Free Republic
Browse · Search
General/Chat
Topics · Post Article

Skip to comments.

The Oracle of Arithmetic
Quanta ^ | 28 Jun, 2016 | Erica Klarreich

Posted on 07/04/2016 4:38:42 PM PDT by MtnClimber

At 28, Peter Scholze is uncovering deep connections between number theory and geometry. In 2010, a startling rumor filtered through the number theory community and reached Jared Weinstein. Apparently, some graduate student at the University of Bonn in Germany had written a paper that redid “Harris-Taylor” — a 288-page book dedicated to a single impenetrable proof in number theory — in only 37 pages. The 22-year-old student, Peter Scholze, had found a way to sidestep one of the most complicated parts of the proof, which deals with a sweeping connection between number theory and geometry.

“It was just so stunning for someone so young to have done something so revolutionary,” said Weinstein, a 34-year-old number theorist now at Boston University. “It was extremely humbling.”

Mathematicians at the University of Bonn, who made Scholze a full professor just two years later, were already aware of his extraordinary mathematical mind. After he posted his Harris-Taylor paper, experts in number theory and geometry started to notice Scholze too.

Since that time, Scholze, now 28, has risen to eminence in the broader mathematics community. Prize citations have called him “already one of the most influential mathematicians in the world” and “a rare talent which only emerges every few decades.” He is spoken of as a heavy favorite for the Fields Medal, one of the highest honors in mathematics.

Scholze’s key innovation — a class of fractal structures he calls perfectoid spaces — is only a few years old, but it already has far-reaching ramifications in the field of arithmetic geometry, where number theory and geometry come together.

(Excerpt) Read more at quantamagazine.org ...


TOPICS: Education; Science
KEYWORDS: arithmetic; fractal; geometry; harristaylor; mathematics; numbertheory; perfectoid; peterscholze; stringtheory
Navigation: use the links below to view more comments.
first 1-2021-34 next last

1 posted on 07/04/2016 4:38:42 PM PDT by MtnClimber
[ Post Reply | Private Reply | View Replies]

To: MtnClimber

It is amazing that new mathematical methods continue to be developed.


2 posted on 07/04/2016 4:40:38 PM PDT by MtnClimber (For photos of Colorado scenery and wildlife, click on my screen name for my FR home page.)
[ Post Reply | Private Reply | To 1 | View Replies]

To: MtnClimber

These people are Freaks of Nature, and we are all blessed by their existence.


3 posted on 07/04/2016 4:45:01 PM PDT by Paradox (Opinions can evolve, but Principles should be immutable.)
[ Post Reply | Private Reply | To 1 | View Replies]

To: MtnClimber

Wow. Reaching into the mind of God...


4 posted on 07/04/2016 4:51:20 PM PDT by MeneMeneTekelUpharsin (Freedom is the freedom to discipline yourself so others don't have to do it for you.)
[ Post Reply | Private Reply | To 1 | View Replies]

To: Paradox
Freaks of Nature, and we are all blessed by their existence

Freaks of Nature, like this?

Or perhaps God's way of saying, "There is far more beauty & wonder out there than you can ever imagine!"

e.g. Mandelbrot diagrams


5 posted on 07/04/2016 4:57:24 PM PDT by BwanaNdege
[ Post Reply | Private Reply | To 3 | View Replies]

To: Paradox

You’d be amazed at how many fit into the autistic spectrum.


6 posted on 07/04/2016 5:07:13 PM PDT by meatloaf
[ Post Reply | Private Reply | To 3 | View Replies]

To: MtnClimber

Obama would say he didn’t think that.


7 posted on 07/04/2016 5:07:41 PM PDT by AU72
[ Post Reply | Private Reply | To 1 | View Replies]

To: MtnClimber

Discovered. God already developed them. We discover them.


8 posted on 07/04/2016 5:08:46 PM PDT by Secret Agent Man (Gone Galt; Not averse to Going Bronson.)
[ Post Reply | Private Reply | To 2 | View Replies]

To: MtnClimber

I thought that 1+1 = 3 was settled science.

On a less /s note, science (and math which describes it) is the description of the Created Universe (Guess Who created it).

So, of course, wonderments in science and math are just a peek at the God of Creation.

PS. God says 1+1=2 ... settled!!!


9 posted on 07/04/2016 5:10:44 PM PDT by Scrambler Bob (As always, /s is implicitly assumed. Unless explicitly labled /not s. Saves keystrokes.)
[ Post Reply | Private Reply | To 1 | View Replies]

To: MtnClimber

10 posted on 07/04/2016 5:18:22 PM PDT by Daffynition ("We have the fight of our lives coming up to save our nation!" ~ Jim Robinson)
[ Post Reply | Private Reply | To 1 | View Replies]

To: Paradox
AKA geeks. Bless their hearts.


11 posted on 07/04/2016 5:28:52 PM PDT by Daffynition ("We have the fight of our lives coming up to save our nation!" ~ Jim Robinson)
[ Post Reply | Private Reply | To 3 | View Replies]

To: BwanaNdege

Have you ever seen a clash of colors in nature?


12 posted on 07/04/2016 5:30:25 PM PDT by PUGACHEV
[ Post Reply | Private Reply | To 5 | View Replies]

To: MtnClimber

the first Theorem alone made my head hurt.

i can’t even post it because the interpreter thinks it’s all HTTP...

http://www.math.uni-bonn.de/people/scholze/PerfectoidSpaces.pdf


13 posted on 07/04/2016 6:05:36 PM PDT by Chode (Stand UP and Be Counted, or line up and be numbered - *DTOM* -w- NO Pity for the LAZY - Luke, 22:36)
[ Post Reply | Private Reply | To 1 | View Replies]

To: MtnClimber

And we have a legion of Ivy League and big name colleges that can’t even do big math ... like balancing a budget!!!!


14 posted on 07/04/2016 6:19:31 PM PDT by RetiredTexasVet (The Mofia is a private crime family; whereas, the DOJ is the gov't's political crime family.)
[ Post Reply | Private Reply | To 1 | View Replies]

To: RetiredTexasVet

Balancing a budget is common sense. Something absent in leftist elitists who run most universities.


15 posted on 07/04/2016 6:23:53 PM PDT by MtnClimber (For photos of Colorado scenery and wildlife, click on my screen name for my FR home page.)
[ Post Reply | Private Reply | To 14 | View Replies]

To: Chode

I could not follow it either.


16 posted on 07/04/2016 6:25:34 PM PDT by MtnClimber (For photos of Colorado scenery and wildlife, click on my screen name for my FR home page.)
[ Post Reply | Private Reply | To 13 | View Replies]

To: MtnClimber

Three of my five sons sit around the dinner table discussing higher level mathematics and consider it entertainment and great fun. Eldest has 4 (simultaneous) degrees in Math, Computer Science, Physics and Greek, Summa Cum Laude, Phi Beta Kappa (when a junior); another is a Civil Engineer, P.E. now writing complex engineering calcs in C Sharp; the youngest a senior getting a degree in Mechanical Engineering.

I can barely understand what they are talking about - but this is right up their alley - so thanks for the post - sending it on to them. They will love it......

No hope I’ll ever understand it...........


17 posted on 07/04/2016 6:32:26 PM PDT by Arlis
[ Post Reply | Private Reply | To 1 | View Replies]

To: BwanaNdege

Check my tag line.


18 posted on 07/04/2016 8:31:32 PM PDT by mkleesma (`Call to me, and I will answer you and tell you great and unsearchable things you do not know.')
[ Post Reply | Private Reply | To 5 | View Replies]

To: MtnClimber

Just as I thought.


19 posted on 07/04/2016 9:13:37 PM PDT by SuperLuminal (Where is another agitator for republicanism like Sam Adams when we need him?)
[ Post Reply | Private Reply | To 1 | View Replies]

To: Arlis

You are blessed.


20 posted on 07/04/2016 9:23:47 PM PDT by Mama Shawna
[ Post Reply | Private Reply | To 17 | View Replies]


Navigation: use the links below to view more comments.
first 1-2021-34 next last

Disclaimer: Opinions posted on Free Republic are those of the individual posters and do not necessarily represent the opinion of Free Republic or its management. All materials posted herein are protected by copyright law and the exemption for fair use of copyrighted works.

Free Republic
Browse · Search
General/Chat
Topics · Post Article

FreeRepublic, LLC, PO BOX 9771, FRESNO, CA 93794
FreeRepublic.com is powered by software copyright 2000-2008 John Robinson