Three to Expect a Lot From

An interesting piece on 3 leading, young European mathematicians,  Peter Scholze,  James Maynard, and Sara Zahedi, who are "surprisingly young -- and very down-to-earth" (h/t to Egan Chernoff for this one):

http://www.dw.com/en/dont-call-me-a-prodigy-the-rising-stars-of-european-mathematics/a-19421389

The Power of Biography

courtesy of pixabay.com

 I always enjoy learning which popular math books have inspired other mathematicians along their way. One of the volumes that most frequently comes up, to my surprise, is E.T. Bell's "Men of Mathematics." In fact, it arose again in an obituary for John Nash over the weekend, mentioning it as one of his favorites. (Of course both the Sylvia Nasar bio and the movie about Nash's own life were huge popular hits as well.)

I do like biographies, but Bell's 80-year-old volume never much grabbed me, probably because it runs from Zeno to Cantor, missing all those who would interest me since Cantor's time. Paul Erdös, Ramanujan, Benoit Mandelbroit, H.M.S. Coxeter, John von Neumann, and of course Gödel, are some other 20th century mathematicians with bios or autobios available. Stanislaw Ulam and Norbert Wiener also wrote autobiographical accounts, and there have been some more recent compendiums, like Bell's original book, as well. Anyway, it's interesting how easily moved we are by the lives of others, and I wonder which of our modern day mathematicians will one day have important bios written about them, inspiring future generations of mathematicians.

Surely, there will be a biography of Terence Tao at some distant point in time. Andrew Wiles seems another likely candidate; perhaps Donald Knuth or Bill Thurston.  Of course, Martin Gardner (more strictly a philosopher and writer than a mathematician), did his own autobiography and also has an official biography in the works. I suspect Raymond Smullyan, again more strictly a logician than a mathematician, will eventually have a biography of his incredible life as well. And John Nash's too-sudden death may spur an additional biography or two of him. Who else? There are a lot of possibilities... one for certain, and highly anticipated (due out in just a couple of months), is Siobhan Roberts' bio of John Conway ("Genius At Play"), who is still with us, and no doubt a fantastic character for a book-length profile!

And speaking of biographical stuff, any of you 60s/70s fans out there may enjoy this recent profile of a one-time math teacher by the name of... Art Garfunkel:

http://tinyurl.com/mzfw8hu

Done Too Soon...

First, to put you in the right mood (some old Neil Diamond)…



   A short while back, Guillermo Bautista compiled an annotated list of 10 notable mathematicians who died too young (between the ages of 20 and 40):

http://tinyurl.com/mabghvl

Calculus Is Beautiful...

As someone who has diddly artistic talent I often think that working artists literally perceive the world differently than those of us who don't do art… I suspect a painter or drawer may actually see his/her subject differently than the way my eyes see it.
And perhaps the same is true for those of us who love mathematics… we perceive the world, or at least think about it, differently than those who fear or dislike math… the 'beauty' of math (as I've noted often before) is obvious to some and oblivious to others.

Evelyn Lamb has a transcribed interview over at her Scientific American blog with two female mathematicians (in the field of dynamical systems), Laura DeMarco and Amie Wilkinson. So many great responses, especially if you're interested in the experience of female mathematicians. Please give it a read. But here's a small excerpt that touches on the 'beauty' aspect (as related to calculus) that always catches my attention:

Lamb: Are there any math topics that are particularly appealing or beautiful for you?

Wilkinson: I like calculus a lot, probably because I learned it when I was young, and I learned it well. To me, it’s always comforting to use calculus to do something. The invention of calculus was certainly revolutionary.
 
DeMarco: A conceptual breakthrough.

        Wilkinson: It’s funny, because it’s like we just toss it out there to high   
        school students, and I think a lot of them have no idea of the beauty.  

        DeMarco: What the ideas really were.

Wilkinson: Certainly some of the most beautiful mathematics I’ve learned is just calculus.

DeMarco: It’s funny you mention calculus. I don’t think I really appreciated it until I taught it as a graduate student. I was lecturing to these first-year students. I was just wowed by this subject. I had this moment of, holy cow, this is really beautiful! I remember my grandmother asking me what I was thinking about these days. I said, “Well, I’m teaching calculus right now, and you know what, calculus is really beautiful.” She said, “OK, Laura, what is calculus? Can you just tell me in 20 minutes, what is calculus?” And it was just the greatest thing to have this opportunity to just sit down with my grandmother, of all people, and tell her.

This section happened to strike a chord for me, but if you're a female and interested in mathematics there are so many other passages that will be of special interest, so do check out the whole interview (...and guys can read it too; I did ;-):

http://blogs.scientificamerican.com/roots-of-unity/2013/06/11/mathematics-live-demarco-wilkinson/

Read All About 'Em!

Today, just a list of links to Wikipedia for many of the best math popularizers/writers around. I've included Martin Gardner (deceased), but otherwise all others are still alive (at time of posting) and are listed in alphabetical order. Some Wikipedia entries are much more extensive than others:

Arthur Benjamin: http://en.wikipedia.org/wiki/Arthur_T._Benjamin
Gregory Chaitin: http://en.wikipedia.org/wiki/Gregory_Chaitin
John Conway: http://en.wikipedia.org/wiki/John_Horton_Conway
Philip J. Davis: http://en.wikipedia.org/wiki/Philip_J._Davis
Keith Devlin: http://en.wikipedia.org/wiki/Keith_devlin
Persi Diaconis: http://en.wikipedia.org/wiki/Persi_Diaconis
Martin Gardner: http://en.wikipedia.org/wiki/Martin_gardner
Tim Gowers: http://en.wikipedia.org/wiki/Tim_Gowers 
George Hart: http://en.wikipedia.org/wiki/George_W._Hart
Vi Hart: http://en.wikipedia.org/wiki/Vi_Hart
Reuben Hersh: http://en.wikipedia.org/wiki/Reuben_Hersh
Mario Livio: http://en.wikipedia.org/wiki/Mario_Livio
Eli Maor: http://en.wikipedia.org/wiki/Eli_Maor
Barry Mazur: http://en.wikipedia.org/wiki/Barry_Mazur
Joseph Mazur: http://en.wikipedia.org/wiki/Joseph_Mazur 
Danica McKellar: http://en.wikipedia.org/wiki/Danica_McKellar
John Allen Paulos: http://en.wikipedia.org/wiki/John_Allen_Paulos
Ivars Peterson: http://en.wikipedia.org/wiki/Ivars_Peterson
Clifford Pickover: http://en.wikipedia.org/wiki/Clifford_A._Pickover
Alfred Posamentier: http://en.wikipedia.org/wiki/Alfred_Posamentier
Rudy Rucker: http://en.wikipedia.org/wiki/Rudy_Rucker
Marcus du Sautoy: http://en.wikipedia.org/wiki/Marcus_du_Sautoy
Raymond Smullyan: http://en.wikipedia.org/wiki/Raymond_Smullyan
Ian Stewart: http://en.wikipedia.org/wiki/Ian_Stewart_%28mathematician%29
Steven Strogatz: http://en.wikipedia.org/wiki/Steven_Strogatz

Strange Genius

In his 2001 volume "Wonders of Numbers," Clifford Pickover ranked the "5 Strangest Mathematicians Who Ever Lived." One could offer a lot of suggestions and debate on this subject, but here is Pickover's slate, with links to their Wikipedia pages:

1. Paul Erdos

2. Srinivasa Ramanujan

3. Pythagorus

4. Theodore Kaczynski

5. John Nash

(I'll throw in a couple more that quickly come to mind: Grigori Perelman and Alexander Grothendieck.)

The oddest member in this whole group, from my viewpoint, is Kaczynski, who in case you've forgotten or didn't know, was a loner, domestic terrorist also known as the "Unabomber" (and also a Harvard grad and Michigan math PhD.) who eluded law enforcement for over 17 years, living a spartan, reclusive life in rural Montana, while sending out his occasional mail bombs and manifestos.

My Fab Four

Speaking of Euler, as I did in the prior post....

It's of course impossible to name the four most important or influential or greatest mathematicians of all time. The arguments could go 'round-and-'round forever without resolution, and math is a surprisingly diverse, robust field where different individuals make all kinds of different contributions.

Nonetheless, one of the math T-shirts I offer at my Zazzle store is "The Fab Four" where I've designated the four I would pick out for such an honor if forced to choose. For the combined breadth, depth, and variety of their contributions they are (with their Wikipedia links):

Leonhard Euler
(1707 - 1783)

Carl Friedrich Gauss
(1777 - 1855)

David Hilbert
(1862 - 1943)

G.F. Bernhard Riemann
(1826 - 1866)

I'm leaving out both a lot of hugely important ancient and modern-day mathematicians, but these are just my subjective choices. Who might you choose for a Fab Four? Here's a list of 'greatest mathematicians' as formulated by someone else:

http://fabpedigree.com/james/greatmm.htm