In Quanta Erica Klarreich recently wrote up Yaroslav Shitov’s new counter example which disproves Stephen Hedetniemi’s 50 year old conjecture, original dissertation, that the number of colors required to color the tensor product of two graphs is the lesser of the numbers used to color the original graphs. These colorings have applications in areas from scheduling to seating plans, and it is clear from Klarreich’s reporting that mathematicians are excited about this result. In fact, Hedetniemi responded very positively when asked by Klarreich about the counter example, saying it “has a certain elegance, simplicity and definitive quality to it.” The counter-example may show Hedetniemi’s conjecture is not true, but Klarreich points out that we do not yet know just how false it is. So, while Shitov has closed one door on this problem, there are still many which are open.
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Following 2013’s amazing bounded gaps between primes result, mathematician Yitang Zhang has gone from an unknown maths lecturer to a mathematical celebrity. The Mathematical Research Sciences Institute at Berkeley has put together a film telling the story of Zhang’s proof, and his life before and after the announcement.
The film, which was funded by the Simons Foundation, has contributions from a large number of mathematicians, including Daniel Goldston, Kannan Soundararajan, Andrew Granville, Peter Sarnak, Enrico Bombieri, James Maynard (based at Oxford, who did further work to reduce the prime gap following on from Zhang’s), Nicholas Katz, David Eisenbud, Ken Ribet, and Aperiodihero Terry Tao, as well as Zhang himself.