You are currently browsing the monthly archive for August 2012.

I urge others to read the two links under the heading “The human side of mathematics”. I read “On progress and proof in mathematics” back in March of this year and just read “What’s a mathematician to do?” on MO last night.

Bill Thurston died on the evening of August 21st. His son Dylan writes “He was surrounded by family, and went very peacefully, after a fight with melanoma since spring 2011. Please pass this on as appropriate.”

I knew Professor Thurston only through his writing, first in publication and recently on Mathoverflow. It was always a joy. I have avoided more routine obligations than I care to admit by reading and rereading his papers. He believed that mathematics was a fundamentally human task, and that his goal was not simply to provide the reader with a bulleted list of truths, but to provide a picture and an intuition that made them obvious.

I had the thought to organize a blogfest, where various math bloggers would write up expositions of some aspect of his work. But I ran into an obstacle: What subject did I think I could explain better than he…

View original post 215 more words

We had three lectures on `Numbers’, as part of the Cambridge Maths Sutton Trust summer school in August 2012. Here are some suggestions for further reading.

In the first lecture, we talked about Euclid‘s algorithm and Bézout‘s lemma. In the second, we mentioned the Fundamental Theorem of Arithmetic, and we learned about modular arithmetic. In the third and final lecture, we mentioned that $latex \sqrt{2}$ is irrational, and talked about continued fractions. There are many proofs that $latex \pi$ is irrational. We mentioned that there are many more irrational numbers than rational; that’s because the rationals are `countable’, whereas the irrationals are `uncountable’. A couple of the problems on the examples sheet are related to the Chinese Remainder Theorem.

Other mathematicians who were mentioned during the week: Cantor, Cardano, Diophantus, Fermat, Galois, Tartaglia,

View original post 104 more words