A Name to Know; Work to Be Aware Of

From Erica Klarreich at Quanta, a fascinating piece about a fascinating young mathematician, his fascinating work in number theory, making fascinating, groundbreaking connections between disparate areas of math:

https://www.quantamagazine.org/20160628-peter-scholze-arithmetic-geometry-profile/

Did I mention this is fascinating stuff....

Peter Scholze is a 28-year-old German wunderkind, probable Fields Medal candidate, and by several accounts, "one of the most influential mathematicians in the world," who works at the intersection of number theory and geometry. That might sound simple, but it is cutting edge, and for most, unexplored territory. Yet Peter seems to possess a strong intuitive sense for it (the article is aptly titled, "The Oracle of Arithmetic"). 

A couple of quick sentences from the piece:
"'I’m interested in arithmetic, in the end,' he [Scholze] said. He’s happiest, he said, when his abstract constructions lead him back around to small discoveries about ordinary whole numbers."

Almost makes it sound as if we rookies could understand what he does ;-); but that'll be the day. He's delving into deep, rich, abstract areas of mathematics, that most of us will never encounter, but the article makes clear he is also open, generous, and patient in his willingness to explain it to those who are able to take the leap.

Klarreich writes that Scholze "avoids getting tangled in the jungle vines by forcing himself to fly above them," which reminded me so much of Keith Devlin's early metaphor of reaching the top of a mathematical woodland canopy where he could look down and suddenly see that the whole forest was inter-connected.
Part of Scholze' work deals with what is called "reciprocity" and its linkage to hyperbolic geometry, including "perfectoid spaces," all of which leads to the Langlands Program and "frontiers of knowledge" which may eventually unify the field of mathematics (slightly akin to the so-called "Theory of Everything" searched for in physics).

But I can't do Scholze or Klarreich's writing justice here, so go read her article NOW!

Weekend Potpourri

So many mathy reads to choose from this weekend, if you've missed them (really enough for a couple of weekends!)....

1) Brand new from Sol Lederman, a wonderful podcast with mathematician/writer Erica Klarreich:

http://www.buzzsprout.com/5316/78729-erica-klarreich-inspired-by-math-22

I've previously mentioned my belief that interviewing lesser-known math figures is almost more enticing than interviewing the titans in the field because readers/listeners already know so much about the 'big names' out there that much of what they say may seem repetitious (even if important) of things they've voiced before. Lesser-known folks have a fresher appeal as there is so much new to learn about them, and I think this podcast demonstrates my point. I was fascinated hearing Erica's views and experiences on a wide range of topics. See if you don't agree.
And below, some of Erica's prior writings for the Simons Foundation:

https://simonsfoundation.org/?s=erica+klarreich&submit

2) MIT physicist Max Tegmark is famous for his belief that the Universe is "built" of mathematics. He expresses his viewpoint in this straightforward interview from the ScienceNow site… and attracts a lot of comments in the process (including cynical ones):

http://news.sciencemag.org/sciencenow/2013/02/do-we-live-inside-a-mathematical.html

3) Julie Rehmeyer, who I just posted about a few days ago, has a new piece on Fermat's Last Theorem and its axiomatic basis, in ScienceNews here:

http://tinyurl.com/a4ujnx5

4) Patrick Honner again laments a question from a NY State Regents Math exam that entails unstated assumptions and in so doing short-circuits deep mathematical thinking:

http://mrhonner.com/2013/02/21/regents-recap-january-2013-unstated-assumptions/

5) Some bloke named Keith Devlin has a fantastic longread on math games in American Scientist, leading up to release of his own company's new animated game for math learning. He sets forth the criteria or qualities a video needs to possess to be successful as a math instruction tool (and explains why MOST games FAIL):

http://www.americanscientist.org/issues/pub/the-music-of-math-games

From the description, it sounds to me as if the prospective player (young person) of these new games will learn math in a manner reminiscent of the original Karate Kid (the movie) learning karate without ever knowing it from his master Mr. Miyagi. Keith's discussion of the "symbol barrier" and symbol manipulation in math is especially enlightening, but the entire piece is GREAT. He employs a music (piano) metaphor to explain what a successful math game should be like.

6) The brilliant Barry Mazur, recent recipient of the National Medal of Science, gives us a rich (and philosophical) piece called "Shadows of Evidence" on what constitutes "evidence" in the realm of mathematics. The essay ends with a quote from Chris Anderson essentially arguing that "modeling," as traditionally used in science, is becoming obsolete (because ALL models are, technically, flawed), and that with the advent of computer number-crunching ability, only "correlation" derived from huge data sets will be needed. To which Mazur responds that, "correlation alone will never replace the explanatory power of mathematics.":

http://tinyurl.com/bhzrjgf

This essay in turn leads to an even longer Mazur read entitled "What Is Plausible" here (pdf):

http://www.math.harvard.edu/~mazur/papers/Plausibility.Notes.3.pdf

7) Finally, perhaps appropriately after all of the above, I'll end with 50 varied quotations just put up by Guillermo Bautista on what mathematics is:

http://mathandmultimedia.com/2013/02/23/50-mathematics-quotes/

a few of my favorites:

"Mathematics is no more computation than typing is literature." – John Allen Paulos

"Mathematics, in the common lay view, is a static discipline based on formulas…But outside the public view, mathematics continues to grow at a rapid rate…the guide to this growth is not calculation and formulas, but an open ended search for pattern."  -- Lynn A. Steen

"Mathematics compares the most diverse phenomena and discovers the secret analogies that unite them." — Joseph Fourier 

.... ADDENDUM:  Experimenting with shorter time segments, Sol Lederman has already put up another podcast interview (22 mins.), this time with Jason Ermer, creator of the "Collaborative Mathematics" project (who I referenced a bit ago):

http://www.buzzsprout.com/5316/78788-jason-ermer-inspired-by-math-23

Mathematicians have been at the forefront of bringing productive Web collaboration to academic subjects, and now Jason is attempting it at lower levels. Check it out!