Monday, September 24, 2018

Atiyah's proposed proof of the Riemann Hypothesis

 

After much anticipation, M. Atiyah unveils his proposed proof of the Riemann hypothesis.  It depends on an interesting function called the Todd function.  His approach of course still must be properly evaluated and time will reveal if all assumptions are sensible.

Update: Sir M. Atiyah has passed on January 11, 2019.  He leaves a brilliant mathematical legacy behind, and a spirit of inquiry even E. Witten admired.


Wednesday, March 14, 2018

Hawking's Legacy

















On this 14th day of March, 2018, the world honors Stephen Hawking as an extraordinary scientist, teacher and futurist.  From A Brief History of Time to The Universe in a Nutshell, it is clear Hawking's deepest fascination has been the quest for a unified theory of physics.  In particular, Hawking was anticipating the completion of M-theory.

When can we expect the completion of M-theory?  Is it really an 11-dimensional completion of 11D supergravity and 10D superstring theory?  Or is it much more?  Ed Witten once mused, "String theory is 21st century physics that fell accidentally into the 20th century."  So the joke continues, in that 22nd century mathematics is needed to solve M-theory.  Might M stand for motive?  Time will tell.