Nice try but I am now 99% confident that Atiyah's proof of RH is wrong, hopeless

The live video stream from Atiyah's talk (9:45-10:30) was mostly overloaded but we may already watch a 49-minute-long recording on the Laureates Forum YouTube channel.

However, we were given two papers that are said to contain the proof:

The Fine Structure Constant (17 pages)

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The Riemann Hypothesis (5 pages)

The second paper contains the proof – which would really be an elementary proof accessible to intelligent undergraduates – on 15 lines of Page 3.

Atiyah's talk on the proof of Riemann Hypothesis scheduled for Monday

Hot, Monday 7:55: Before the 9:45 talk (watch video here and press "triangle play" in the lower left corner if paused; schedule; Laureates' server is overloaded), see this five-page paper by Atiyah. It starts with crackpot-style comments on the fine-structure constant but don't stop too early. The 15-line-long proof by contradiction using his "Todd function" (defined in another paper, thanks, pis.) is on Page 3. The strategy of halving the imaginary part of the Siegel root is exactly what I predicted on Quora! However, I don't understand his "Todd function" that is polynomial in convex sets of the complex plane but not in general. Can't it be proven that a regionally analytic polynomial function is polynomial everywhere? Oh, I see, it's just "weakly analytic". I must see what it means because he seems to mix real and complex analytic functions.

Originally posted on Fri Sep 21st morning

In 2012, Šiniči Močizuki claimed to have a proof of the \(abc\) conjecture. Now, exactly six years later, his proof – distributed over 500+ pages of text, not counting some "background" in additional 500+ pages of text – remains disputed. Some mathematicians claim that it has to be correct but they seem to be "insufficiently independent" of Močizuki. The truly independent ones remain silent or... negative.

In particular, the Quanta Magazine says that Jakob Stix and (the young, celebrated, fresh Fields Medal winner) Peter Scholze claim that they have isolated an unbridgeable gap in the Japanese proof. They met with Močizuki. The two sides couldn't agree. Scholze was just a "cheeky Hun who just barely jumped out of a vagina", Močizuki was a "brownie, gook, and nip", you can imagine that the exchanges between mathematicians keep their highest standards of diplomacy.

I think that this controversy is similar to some controversies in theoretical physics, perhaps including the "de Sitter space in string theory" controversy. In principle, it could just mathematics where everything is clear. But it's complex enough, with a potential for mistakes and some room for replacing detailed solutions by philosophies, so that people may end up believing in very different answers.

Le Pen and psychiatrist, Alex Jones and PayPal

France and the U.S. are turning into full-blown totalitarian countries

Our prime minister is a former communist rat and an unfixable Bolshevik and criminal (and today, we learned about the numbers showing that his "EET" online cash registers to harass the small businesses were indeed the kind of utter failure that all sensible people were predicting – just 1.2% increased collection of the value-added tax) but I am still grateful to live in Czechia. It's becoming a paradise, relatively speaking.



Pôle emploi, a French government agency, is luring the unemployed French people to Czechia, promising them €1,500 monthly wage before taxation (some 25% above the Czech average), great castles, and super cheap pubs everywhere. Some years in Czechia are surely not a way for a generic Western European to become rich after you return home (and many French get shocked by the "low" number when they see it) but the life expenses are correspondingly lower so that things may indeed be more relaxed in Czechia.

The unemployment in Czechia approaches 2% according to some methodologies so the country does need workers. But I mean "workers", not any "people". Muslim migrants wouldn't be OK because most of them couldn't become "workers".

Frauchiger-Renner: QM is inconsistent with two Wigners and their friends

David Thornton has asked about a new paper that basically claims that quantum mechanics is inconsistent,

Quantum theory cannot consistently describe the use of itself (Nature).

Note that Renner has arguably done some non-rubbish work in the quantum information theory but as explained in an unbelievable video, he also employs a group of women who brag to be f*cking 16 hours a day, going from one pregnancy to another, and being paid as "physicists" – from some European taxpayers' money – for allowing their names to be used in some ludicrous papers about the "quantum foundations".

In April, I discussed one of these crackpot papers in which Renner and Frauchiger asserted that quantum mechanics required many worlds. They used a straightforward physical system of 2 qubits – and several bases of their 4-dimensional Hilbert space.

How path integrals mirror Feynman's personality traits

The two-day silence is mostly due to the September 19th bike trip, 100 kilometers starting in the mountains (Bohemian Forest), sorry.

Courage, playfulness, analogies, shut up and calculate (calculation instead of words), lots of calculations extending simple rules, numbers instead of philosophy, don't give up easily

The most successful theories of classical physics may be formulated in terms of the principle of least action. We may consider alternative histories \(x_i(t)\) where some observables \(x_i\) depend on time \(t\). The principle says that the action \(S\) which is a functional of the history (a collection of functions) \(x_i(t)\) is minimized for the history that is actually allowed by the laws of physics:\[

\delta S [x_i(t)] = 0.

\] Paul Dirac has been convinced that this elegant formalism of classical physics – based on the concept of the action – should have a correspondingly nice role in quantum mechanics. And he found a good guess. In quantum mechanics, one could perhaps calculate the probability amplitudes for the evolution of \(x_i(t_1)\) to \(x_i(t_2)\) as \(\exp(iS/\hbar)\).

That was nice and Dirac presented some basic argument why the Lagrangian (whose integral over time gives the action) is related to the Hamiltonian but he didn't do much with this idea. It looked too heuristic to him.

Paquette vs Yin on the love-hate relationship between math and physics

In 2014, a few Nobel prize winners such as Sheldon Glashow along with the climate skeptic Richard Lindzen, Intelligent Design advocate David Berlinski etc., and a notorious moron Tim Maudlin have teamed up to create an online journal,

Inference-review.com,

a quarterly which is almost as influential as TRF now and where essays on the philosophy of science and reviews of books are regularly posted (I guess that there exists a printed journal, too). There must be lots of deep and inspiring texts over there but I have only learned about them today (although I may have been informed about the plans to establish it by one of the founders already in 2010) which is why my exposure to that journal may start at a somewhat random place (a metaphor for a point that will be made at the very bottom of this blog post).

Not too much time ago, Caltech string postdoc Natalie Paquette posted an essay

A View from the Bridge

that views mathematics and physics as peacefully co-existing traders. In the past, mathematics was helpful for physics. As you may have heard from Brian Greene, me, or someone else, their main relationship got mostly reversed due to the ability of string theory to produce gems that are cool from the mathematicians' viewpoint. She wrote an interesting review about some offspring of string theory that became important in mathematics: topological field theory, Donaldson theory, mirror symmetry, and monstrous moonshine, among others.

Only strings, not branes, can be consistently quantized in the same way

Jee_Jee has asked the following question:

Dear Lubos, thanks for this article. Please excuse my ignorance but could you please briefly explain why we don't find quantization of higher dimensional objects (such as branes) discussed in various standard references? Shouldn't the rules of QM determine the dynamics of branes too? Or may be it is done somewhere but I have not been able to find it.

Well, the reason why this "quantization" isn't discussed in any of these texts is that it is not possible. The question is analogous to the question: "Why don't textbooks of zoology feature photographs of flying elephants that would resemble the flying eagles?" You know, elephants don't fly. In the same sense, there is no "brane theory" that would be fully analogous to "string theory".

You can see a difference between the two situations: most kids can figure out that unlike eagles, elephants don't fly after some time – when they see no flying elephants. Jee_Jee has seen that no counterpart of string theory is being constructed with other objects – but he still believes that this non-existent entity exists. It must have been omitted because string theorists are stupid or they hide some dirty secret or something like that. Why does he believe such a thing instead of making the same straightforward conclusion as the kid makes about the flying elephants?

Top Czech players denounce Serena, her claims on sexism, an official support for her

Czech women don't have much tolerance for the so-called feminism. Many of us love America, some of us know it rather well, but people were getting increasingly familiar with the kind of shocking arrogance by women that was selectively encouraged by the pathological ideology of feminism.

The shocking events that were often started in the U.S. include the incredible witch hunt named #MeToo. A very recent event that shows a similar point was a hysterical meltdown of Ms Serena Williams, currently the #16 top female tennis player (WTA), with an umpire.

Czechia is a tennis superpower, one of the 3 countries that won the Davis Cup and Fed Cup on the same year, one of the most successful countries in these cups, and a cradle of numerous #1 players such as Lendl, Navrátilová, Kvitová, Plíšková.

Tim Gowers' conceptual thinking sucks

Four days ago, I discussed – and many of us talked about – the retroactive silent erasure of Ted Hill's already published article from an electronic journal because the paper implies conclusions that are considered politically undesirable. The focus was on the sociology and dirty politics.

Here I want to focus on the content of Ted Hill's paper (read on the arXiv) and the quality of its arguments and counter-arguments, especially those from Tim Gowers, a famous mathematician. Another famous mathematician, Terry Tao, wrote just three paragraphs whose main purpose seems to be to express some loyalty to the powerful leftwingers in his environment.

Petrov, Bashirov look suspicious to me

A week ago, I mentioned Petrov and Bashirov, two Russian nationals that were named as suspects in the Skripal poisoning case. I was mocking the British accusation but now I must say that the two Russian guys' defense looks even stranger and locally comical to me.

Read the transcript of an RT interview (The Telegraph)

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90-second video excerpt from that Margarita Simonyan interview; for full interview, see the bottom

It's really the cathedral that made me laugh. Just to be sure, I do realize that none of the feelings I have may be considered terribly strong evidence. People have different interests. And most importantly, if these two men attempted to poison Skripal and/or his daughter, it doesn't mean that the Kremlin or any other Russian authority is involved.

Article 7 against Hungary is an effeminate version of the 1956, 1968 invasions

When I returned home from a trip, one of the first news that appeared on the displays was that the European Parliament has voted to launch Article 7 against Hungary: 448 for, 197 against, 48 abstained.

It's a nuclear option allowed by the Treaty of Lisbon (a treaty that turned the European Union into a new Soviet Union a decade ago) that starts a process that may end up with the annihilation of Hungary's voting rights within the EU and/or all the financial inflows from the EU, among other sanctions. I hope and I still understand the situation so that Poland will ultimately be capable of vetoing all these plans (Article 7.2 still requires a unanimous vote in the European Council which has folks from all EU member states) but I am no longer sure. The EU could preemptively remove the Polish and Hungarian votes in the European Council and squeeze everyone else.

The same article has been launched against Poland – not by the European Parliament but rather by the European Commission (the "government of Europe"). Hungary considers the vote to be a fraud, a petty revenge for Hungary's asylum and immigration policies, and – as Orbán said – an insult to the Hungarian history. A Fidesz MEP called the decision "legally invalid" because voting rules were breached.



"The Mézga [Mr Badluck's] Family", here the theme music with Czech lyrics (orig. here; in Czech, the main characters got native Czech names), is the most famous Hungarian cartoon for my and somewhat older generation. It's a clear counterpart of The Simpsons except that the Hungarian show was 20 years older (1969-1978). The Simpsons were first aired in 1989. I think that (not only) Yankees should watch a couple of cartoons like that to get rid of the incorrect idea that the world would be impossible without the U.S.

The development wasn't quite unexpected but it's still infuriating to see that it has actually taken place. Most Czech voters must have been shocked what sort of unreliable allies in the Visegrád Group Czechia is. Ten Czech MEPs voted against the proposal to harass Hungary, nine MEPs have supported it. So a majority is against the proposal but the majority is infinitesimal. There are 4 deputies for billionaire PM Babiš's ANO movement among the 9 traitors – and, thankfully, zero MEPs for the center right ODS. The social democrats were perfectly diverse: 1 yes (the proposed minister of foreign affairs Poche), 1 no, 1 neutral, 1 absent.

French education minister: kids must learn Arabic

My countrymates are somewhat obsessed with watching the collapse of the politically Western civilization in the geographically Western Europe – we really need to distinguish these two types of the adjective "Western". One of the most recent shocking developments has something to do with France and the languages.

The French minister of education Mr Jean-Michel Blanquer has brought an ingenious new idea: French kids should learn Arabic (RT, Google News, original).

Why string theory is quantum mechanics on steroids

In many previous texts, most recently in the essay posted two blog posts ago, I expressed the idea that string theory may be interpreted as the wisdom of quantum mechanics that is taken really seriously – and that is applied to everything, including the most basic aspects of the spacetime, matter, and information.

People like me are impressed by the power of string theory because it really builds on quantum mechanics in a critical way to deduce things that would have been impossible before. On the contrary, morons typically dislike string theory because their mezzoscopic peabrains are already stretched to the limit when they think about quantum mechanics – while string theory requires the stretching to go beyond these limits. Peabrains unavoidably crack and morons, writing things that are not even wrong about their trouble with physics, end up lost in math.

Other physicists have also made the statement – usually in less colorful ways – that string theory is quantum mechanics on steroids. It may be a good idea to explain what all of us mean – why string theory depends on quantum mechanics so much and why the power of quantum mechanics is given the opportunity to achieve some new amazing things within string theory.