As well as being an excellent monthly pub-based meeting, MathsJam also has an annual conference, which takes place every November. Registration is now open for the 2013 conference, which takes place on 2^nd and 3^rd November.

MathsJam is an opportunity for like-minded self-confessed maths enthusiasts to get together in a pub and share stuff they like. Puzzles, games, problems, or just anything they think is cool or interesting. The annual conference is a weekend of lightning talks, where you can show or demonstrate something you want to share, followed by lengthy coffee breaks for conversation and socialising. And coffee.

Details about the conference, as well as the chance to register and secure your place, can be found at the MathsJam conference website.

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+

“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

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.

The twin primes conjecture states that there are infinitely numbers $n$ such that $n$ and $n+2$ are prime. David Roberts on Google+ refers to this as “to put it mildly, EXTREMELY HARD to prove”. An equivalent statement is that there are infinitely many primes $p$ and $q$ such that $|p-q|<3$, and this, says David, allows the production of weaker conjectures:

Conjecture($N$): there are infinitely many primes $p$ and $q$ such that $|p-q|<N$.

Anyway, according to a blog post by Peter Woit of Columbia University, who apparently got an email announcing it, there is a seminar today at Harvard at 3pm local time, in which “Yitang Zhang will present new results on ‘Bounded gaps between primes’”. Peter says that Zhang claims a proof of Conjecture($70,\!000,\!000$), that is: there are infinitely many primes $p$ and $q$ such that $|p-q|<70,\!000,\!000$.

We await further news.

Source: Peter Woit’s post announcing the seminar: Number Theory News.

via David Roberts on Google+

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.

via Haggis the Sheep on Twitter

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)

They’ve now announced that they’re additionally in search of images to illustrate the book, and are seeking submissions. Here’s an extract from their request for submissions.

Illustrations, photographs, computer simulations or even clever doodles — anything that’s colourful and inspirational. […] The idea is that these images should be able to stand alone, like pictures in an art gallery, with minimal explanation. They should ideally be approximately square or portrait style and sufficiently striking to be readable when reproduced at a size of approximately 10cm^2. You need to hold the copyright for the image. […] We also plan to reuse the best images (fully credited to you) in publicity for the IMA, especially its 50th Anniversary.

We’re assuming that here “10cm^2” means 10cm by 10cm, and not having an area of 10cm², meaning $\sqrt{10}$cm by $\sqrt{10}$cm. Submissions are to be emailed, in a low resolution format initially, to ima50@maths.cam.ac.uk by or before 12th May 2013, along with any appropriate explanation or attribution text, using the word IMAGE in the header.

The IMA is also holding a competition, open to all IMA members, for articles to go in the book. Details of their anniversary celebrations, and the competition, can be found on the IMA website.

More information

We want your maths images! at Plus Magazine

IMA 50th Anniversary

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.

• 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!

Today is Euler’s $-306 \times e^{i \pi}$^th birthday, and Google have chosen to celebrate (despite ignoring several other prominent mathematical birthdays, including Erdős’s centenary – see the @MathsHistory twitter feed for a full list) by creating a Google doodle on their homepage.

For anyone who isn’t aware, this is when Google changes the image above the search box on the homepage at Google.com, so it still says ‘Google’ but using an appropriate image, which sometimes has built-in interactive elements. I thought it was worth pointing out some of the fantastic maths they’ve included in today’s doodle.

In celebration of the Swiss mathmo’s achievements, the Google doodle today includes:

• The formula for the Euler characteristic, $V – E + F = 2$, which relates the number of vertices, edges and faces of a spherical polyhedron. The doodle also features some polyhedra (icosahedron and tetrahedron). The formula also applies to a diagram of vertices, edges and faces drawn on a flat plane, or on a sphere – and a similar one can be used for on other surfaces, by subtracting 2 from the right hand side for each hole in the object (so on a donut, $V – E + F = 0$).
• The famous ‘Seven bridges of Königsberg‘ problem, drawn as both the layout of bridges and a graph. Euler pioneered graph theory; an Eulerian graph is one which can be fully traversed starting from any point (equivalently, one where each node has an even number of arcs coming into it). Since the ‘bridges of Königsberg’ graph has an odd number of arcs coming into every node, it can’t be traversed from any start point – although if a graph has all even nodes apart from two, it’s called semi-Eulerian, and can be traversed only if you start at one odd node and end at the other.
• Euler’s identity, $-1 = e^{i \pi}$. This is often described as one of the most beautiful equations in mathematics – if you rewrite it as $e^{i \pi} + 1 = 0$, you have a relation involving five amazing constants (the additive and multiplicative identities, $0$ and $1$, plus the exponential constant $e$, circle constant $\pi$ and the imaginary number $i$) as well as all the major mathematical operations – addition, multiplication (between $i$ and $\pi$) and exponentiation. This relationship expresses nicely the connection between trigonometry and the exponential function, and it’s boss as heck.
• There’s also a geometrical interpretation of Euler’s formula, which shows how as the angle changes, the real and imaginary parts of the points on a circle in the complex plane change according to trigonometric functions.
• At the centre of the Google doodle is a three-dimensional representation of a sphere, which you can drag around and it will rotate in all three axes. Within the sphere you can see three orthogonal sections, creating a cross in each plane. Euler introduced the idea of Euler angles, to describe the orientation of a rigid body using an angle of rotation around each of the three Cartesian axes. This way of describing angles is widely used, from Euler’s time right through to modern day technology such as accelerometers – these are used in mobile computing devices and controllers to measure the position and motion in space of the object, which can be used to control the device (think Wiimotes, and tilty marble games on your phone, and then think of Euler and be grateful.)

Props to Google for popularising Euler’s amazing work, and for making such a lovely doodle! Also, Google, if you’re looking to employ someone to research and create amazing mathematical doodles like this in future, I’m totally available. Although I imagine there are enough Google employees interested enough in maths that they don’t have a problem there.