Tuesday, August 31, 2010

Stefan Banach (1892-1945)

"Good mathematicians see analogies. Great mathematicians see analogies between analogies"
Stefan Banach - quote reportedly provided by Stanisław Ulam.
Banach died on August 31, 1945 at age 53
Home Page of Stefan Banach
Mac Tutor biography
Stefan Banach at MGP

Monday, August 30, 2010

Twenty-Five Years with Nicolas Bourbaki, 1949–1973

Interesting article by Armand Borel: Twenty-Five Years with Nicolas Bourbaki, 1949–1973 
Notices of the AMS
March 1998, 373-380

Constantin Brâncuşi

"I have grinded the matter to find the continuous line. And when I realized I could not find it, I stopped, as if an unseen someone had seen me and slapped my hands."

Constantin Brâncuşi (1876-1957). In the picture: Brâncuşi in Paris (1922), photograph taken by Edward Steichen (source)

Thursday, August 26, 2010

Taming the greatest prime factor...

Logarithmic plot of the first 500 terms of the prime sequence recursively defined as L[k]=P(2010*L[k-1]+83), with P being the greatest prime factor function, and L[1]=2. The sequence is eventually periodic, with a period of 120. The largest term of the sequence (and of the limit cycle too) is precisely... 2617998905649748013.

Monday, August 16, 2010

Recent Progress in Additive Prime Number Theory

Terence Tao, 2006 Fields Medal Recipient - on Recent Progress in Additive Prime Number Theory
2009 Moursund Lectures, Day 1

Abstract: Additive prime number theory is the study of additive patterns in the primes. We survey some recent advances in this subject, including the results of Goldston, Pintz, and Yildirim on small gaps between primes, the results of Green and myself on arithmetic progressions in the primes, and the results of Bourgain, Gamburd, and Sarnak for detecting almost primes in orbits.

Eadem mutata resurgo

Commemorating Jacob Bernoulli...

Eadem mutata resurgo
"Though changed I shall rise the same"

Inscribed on Jacob Bernoulli's tombstone (he died on August 16, 1705 in Basel), this motto refers to the logarithmic (equiangular) spiral (N.B. the spiral that was actually imprinted on the tombstone is not equiangular). Through this self-similar object Jacob Bernoulli symbolically points to the ‘fortitude and constancy in adversity, or of the human body, which after all its changes, even after death, will be restored to its exact and perfect self ’ - as quoted in Mario Livio's book "The Golden Ratio..." (via here).

Jacob Bernoulli at the Mathematics Genealogy Project.

The Whirlpool Galaxy...