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Classic Mathematical Problems & Their Occasional Solution

Definitely a candidate for Strange Folk:

World's cleverest man turns down $1million prize after solving one of mathematics' greatest puzzles
By Will Stewart
Last updated at 10:11 AM on 23rd March 2010

A Russian awarded $1million (£666,000) for solving one of the most intractable problems in mathematics said yesterday that he does not want the money.
Said to be the world's cleverest man, Dr Grigory Perelman, 44, lives as a recluse in a bare cockroach-infested flat in St Petersburg. He said through the closed door: 'I have all I want.'

The prize was given by the U.S. Clay Mathematics Institute for solving the Poincare Conjecture, which baffled mathematicians for a century. Dr Perelman posted his solution on the internet.
He failed to turn up to receive his prestigious Fields Medal from the International Mathematical Union in Madrid four years ago.

At the time he stated: 'I'm not interested in money or fame. I don't want to be on display like an animal in a zoo.
'I'm not a hero of mathematics. I'm not even that successful, that is why I don't want to have everybody looking at me.'

Neighbour Vera Petrovna said: 'I was once in his flat and I was astounded. He only has a table, a stool and a bed with a dirty mattress which was left by previous owners - alcoholics who sold the flat to him.
'We are trying to get rid of cockroaches in our block, but they hide in his flat.'

It was in 2003 that Perelman, then a researcher at the Steklov Institute of Mathematics in St. Petersburg, began posting papers online suggesting he had solved the Poincare Conjecture, one of seven major mathematical puzzles for which the Clay Institute is offering $1 million each.

Rigorous tests proved he was correct.

The topological conundrum essentially states that any three-dimensional space without holes in it is equivalent to a stretched sphere.
The puzzle was more than 100 years old when Perelman solved it - and could help determine the shape of the universe.

After 2003 Perelman gave up his job at the Steklov Institute. Friends have been reported as saying he has resigned from mathematics altogether - finding the subject too painful to discuss.

Read more: http://www.dailymail.co.uk/news/worldne ... z0izymAVYm
 
rynner2 said:
Definitely a candidate for Strange Folk:

World's cleverest man turns down $1million prize after solving one of mathematics' greatest puzzles
By Will Stewart
Last updated at 10:11 AM on 23rd March 2010

A Russian awarded $1million (£666,000) for solving one of the most intractable problems in mathematics said yesterday that he does not want the money.
Said to be the world's cleverest man, Dr Grigory Perelman, 44, lives as a recluse in a bare cockroach-infested flat in St Petersburg. He said through the closed door: 'I have all I want.'

:shock:

A clever man would surely at least invest in some roach repellent! :lol:
 
McAvennie_ said:
:shock:

A clever man would surely at least invest in some roach repellent! :lol:

Perhaps the cockroaches are his friends...
 
Mathematician rejected $1 million prize 'because it is unfair'
A Russian mathematician rejected a $1 million prize for solving one of the most challenging problems because he considers it unfair.
Published: 5:09PM BST 01 Jul 2010

Grigory Perelman told the Clay Mathematics Institute in Cambridge, Massachusetts, he was turning down the prize., according to the Interfax news agency.

Mr Perelman was quoted by Interfax as saying he believes his contribution in proving the Poincare conjecture was no greater than that of US mathematician Richard Hamilton, who first suggested a program for the solution.

The Clay Mathematics Institute confirmed in a statement on its website that Mr Perelman had informed it of his refusal to accept the prize.

The Poincare conjecture, one of seven problems on the institute's Millennium Prize list, deals with shapes that exist in four or more dimensions.

Mr Perelman, 43 did not appear in Paris on Tuesday 22nd June to collect his $1m prize for solving a problem that has puzzled scientists for more than a century.

Mr Perelman, who lives in a small apartment in St Petersburg with his elderly mother, is unemployed and neighbours say he lives in poverty.

He has rejected job offers from several top US universities.

http://www.telegraph.co.uk/news/worldne ... nfair.html
 
Not terribly surprising, he's well known in the Mathematics community for being asocial. It was actually expected he'd turn it down.
 
Re: Millenium Problems = Very Hard Maths

_TMS_ said:
For the Millenium, The Clay Mathematics Institute set a bounty of 1 Million Dollars for solving what they considered the most difficult of mathematical problems.

...

3 Navier-Stokes equation: The answers to wave and breeze turbulence lie somewhere in the solutions to these equations
Kazakh mathematician may have solved $1 million puzzle
15:09 22 January 2014 by Jacob Aron and Katia Moskvitch

Mathematics is a universal language. Even so, a Kazakh mathematician's claim to have solved a problem worth a million dollars is proving hard to evaluate – in part because it is not written in English.

Mukhtarbay Otelbayev of the Eurasian National University in Astana, Kazakhstan, says he has proved the Navier-Stokes existence and smoothness problem, which concerns equations that are used to model fluids – from airflow over a plane's wing to the crashing of a tsunami. The equations work, but there is no proof that solutions exist for all possible situations, and won't sometimes "blow up", producing unrealistic answers.

In 2000, the Clay Mathematics Institute, now in Providence, Rhode Island, named this one of seven Millennium Prize problems offering $1 million to anyone who could devise a proof.

Otelbayev claims to have done just that in a paper published in the Mathematical Journal, also based in Kazakhstan. "I worked on the problem on and off, for 30 years," he told New Scientist, in Russian – he does not speak English.

However, the combination of the Russian text and the specialist knowledge needed to understand the Navier-Stokes equations means the international mathematical community, which usually communicates in English is having difficulty evaluating it. Although mathematics is expressed through universal symbols, mathematics papers also contain large amounts of explanatory text.

"Over the years there have been several alleged solutions to the Navier-Stokes problem that turned out to be wrong," says Charles Fefferman of Princeton University, who wrote the official formulation of the problem for Clay. "Since I don't speak Russian and the paper is not yet translated, I'm afraid I can't say more right now."

Otelbayev is a professional, so mathematicians are paying more attention to his proof than is typical for amateur efforts to solve Millennium Prize problems, which are regularly posted online. 8)

The Russian-speaking Misha Wolfson, a computer scientist and chemist at the Massachusetts Institute of Technology is attempting to spark an online, group effort to translate the paper. "While my grasp on the math is good enough to enable translation up to this point, I am not qualified to say anything about whether or not the solution is any good," he says.

Stephen Montgomery-Smith of the University of Missouri in Columbia, who is working with Russian colleagues to study the paper, is hopeful."What I have read so far does seem valid," he says "but I don't feel that I have yet got to the heart of the proof."

Otelbayev says that three colleagues in Kazakhstan and another in Russia agree that the proof is correct.

Understandably, a high burden of proof is required to claim the $1 million prize. Clay's rules say the solution must be published in a journal of "worldwide repute" and remain unchallenged for two years before it can even be considered. Nick Woodhouse, president of the Clay Mathematics Institute, declined to comment on Otelbayev's proof.

"It is currently being translated by my students, and will be available soon," says Otelbayev. He says that he will publish it again once it is translated into English – initially in a second Kazakh journal, and then perhaps abroad.

To date, only one Millennium Prize problem has been officially solved. In 2002, Grigori Perelman proved the Poincaré conjecture, but later withdrew from the mathematical community and refused the $1 million prize.

A possible solution for another problem, known as P vs NP, caught mathematicians' attentions in 2010, but later proved to be flawed. Whether Otelbayev's proof will share the same fate remains to be seen.

http://www.newscientist.com/article/dn2 ... urce=NSNS&
 
Mathematicians Prove Universal Law of Turbulence

Source: Quanta Magazine
4 February, 2020

By exploiting randomness, three mathematicians have proved an elegant law that underlies the chaotic motion of turbulent systems.

Mixing liquids and other turbulent systems have long been observed to follow a universal rule known as Batchelor’s law. Researchers have finally proved it mathematically.

Picture a calm river. Now picture a torrent of white water. What is the difference between the two? To mathematicians and physicists it’s this: The smooth river flows in one direction, while the torrent flows in many different directions at once.

Physical systems with this kind of haphazard motion are called turbulent. The fact that their motion unfolds in so many different ways at once makes them difficult to study mathematically. Generations of mathematicians will likely come and go before researchers are able to describe a roaring river in exact mathematical statements.

But a new proof finds that while certain turbulent systems appear unruly, they actually conform to a simple universal law. The work is one of the most rigorous descriptions of turbulence ever to emerge from mathematics. And it arises from a novel set of methods that are themselves changing how researchers study this heretofore untamable phenomenon.

https://www.quantamagazine.org/mathematicians-prove-batchelors-law-of-turbulence-20200204/
 
Note that Terrance Tao, the Tao mentioned below, is a recipient of the Fields Medal, the highest honor in the field of maths.

"Then this past August an anonymous reader left a comment on Tao’s blog. The commenter suggested trying to solve the Collatz conjecture for “almost all” numbers, rather than trying to solve it completely. "

This suggestion led Tao to make a massive improvement in solving a maths problem considered "the simplest unsolved problem in mathematics"

https://getpocket.com/explore/item/mathematician-proves-huge-result-on-dangerous-problem

However this isn't the only anonymous internet post leading to huge advances in maths problems. When someone on an anime forum asked a question about watching some anime, the anonymously posted answer was a proof for a problem that had been unsolved in maths for at least 20 years.

https://www.theverge.com/2018/10/24/18019464/4chan-anon-anime-haruhi-math-mystery

So, is there a mystery genius maths person out there? Someone able to tell even the top mathematicians in the world how to solve problems?
 
So, is there a mystery genius maths person out there? Someone able to tell even the top mathematicians in the world how to solve problems?

l don’t think that we need to posit some anonymous, reclusive genius randomly spreading the seeds of inspiration.

l would imagine that top-flight academic mathematicians have a huge correspondence, both official and private. All it would take would be for some chance remark - via email for instance - to spark a chain of thought leading to a revelation.

Scientific leaps have occurred based on even more tenuous foundations, e.g. the dream that inspired Kekulé's discovery of the structure of benzene.

maximus otter
 
Note that Terrance Tao, the Tao mentioned below, is a recipient of the Fields Medal, the highest honor in the field of maths.

"Then this past August an anonymous reader left a comment on Tao’s blog. The commenter suggested trying to solve the Collatz conjecture for “almost all” numbers, rather than trying to solve it completely. "

This suggestion led Tao to make a massive improvement in solving a maths problem considered "the simplest unsolved problem in mathematics"

https://getpocket.com/explore/item/mathematician-proves-huge-result-on-dangerous-problem

However this isn't the only anonymous internet post leading to huge advances in maths problems. When someone on an anime forum asked a question about watching some anime, the anonymously posted answer was a proof for a problem that had been unsolved in maths for at least 20 years.

https://www.theverge.com/2018/10/24/18019464/4chan-anon-anime-haruhi-math-mystery

So, is there a mystery genius maths person out there? Someone able to tell even the top mathematicians in the world how to solve problems?
I think the issue is with the education these maths genius' have, usually, upon their savant abilities being noticed at an early age, they are taught from the same books and the same theories that all the mathamaticians before them have been taught from, therefore the ability to solve unsolved equations remain the same, as they are coming at the problem from the same position, and with the same learning of how the problem 'should' be able to be solved, sometimes it takes someone who hasnt had a formal educaion in advance maths, to look at the problem and come up with a theory about how to solve the problem from an abstract angle, often one simple enough that all the massively talented and educated have either not thought of or assumed 'someone must have tried that before, so im not going to waste my time on it'.
 
Let met put this here. It fits a bit.

ABC is Still a Conjecture | Not Even Wrong (columbia.edu)

Why the Szpiro Conjecture is Still a Conjecture | Not Even Wrong (columbia.edu)

This is totally above anyone's head, but the social drama around the proof of the "ABC conjecture" is fascinating. There's a proof nobody fully understands, there are counterarguments that are not accepted, and there might be collusion in there referee process. I follow this with popcorn and cola, while totally not understanding the math (maybe nobody does).

From the comments - and note that this is about real, serious math:

The 65 page document has a clear message: to understand what IUT is, you need to think about it for 6 months or 3 years (section 1.6), come to Japan (sections 1.6 and 1.9), talk to “M” for a long time, and think about it, discussing with “M”, until you understand it. As a result, the worldwide number of people who understand it is of the “order of 10” (section 1.6), centered around Kyoto.

The math examples that “M” gives are so simple that nobody will ever believe that Scholze and Stix stumbled over such issues.
“M” clearly states, page over page, that Scholze and Stix are stupid. In fact, the document states that all his critics are stupid. Above all, the document shows that “M” is abusive towards people of different opinion.

The whole paper is clearly written by an aspiring leader of a sect. There is no need to come to Japan to understand this. I have lived in Japan, and this type of sect leaders is common there. It is sad to see that such people exist in mathematics, and especially sad to see that they exist at Kyoto University, one of the best in Japan.


Peter Scholze, one of the doubters of the ABC proof, is also a fascinating figure, although in a more normal fashion:
Peter Scholze and the Future of Arithmetic Geometry | Quanta Magazine
 
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This is a huge breakthrough although I only understand 1%.
https://www.quantamagazine.org/with-a-new-shape-mathematicians-link-geometry-and-numbers-20210719/

And isn't it cool that the mathematician is so young:
https://www.quantamagazine.org/peter-scholze-and-the-future-of-arithmetic-geometry-20160628/

And the article mentions Grothendieck, a weirdo genius who vanished in the Pyrenees:
https://forums.forteana.org/index.php?threads/strange-folk.471/post-2084810

1646252205484.png

But still not as cute as Terence Tao, also a math genius (on the right, with Paul Erdos, another genius):

1646252303546.png
 
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