Wednesday, November 2, 2016

The amazing Grothendieck's view on research...

I am not really doing research, just trying to cultivate myself.
Alexander Grothendieck (1928–2014)

Sunday, March 27, 2016

An amazing "prime conspiracy" discovered by Lemke Oliver and Soundararajan

Mathematicians Discover Prime Conspiracy
A previously unnoticed property of prime numbers seems to violate a longstanding assumption about how they behave. 

Terrence Tao: Biases between consecutive primes

Lemke Oliver and Soundararajan  ArXiv article

Richard Feynman: 'Greek' versus 'Babylonian' mathematics LIVE

Mathematics as Hidden Reality - Edward Frenkel

"There's a secret world out there. A hidden parallel universe of beauty and elegance, intricately intertwined with ours. And it's invisible to most of us."

Imagine that you had to take an art class in which they taught you only how to paint a fence or a wall, but never showed you the paintings of the great masters. Alas, this is how math is taught, and so for most of us it becomes the intellectual equivalent of watching paint dry. Edward Frenkel wants to open this secret world to all of us because it can teach us so much about the mysteries of the Universe. In this talk, he weaves the discovery of math with his personal journey, addressing the existential questions of finding out who we are; of truth, courage, and passion.

Edward Frenkel is a professor of mathematics at the University of California, Berkeley, which he joined in 1997 after being on the faculty at Harvard University. He is a member of the American Academy of Arts and Sciences, a Fellow of the American Mathematical Society, and the winner of the Hermann Weyl Prize in mathematical physics. Frenkel has authored three books and over eighty scholarly articles in academic journals, and he has lectured on his work around the world. His YouTube videos have garnered over 3 million views combined.

Frenkel’s latest book "Love and Math" was a New York Times bestseller and has been named one of the Best Books of 2013 by both Amazon and iBooks. It is being translated into 14 languages. Frenkel has also co-produced, co-directed and played the lead in the film "Rites of Love and Math" (2010).

Edward Frenkel: Let's Stop Hating Math

Saturday, February 27, 2016

primes as "experimental data"...

"Although the prime numbers are rigidly determined, they somehow feel like experimental data." 
T. Gowers, "Mathematics: A Very Short Introduction (Oxford Univ. Press, 2002) p.118 (apud source)

Thursday, January 7, 2016

Tenure matters. Research by proxy - a big "no"

That's a potential problem with tenure-track faculty at smaller colleges. In order to get credit for scholarly activity, some of them encourage/coach students to present materials at conferences (mainly state or local). The materials are mostly elementary and well known (so that they would not count as a significant scholarly activity for any self-respecting faculty working towards his/her tenure), however having student presenters is strongly encouraged by the organizers of said conferences, and their contributed presentations are benevolently welcomed (and rightfully so). While it is OK (and arguably a formative experience) for students to present such materials, it is not OK for their faculty advisors to claim credit for scholarship (via 'undergraduate research') on the basis of having student advisees presenting at conferences (while they avoid having their names as coauthors alongside their students). That's a big "no". There is no such thing as "research by proxy". If they help students to give contributed talks on general topics, this is actually a credential for teaching effectiveness, not a scholarly credential. If they want scholarly credential they should "man up" and sign up as co-authors in the presentations with their advisees (and consequently face the "tune" of assessment after they claim scholarly credit for said presentations), or, even better - so that every doubt will be removed - publish with student co-authors (or without, for that matter). There is no undergraduate research without faculty research.

Monday, December 28, 2015

Why mathematics is exceptional

“Mathematical knowledge is unlike any other knowledge. While our perception of the physical world can always be distorted, our perception of mathematical truths can’t be. They are objective, persistent, necessary truths. A mathematical formula or theorem means the same thing to anyone anywhere – no matter what gender, religion, or skin color; it will mean the same thing to anyone a thousand years from now. And what’s also amazing is that we own all of them. No one can patent a mathematical formula, it’s ours to share. There is nothing in this world that is so deep and exquisite and yet so readily available to all. That such a reservoir of knowledge really exists is nearly unbelievable. It’s too precious to be given away to the “initiated few.” It belongs to all of us.” ― Edward Frenkel (Love and Math: The Heart of Hidden Reality - via