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Wednesday, June 29, 2016

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!


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