with a novel twist”.
Kit Yates tweets to tell us that the second series of Dara O Briain: School of Hard Sums will be shown Wednesdays at 8pm from 1st May on Dave. Kit also makes this bold claim: “I set the problems so let me know if you have feedback”. Pedants, go! That’s @Kit_Yates_Maths on Twitter.
The following promo is available. I notice that YouTube commenter Vergast has left the following considered review: “This is a thing? Aweome!”
More information: Dara O Briain: School of Hard Sums on Dave.
Happy 25/4! On this day in history:
- in 1840 Siméon Poisson died :(
- in 1849 Felix Klein was born :)
- in 1903 Andre Kolmogorov was born :)
- in 2012 The Aperiodical launched! :D
So we’re a year old. Thanks for reading! Have a slice of cake:
To celebrate, CP has been hard at work redesigning the site. Hope you like it!