Wednesday, December 04, 2013

For Fellow Mathurbators

  1. Courtesy Wired, exciting new developments on the Twin Prime Conjecture front. The classic tale of the loner mathematician, Yitang Zhang, who despite a long history of being ignored and savagely underemployed (he worked in a Subway sandwich shop for a while) makes astonishing advances by putting a finite bound on the separation of successive primes, thereby bringing down the gap between successive primes from infinity to 70 million! This puts the ball rolling and teams of number theorists worldwide (led by the obscenely brilliant Terence Tao) begin a race to bring the gap down. Within months the gap has been shortened significantly and mathematicians are rejoicing until another outsider, a non-participant of the group project (whose progress is being chronicled here in Terence Tao's blog's Polymath project) - a postdoc from U Montreal, James Maynard - brings the gap down to a stunning 600! This very exciting, fast-paced, wonderful math reporting reads like a thriller and offers plenty of commentary on the two schools of doing math - "the lone wolves" as exemplified by those like Yitang Zhang and James Maynard (and also by Grigori Perelman and Shinichi Mochizuki); contrasted with the "workman's way" exhibited by those like the more mainstream genius Terence Tao. Heady, fabulous stuff! Read the full story here: Sudden Progress on Prime Number Problem Has Mathematicians Buzzing.
  2. From the Scientific American, dispute over two possible alternative extensions of axiomatic set theory (the ZFC: Zermelo Fraenkel Set Theory with the Axiom of Choice). Set theorists are fighting over which appendages are more appropriate - Forcing Axioms - that will disprove the Continuum Hypothesis (the hypothesis that there is no infinity "between" that of the natural numbers and that of the real numbers); and the Inner-Model Axiom - that will validate it. Critics of the Inner-Model axiom posit that it restricts the kind of multifarious infinities that may otherwise exist and that holding on to the Continuum Hypothesis may be too high a price to pay for future mathematical growth. Their opponents claim that Forcing Axioms are ugly, inelegant and workmanlike. Which one will survive? And what would it mean for tomorrow's Mathematics?  The future is pregnant with exciting possibilities! An excellent read: Dispute Over Infinity Divides Mathematicians.

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