Graph Isomorphism panto: oh no it isn’t; oh yes it is!

As we reported back in November 2015, László Babai came up with an algorithm to decide if two graphs are isomorphic in quasipolynomial time. At the time, this proof still needed peer review, and in the last week or so, two big developments have occurred on that front.

On Wednesday 4th January, an error was discovered in the proof. Harald Helfgott (of the University of Göttingen in Germany and France’s National Center for Scientific Research), who studied the paper for several months, discovered that the algorithm was not quasipolynomial ($\displaystyle{ 2^{\mathrm{O}((\log n)^{c})} }$ for some fixed $c>0$) as claimed, but merely subexponenential: growing faster than a polynomial but still significantly slower than exponential growth).

Adorably, Babai posted this message on his website:

I apologize to those who were drawn to my lectures on this subject solely because of the quasipolynomial claim, prematurely magnified on the internet in spite of my disclaimers. I believe those looking for an interesting combination of group theory, combinatorics, and algorithms need not feel disappointed.

But maths is all about the drama, so on Monday 9th January Babai announced a fix for the error, and it’s now back on the quasipolynomial table. This has now been confirmed (as of 14th Jan) by Harald Helfgott himself at the Bourbaki seminar in Paris. Amusingly, Helfgott had only been studying the paper in such detail in order to give the seminar, and it was this close scrutiny which allowed him to discover the mistake.

More information

Announcement on Babai’s website

Fixing the UPCC Case of Split-or-Johnson – Babai’s paper detailing the fix (PDF)

Graph Isomorphism Vanquished — Again, at Quanta Magazine

Bourbaki Seminar – Harald Helfgott, on YouTube

Mathematical genius: extrapolate from your own experience?

The BBC biography series Great Lives covered in its most recent episode Srinivasa Ramanujan. In the closing minutes of the programme, host Matthew Paris said this, which I found quite interesting (or at least, interestingly expressed):

I’m so far from understanding the mind of a mathematical genius that it’s simply inconceivable that you could tell a person an apparently random number and he could intuit or deduce the kind of fact that he deduced about that taxi license number. I mean, I can’t run a four-minute mile, but I once ran a five-minute mile, and I can extrapolate from my own experience, in a way understand how someone might just be a lot better than me at something that, in an inferior way, I can also do. But Ramanujan isn’t like that. It’s as though this man were a different species, not just a superior example of the same species. Can you learn to do this kind of thing? Could I, if I had applied myself? Or is it that goddess again, is it really just genius?

Answers on a postcard!

Particularly mathematical New Year Honours 2017

Usually at this time of year, I have a look through the New Year Honours list for particularly mathematical appointments. Here are the names I’ve found that are particularly mathematical.

  • Tricia Dodd, Chief Methodology Officer, UK Statistics Authority, appointed MBE “for services to Statistics and Research”.
  • Dave Watson, director of IBM Research in the UK, who apparently has a focus on big data, appointed CBE “for services to Science and Engineering Research”.
  • Maggie Philbin, appointed OBE “for services to Promoting careers in STEM and Creative Industries”.
  • Anne-Marie Imafidon, co-founder and CEO of Stemettes, appointed MBE “for services to Young Women within STEM Sectors”.

I think every time I have done this (for New Year and Birthday Honours since 2013), there has been at least one person on the list, and usually several, specifically included for services to mathematics or mathematics education. This time, this is not the case, though there is one mention of statistics.

Are there any others I’ve missed? Please add any of interest in the comments below. A full list may be obtained from the UK Government website.

Call for submissions for Math Teachers at Play blog carnival

Readers of The Aperiodical are probably familiar with the Carnival of Mathematics, a monthly blog roundup which takes any maths-related content. Did you also know there is a related blog carnival called Math Teachers at Play?

The Math Teachers at Play (MTaP) blog carnival is a monthly collection of tips, tidbits, games, and activities for students and teachers of preschool through pre-college mathematics. We welcome entries from parents, students, teachers, homeschoolers, and just plain folks. If you like to learn new things and play around with ideas, you are sure to find something of interest.

I’ll be hosting the January 2017 edition of MTaP here at Travels in a Mathematical World. Of course, a blog carnival is only as good as its submissions, so if you join me in aspiring to the claim “you are sure to find something of interest” then please keep your eyes open for interesting blog posts and submit them to MTaP. Please submit posts you’ve enjoyed by others or yourself. Posts you wrote that are appropriate to the theme are strongly encouraged. Submit through the MTaP submission form, leave a comment here or tweet me. Thank you!

Submissions are open now, and anything received by Friday 20th January 2017 will be considered for the edition hosted here.