From the Simpsons to black holes: fascinating forays into Further Mathematics

Twenty-three Year 12 pupils studying Further Mathematics learned from some of the country's most entertaining mathematicians at a festival for schools.

Maths Fest 2017 at The Camden Centre, which was organised by ‘stand-up mathematician’ Matt Parker and Mathematics author Rob Eastaway, looked at how Mathematics is being used across a hugely diverse range of fields.

QE sixth-former Karnan Sembian said: "The trip was useful in illustrating the hidden applications of Maths, from coding messages in wars to computer graphic simulations to cartoons to theme park rides."

The festival speakers included:

• Simon Singh, author and broadcaster, who spoke on the Mathematics in The Simpsons TV programme
• Eugenie von Tunzelmann, visual effects artist, who displayed computer graphics that she had used in the film, Interstellar, and in her theme park work
• James Grime, internet Mathematics personality, whose session looked at coding and how the alphabet can be expressed in binary and then coded and decoded. He spoke on the World War II Lorenz cipher machine, which was more difficult to 'crack' than the more famous Enigma machine, and examined how a particular message can be distinguished from all the others that are 'floating around'
• Katie Steckles, Mathematics speaker and puzzle-maker, led an interactive session, with pupils trying to solve puzzles. She also spoke about some number theory problems, such as the Collatz conjecture on hailstone numbers, which appear simple but are yet to be solved.

The QE boys were accompanied by Mathematics teachers Jillian Simms and Gregory Lee.

"Eugenie von Tunzelmann's graphics were amazing and the thing that was really interesting was she actually showed the paper notes revealing the maths she had used to work out the trajectory of the light rays bending around a black hole – lots of matrices and complex numbers!" said Mrs Simms.

"My favourite session, though, was Simon Singh's: I love the idea that some really hard maths is hidden in the Simpsons stories, such as the fact that the weight of the Higgs Boson was predicted in the programme 12 years before the particle was actually found."

The festival included Maths Slam, in which students gave prepared presentations in under five minutes on topics including: Fibonacci numbers and astrology; the binary and duodecimal system, and the irrationality of the proof of root 2.

Another highlight of the day was the UK final of Who wants to be a mathematician? in which the finalists had to answer questions put to them on stage by Matt Parker.

Pupil Hariish Paveendran said: "It was a fascinating day out; I especially enjoyed learning about the use of computer graphics in films," while Abhijeet Vakil added: "It gave me a greater understanding of the working behind the Mathematics we learn."

Two Mathematics conundrums, from Katie Steckles’ session:

• The Collatz conjecture on hailstone numbers involves taking a positive integer and then, if it is even, dividing it by 2, and, if odd, multiplying by 3 and adding 1. If the process is repeated, a cycle of 4, 2 and 1 occurs: for example, 16 … 8 … 4 … 2 … 1. But, the boys were asked, how do we know if it always ends up in such a cycle and how do we know there is not another cycle
• The pancake-sorting problem, with which she ended her session, begins with a disordered stack of different-sized pancakes, where the challenge is to sort out the pancakes into size order with a spatula. A spatula can be inserted at any point in the stack and used to flip all the pancakes above it. The pupils learned that for a stack of three pancakes, all of different sizes, it can be demonstrated that the minimum number of flips required can vary between 0 and 3, depending on the arrangement of the pancakes in the stack. However, for a stack of 20 pancakes, no one has yet been able to find the maximum number of flips that could be required!