Mathematics, in fact all of science, is not done in a vacuum. All the work that is done today builds off of the work of generations of thinkers, inventors, and researchers. When a mathematician decides to shuck off the yoke of previous work they find themselves staring up from a hole that might as well go all the way to the center of the earth. One of the classic examples of this is the work Principia Mathematica by Bertrand Russel and Albert North Whitehead where they decided to tear down mathematics and build it back up from a foundation centered only upon the most elementary of logic. The Principia was never finished, in fact not two decades later it was proven that such a treatment of the subject could not be done, they ended up using the first 362 pages to prove the statement 1+1=2. Of course mathematicians can also find themselves indebted to someone well outside of their field. A wonderful example of this is the work of Duncan Watts and Steve Strogatz on the topic of Small World Networks which all started because Watts remembered his father once telling him that everyone is separated by only six handshakes, and idea popularized in 1929 by Frigyes Karinthy in his short story Chains.

This debt to what has come before is treated very differently by mathematicians, and while few would completely disavow what they owe none take it more seriously than Grigori Perelman. A Russian mathematician, Perelman gained international renown in November 26 for his proof of the Poincaré conjecture, one of the Clay Mathematics Millennium Problems which have a million dollar bounty on their solutions, which had stood unsolved since 1904. This work was so important and groundbreaking that in 2006 they earned Perelman the highest award that a mathematician can earn, a Fields Medal. An award that, with a mind at least partially thinking of the debt to the mathematical community that comes with accepting such a high honor, Perelman declined, citing that he did not want to displayed like a zoo animal. This was only the first award that Perelman declined, he also turned down the million dollar Millennium Prize bounty and this time his refusal was clearly to deal with debt. Perelman’s proof of the Poincaré conjecture came from following what is known as the Hamilton program, essentially a plan for producing a solution to the conjecture that was developed by American mathematician Richard Hamilton. Perelman thought that it was unjust that he alone was getting all of the accolades, and prizes, for the work and Richard Hamilton, a man to whom Perleman clearly feels a great debt, was languishing on the sidelines. There is hope that Perelman’s thoughts about the unjust nature of the mathematical community, which have cause him to withdraw from the community, may still be assuaged as Richard Hamilton was a co-award winner of the Shaw prize for the work he did towards the proof.

While Perelman’s empathy towards those whose work he used as stepping stool to new results is unusual, it is illustrative of just how important previous work is to those who really notice.

Yesterday Benoit Mandelbrot, one of the most important and influential mathematicians of the past century passed away. Sadly I do not know much about the life and work of mandelbrot with the obvious exception of the Mandelbrot Set. This video by Pisut Wisessing for the Jonathon Coulton song is a wonderful send off though.

The Nature of Things / Martin Gardner from Wagner Brenner on Vimeo.

Alex Bellos author of Alice’s Adventures in Numberland and twitterer extraordinaire has posted up this video illustrating a wonderful visual method of multiplying numbers. I had not heard of this method but I might just start to use it for large numbers.  (via maanow)

Make sure to check out the rest of the videos on Knill’s site, got even one more link in right here, to see just what we missed.

Watch Marcus Dusautoy and other discuss Zero and Infinity. The more great maths videos and articles that come from England the more I want to be a part of that scene.

In this podcast:

• Tom and Nick are not as happy with Pi Day as you’d expect.
• Why do Hippies like Pi so much?
• Where does pi come from, and why do we care?
• Is mounting a Ferris Wheel on a Flat-Bed Truck a good idea?
• How many digits of pi can YOU recite?  I’ll bet not 69,000!
• Nick and Tom give you back 23 hours and 40 minutes of your life … ish

Math for Primates Blog Post