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Hedetniemi’s Conjecture in graph theory disproved

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.

via Thomas Lin on Twitter.

One Mathematically Gifted and Black person every day this Black History Month

February is Black History Month in the USA, so the website Mathematically Gifted and Black is honouring a different black mathematician each day in February, for the third year.

Gerrymandering Gives Mathematics’s Moon a Day in the Sun

If you pay attention to United States politics you have probably noticed that mathematics is currently enjoying a rare moment of relevance. You probably also know this is not happening because all of a sudden politicians have decided that mathematics is clearly the coolest thing in the world, even though it clearly is, but instead because gerrymandering has become one of the major issues du jour.

Robert Schneider, Mathematical Musician/Musical Mathematician

(This article is based on an interview that was originally conducted for the podcast Relatively Prime)

Robert Schneider is a rock star mathematician. I do not mean that in the metaphorical sense, as when it is applied, with a rather unmathematical lack of precision, to celebrity mathematicians such as Terry Tao, Cedric Villani, or Timothy Gowers. I mean it in the most literal sense: Robert Schneider is a mathematician and Robert Schneider is a rock star.

Relatively Prime, All in a Name

“Prime. Prime? Prime! Prime factors, twin primes, pseudo-primes? No, no no. Relatively Prime? Yes, Relatively Prime.”

I have a problem, no matter how good an idea I have I can not start to work on it until I have a name. Some names are easy, Combination and Permutations was a name well before I ever had a show to use it, Science Sparring Society followed directly from the concept, and ACMEScience NEWS NOW actually told me what type of show I would be making. Other names are hard.

I had the underlying idea for Relatively Prime (get the first episode here) in an extreme bout of egotism and delusion of grandeur where I spent too long listening to Radio Lab, This American Life, and Snap Judgment and began to think, “Hey, I could do that, but for math.”

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