Copyright: MFO
Here’s a small collection of links to articles about Alexandre Grothendieck, French/German mathematician and algebraic geometer, who died on Wednesday 13 November aged 86. He was a pioneer in the field, and has been described as ‘the greatest mathematician of the 20th century’.
The Great Internet Mersenne Prime Search, the premier distributed-computing prime finding initiative, has reported that $M_{32582657} = 2^{32,582,657}-1$, the 44th Mersenne prime to be discovered, is also the 44th Mersenne Prime in numerical order. It was found by Steven Boone and Curtis Cooper in 2006 (Cooper also discovered the current largest prime as reported here in February), but until now it was not known for certain that other, smaller primes had not been overlooked. GIMPS has now checked all the intervening Mersenne numbers for primality and having found nothing, $M_{32582657}$ is secure in its 44th-ness.
The Great Internet Mersenne Prime Search (announcement on the front page as of November 10)
Their page for the prime itself
Mersenne Prime at Wolfram Mathworld
via @mathupdate on Twitter
Friend of the Aperiodical Samuel Hansen has launched a Kickstarter to fund a second series of his maths podcast Relatively Prime. The first series was successfully funded in 2011 and consisted of eight hour-long episodes telling “stories from the mathematical domain”, including interviews with Tim Gowers, Matt Parker, David Spiegelhalter and more.
The big news last year was the quest to find a lower bound for the gap between pairs of large primes, started by Yitang Zhang and carried on chiefly by Terry Tao and the fresh-faced James Maynard.
Now that progress on the twin prime conjecture has slowed down, they’ve both turned their attentions toward the opposite question: what’s the biggest gap between subsequent small primes?
Jordan Ellenberg is an algebraic geometer at the University of Wisconsin and a blogger at Slate. His book How Not To Be Wrong was new when he sent The Aperiodical a copy to review ages ago.
Group theorists, often interested principally in the abstract, have been known to neglect the vital importance of producing funky gizmos that exhibit the symmetries they have theorized about. Internet maths celeb Vi Hart, working with mathematician Henry Segerman, has addressed this absence in the case of $Q_8$, the quaternion group. The object they’ve designed is four-dimensional and made of monkeys, and they’ve done the closest thing possible to making one, which is to 3D-print an embedding of it into our three-dimensional universe, also made of monkeys. Their ArXiv preprint (pdf) is well worth a read, and when you get to the photos of the resulting sculpture (entitled “More fun than a hypercube of monkeys”), you’ll fall off your chair.
The Quaternion Group as a Symmetry Group by Vi Hart and Henry Segerman, on the ArXiv.
Nothing Is More Fun than a Hypercube of Monkeys at Roots of Unity, including an animated gif of a virtual version of the sculpture rotating through 4D-space.
Every year, the Eurovision Song Contest brings with it fresh accusations that the results are affected more by politics than music. But how much of the outcome is in fact determined by mathematics?