Wednesday, 8 November 2017

Looking forward to MathsJam

With only three days to go till the MathsJam Gathering - the best weekend of the year, I've been thinking of some of my favourite MathsJam discoveries. Sticking to pure mathematics, here are my memories of three gems.  I could have chosen many others, but perhaps because these happen to relate to my current teaching, and I showed two of them to my graph theory students immediately upon my return from the gathering, they are the first that come to mind.  Since I believe all MathsJam presentations are available online, further details should be readily available. 

  • Colin Wright's amazing talk on graph colouring, which started by asking us to complete a partially-completed 3-colouring of a small graph, and turned into a more-or-less complete proof, within a 5-minute talk, that there is no polynomial-time algorithm for 3-colouring a graph.
  • Ross Atkins's talk about Braess's Paradox - a simple situation in which adding an extra road to a network, with no increase in traffic, results in longer average journey times.  I should have known about this counter-intuitive result so I'm very glad to have found out about it, and especially with the wonderful demonstration with a network of springs that showed a mechanical realisation of the paradox.
  • David Bedford's "What's my polynomial?"  I love this because it is arguably what the late Raymond Smullyan called a "monkey trick".  David asked you to think of a polynomial p(x) with non-negative integer coefficients, and, for a single value of x of your choice, greater than any of the coefficients, tell him both x and p(x).  He would then tell you your polynomial.  Knowing that one needs n values to determine a polynomial of degree n, I was taken in by this!

I could have chosen many more examples: I'm certainly not ranking these presentations or any others. On another day I might have chosen a completely different set!  But I'm certainly looking forward to coming across more wonderful mathematics this weekend!

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