Math Chat: Mathematical Cognition & The $1,000,000 Math Problems

What is the nature of mathematical cognition or mathematics as a way of thinking? How did this faculty evolve in stone age humans? What selective advantage was conferred to early humans by mathematical cognition? Is the abstraction in mathematics built upon our language faculty? How is doing mathematics like a soap opera? Is mathematics like gossip?

What are the $1,000,000 Math Problems? We will discuss all seven of them: the Riemann Hypothesis, P vs NP Problem, Navier-Stokes Equation, the Poincaré Conjecture, the Birch and Swinnerton-Dyer Conjecture, the Hodge Conjecture, and Yang-Mills and Mass Gap. Help us and we'll split the $1,000,000 with you!

Our Math Chat topic this month is based on the 2 hour Keith Devlin video below. Read CJ's notes on Devlin's lecture (https://plus.google.com/104222466367230914966/posts/PTWAJBRzjRJ).

http://www.youtube.com/watch?v=NnVubBrATIU

Supplementary resources on the $1,000,000 Math Problems. These are optional resources for anyone interested in learning more about these problems.

• The Riemann Hypothesis (http://www.claymath.org/millenium-problems/riemann-hypothesis): Description of the problem (http://www.claymath.org/sites/default/files/official_problem_description.pdf), Paper on the problem (http://www.claymath.org/sites/default/files/sarnak_rh_0.pdf), Video Lecture by Jeff Vaaler (http://claymath.msri.org/riemannhypothesis.mov).

• P vs NP Problem (http://www.claymath.org/millenium-problems/p-vs-np-problem): Description of the problem (http://www.claymath.org/sites/default/files/pvsnp.pdf), Ian Stewart's "Minesweeper" article on the problem (http://www.claymath.org/sites/default/files/minesweeper.pdf), Video Lecture by Vijaya Ramachandran (http://claymath.msri.org/pversusnp.mov).

• Navier-Stokes Equation (http://www.claymath.org/millenium-problems/navier%E2%80%93stokes-equation): Description of the problem (http://www.claymath.org/sites/default/files/navierstokes.pdf), Video Lecture by Luis Cafarelli (http://claymath.msri.org/navierstokes.mov).

• The Poincaré Conjecture (http://www.claymath.org/millenium-problems/poincar%C3%A9-conjecture): Description of the problem (http://www.claymath.org/sites/default/files/poincare.pdf), News Release of the solution (http://www.claymath.org/sites/default/files/millenniumprizefull.pdf), more resources about Perelman's solution (http://www.claymath.org/millennium-problems-poincar%C3%A9-conjecture/perelmans-solution).

• The Birch and Swinnerton-Dyer Conjecture (http://www.claymath.org/millenium-problems/birch-and-swinnerton-dyer-conjecture): Description of the problem (http://www.claymath.org/sites/default/files/birchswin.pdf).

• The Hodge Conjecture (http://www.claymath.org/millenium-problems/hodge-conjecture): Description of the problem (http://www.claymath.org/sites/default/files/hodge.pdf), Video Lecture by Dan Freed (http://claymath.msri.org/hodgeconjecture.mov).

• Yang-Mills and Mass Gap (http://www.claymath.org/millenium-problems/yang%E2%80%93mills-and-mass-gap): Description of the problem (http://www.claymath.org/sites/default/files/yangmills.pdf), Report on the status of the problem by Michael Douglas (http://www.claymath.org/sites/default/files/ym2.pdf), Video Lecture by Lorenzo Sadun (http://claymath.msri.org/yangmillsexistence.mov).