# 2015: A Year in Maths

Although we are well into the first month of 2016, I thought for today’s post I would look back on the top stories of maths in the media during 2015.

John Nash

On May 23rd 2015 – a day after receiving the 2015 Abel Prize in Oslo for his work with Louis Nirenberg on nonlinear partial differential equations and its applications to geometric analysis – he and his wife, Alicia, died in a car accident in New Jersey as they were returning home.

His most notable achievement was winning the Nobel Prize in Economic Sciences in 1994 with game theorists Reinhard Selten and John Harsanyi. However, in 1959, he began developing a mental illness: paranoid schizophrenia. His struggles with his illness and recovery were detailed in the book and Academy Award winning film ‘A Beautiful Mind’.

Pentagonal Tiling Discovery

Casey Mann, Jennifer McLoud and David Von Derau are researchers at the University of Washington Bothell. In 2015 they found a new pentagon that tiles the plane.

Pentagons, in general, are of huge mathematical interest as the are the only ‘-gons’ that are not fully understood. Tiling has great applications to packing problems and these discoveries could aid in increasing efficiency.

The 56th International Mathematics Olympiad (IMO) was held last summer in Chiang Mai, Thailand. IMO scores are based on the number of points scored by individual team members on six problems, which are taken in sets of three in 4 and a half hour sessions over two days. The US team, who finished first, had a combined scored of 185, which just edged out the China team’s score of 181 and the Republic of Korea’s third place score of 161.

Terrence Tao

With a regularly updated blog and praises from journalists such as Gareth Cook in a profile written in The New York Times Magazine, Terrence Tao is currently one of the most famous mathematicians. His work on the twin primes conjecture and the stability of solutions to the Navier-Stokes equations in particular this year have been tremendous, not to mention his proposal of a solution to the Erdos Discrepancy Problem.

Graph Isomorphism Problem

This is a problem on deciding whether two graphs (as pictured below) are isomorphic.

It has been a special problem in complexity theory and there has been great advancement on it this year. László Babai of the University of Chicago submitted a paper in which he described his new work, which suggests that solving the problem takes slightly longer than polynomial time: quasi-polynomial time. This could have implications on the P vs. NP problem and has been recognised as an enormous advance in the field.

Number Theory Discovery

Yitang Zhang, a solitary part-time calculus teacher at the University of New Hampshire, was able to show that there are an infinite number of primes that are a fixed distance apart. Decreasing this distance down to 2 would prove the Twin Primes conjecture. The Polymath Project was started by Tim Gowers and was able to lower the bound on the gap established by Zhang. Further progress has been made by mathematicians such as Terrence Tao, however the conjecture remains unsolved.

2016 Breakthrough Prize

Ian Agol, who is a mathematics professor at the University of California, Berkeley, has received the 2016 Breakthrough Prize for his “spectacular contributions to low dimensional topology and geometric group theory, including work on the solutions of the tameness, virtual Haken and virtual fibering conjectures.”

The Breakthrough prize, which includes a \$3 million dollar award, was founded by Mark Zukerberg and aims to celebrate and recognise outstanding scientists. One of the ways this is done is by generating media coverage through a spectacular televised Hollywood-like award ceremony, broadcasted in the US on the Discovery Channel and Science Channel.

Let me know what your favourite news story in 2015 was! M x