Posted by: Alexandre Borovik | September 13, 2022

A court decision denies Azat Miftakhov early release on parole

On Monday, September 12 a court in Omutninsk denied Azat Miftakhov an early conditional release on parole. The correctional colony administration gave Azat a negative recommendation.

The colony authorities recently gave Azat a formal reprimand, on a manufactured charge of supposedly violating a rule about the number and size of photographs he is allowed to keep.

Prior to the court hearing the colony authorities also had Azat complete a lengthy psychological evaluation questionnaire, which is standard practice when they are trying to sink a prisoner’s chance for parole.

After this court decision Azat is expected to remain in the prison colony for another year, until September 5, 2023.

On the same day a different court, in Chelyabinsk, declared the Russian anarchist movement “People’s self-defense” a ‘terrorist organization’ and banned it throughout Russia. Azat had been formally accused by the FSB of being associated with “People’s self-defense”.

The Azat Miftakhov Committee continues to call for Azat Miftakhov’s immediate release from prison, so that he can resume his mathematical studies and research.

The Azat Miftakhov Committee

My answer to a question in Quora: Why do pure mathematicians keep proving new theorems but don’t know their applications in real life?

I am a pure mathematician, but I have some experience of solving raw engineering problems, that is, problems where engineers have no vaguest idea what kind of mathematics could be applied. In one peculiar case I was using in my solution the classification of finite simple groups, the one of the most notorious achievements of the 20th century algebra — its original solution was spread over 100+ journal papers of about 10,000 pages in total (and contained gaps and holes which required additional hundreds of pages of proofs). It is hard to imagine anything more pure and remote from the so-called “real life” then the classification of finite simple groups.

I already said somewhere on Quora that

mathematics can be useful, but what makes it useful is not the same as what makes it mathematics.

Mathematics is a living organism which has to meet its own needs just to stay alive. It can be usefully compared with a cow. Cow is useful, for example, she gives us milk. Her udder definitely belongs to applied mathematics. But let us accept that the whole remarkably useful cow is applied mathematics.

The cow needs food and water, and air for breathing, etc. For production of milk, once in a year cow needs a rendezvous with a bull. We may perhaps compare pure mathematics with this bull.

Then I comment on a someone else’s answer:

Someone’s answer: There was a mathematician who believed math to be irrelevant if it had real world applications, so he devised a branch of mathematics using only on/off states. His name was George Boole, and the Boolean math he created is the basis of most of the electronic devices in use today. You don’t know what will become useful, but the math will be there for it.

My comment:

I disagree with your assessment of Boole. He designed what is now known as Boolean algebra as a way of checking and resolving logical arguments by some kind of arithmetic with True and False being values used in place of numbers. Prior to 19th century (when Boole lived) the use of logic was confined to Theology and Law, and Aristotelian logic taught to students (as a rule, of privileged classes) who were supposed to become priests or lawyers. As it is clear from his writing, Boole had aim to create logic for the masses, mental tools assisted by calculation on paper, for ordinary working people to understand, for example, court proceedings. He was, in nowadays terminology, a social activists: fought for improvement of working conditions for shopworkers, founded schools, credit unions, etc. The purpose of logical calculus that he invented was very pragmatic.

My answer to a question on Quora: Have you ever gotten answers by intuition in math but don’t know how to explain it?

In mathematics, an answer without explanation (proof) is not an answer. What you call “answer” or “result” (while this result is still not proven) is called a “conjecture”.

  • Yes, mathematicians systematically produce conjectures in the process of work.
  • Yes, they frequently do that using their intuition.
  • These conjectures could be proved (sometimes much later) , or get refuted and die.

Refutation is no less important than proof. Without refutation, mathematics is a car without brakes.

In my life, I produced hundreds of conjectures. Most of them died, some instantly. Some are still open – that is, not proven and not refuted.

My answer to a question on Quora: If you are an autodidact, do you think you were born that way, or did you get so curious because of the environment you grew up in?

If you are an autodidact, what is the “actionable information” in an answer to this question? What will you change in your behaviour after receiving a definite answer “this was all nature” or “this was all nurture”?

But if you are a young parent of a child, I think it is my duty to you to say that I think that all children are born instinctive autodidacts, but this trait is usually destroyed in them by their upbringing in the family, school, etc.

In a parallel development, all children are born with natural abilities for mathematics, but by the age of 16 this gift is usually completely destroyed in them by the criminally bad mathematics education — this is why it is considered to be so rare and so precious.

Posted by: Alexandre Borovik | September 3, 2022

Is relearning math like relearning how to ride a bike?

My answer to a question on Quora: Is relearning math like relearning how to ride a bike?

An excellent question!

It is impossible to unlearn to ride a bike, or to swim, or to drive a car. The same applies to mathematics. But you may need a refresher course, or just some personal time and effort to restore your skills to the previously achieved level. Moving further than that is of course possible, but is more challenging and requires additional effort. What can I add? Be brave and go for it!

Posted by: Alexandre Borovik | August 29, 2022

Implementation of the Kid Krypto Concept

On request from colleagues, I reposted my paper of 2002:

Alexandre V. Borovik. Implementation of the Kid Krypto Concept. Selected Passages from Correspondence with Friends 10 no.~1 (2022), 1–4.

20 years since publication, it was nowhere to find on the Internet. Sic transit gloria mundi.

Posted by: Alexandre Borovik | July 12, 2022

Azat Miftakhov Days Against the War – Program – July 5-6, 2022

In view of the unprecedented brutality and destructiveness of Russia’s criminal aggression against Ukraine, we have renamed our event, that was originally announced before Russia’s invasion of Ukraine, into “Azat Miftakhov Days Against the War”. As we continue to fight for Azat’s release from prison, we stand in solidarity with the Ukrainian mathematicians and the people of Ukraine who suffer the terrible brunt of the war.

The Azat Miftakhov Days Against the War will take place on Tuesday and Wednesday July 5-6, 2022, in solidarity with Azat Miftakhov, a mathematics graduate student from the Moscow State University who has been arbitrarily imprisoned by Russian state authorities since February 2019.

This event is sponsored by the French (SMF and SMAI), EuropeanBelgian and Catalan Mathematical Societies. It is also announced by the American Mathematical Society and the London Mathematical Society.

Registration is mandatory by filling out the form here.

Tuesday July 5, 2022 from 4pm to 7pm Central European Summer Time (UTC+2) – online

4 pm Opening remarks

4:10 pm Alexander Petrov (MPIM)
Title: Representations of Galois groups and families of algebraic varieties (abstract)

5:10 pm Ilya Dumanski (MIT)
Title: Schubert varieties in the Beilinson-Drinfeld Grassmannian (abstractslides)

6:10 pm Slava Rychkov (IHES)
Title: “Bootstrap” method in physics and mathematics (abstractslides)

Wednesday July 6, 2022 from 5pm to 7pm Central European Summer Time (UTC+2) – hybrid

A panel to assess the human rights situation in Russia through the cases of persecuted academics, coorganized by the Azat Miftakhov Committee and the prominent Russian NGO Memorial Human Rights CenterThe panel will make a special emphasis on the Russian academics and students persecuted for opposing Russia’s war in Ukraine.

For technical reasons related to the hybrid nature of the event, this panel is transferred to the Institut des Hautes Études Scientifiques (IHES) in Paris. Instructions to access IHES are available here.

We are very pleased to announce the participation in this panel of

– Chandler Davis, mathematician, University of Toronto

– Alexander Cherkasov, Chair of the Council of the Memorial Human Rights Centre

– Fabien Durand, President of the French Mathematical Society

– Elena Gorban, Azat Miftakhov’s wife

– Anatoly Vershik, former president of the St. Petersburg Mathematical Society, member of the European Academy of Sciences, chief researcher of the St. Petersburg section of the Steklov Institute of Mathematics of the Russian Academy of Sciences

– Barry Mazur, mathematician, the Gerhard Gade University Professor at Harvard University, member of Scholars at Risk Harvard

– Grigory DurnovoOVD-info

– Maria Menshikova DOXA

– Vera Chelishcheva, independent journalist

– Ilya Nuzov, Head of Eastern Europe and Central Asia Desk for the International Federation for Human Rights (FIDH)

– Rachel Denber, Deputy Director of the Europe and Central Asia Division of Human Rights Watch, specializes in countries of the former Soviet Union

– Natalia ZviaginaAmnesty International Moscow Office Director

– Martin Andler, mathematician, Université de Versailles St Quentin, for Memorial France

Registration is mandatory by filling out the form here.

Further information will be available on

The Azat Miftakhov Committee

#StandWithUkraine 🇺🇦

Posted by: Alexandre Borovik | March 21, 2022

Azat Miftakhov Days – July 5-6, 2022

Azat Miftakhov Days – July 5-6, 2022

Registration is mandatory by filling out the form here.

We are pleased to announce that the second Azat Miftakhov Days will take place on Tuesday and Wednesday July 5-6, 2022, in solidarity with Azat Miftakhov, a mathematics graduate student from the Moscow State University who has been arbitrarily detained by Russian state authorities since February 2019. Azat has been mistreated and tortured by the authorities while in detention. His trial, which took place after much delay in the Fall of 2020, was based largely on the testimony of “secret” government witnesses. In a grossly unjust and excessive decision, in January 2021 a court in Moscow sentenced Azat to six years imprisonment in a penal colony for “hooliganism”. Azat is currently serving this sentence in a labor colony in Omutninsk.

  • Tuesday July 5, 2022 from 4pm to 7pm Central European Summer Time (UTC+2) – online

On the first day, we will honor the new generation of Russian mathematicians committed to human rights. The speakers are Ilya Dumanski (MIT), Alexander Petrov (Harvard) and Slava Rychkov (IHES). Their mathematical lectures will be broadcast live on Zoom and youtube.

  • Wednesday July 6, 2022 from 5pm to 7pm Central European Summer Time (UTC+2) – hybrid 

On the second day, we will co-organize with Memorial Human Rights Center a panel to assess the human rights situation in Russia through the cases of persecuted academicsThe panel will be hybrid, online and in person at the École normale supérieure in Paris, open to academics, human rights organizations and journalists.

On 29 December 2021, the Moscow City Court has ordered the closure of the prominent Russian NGO Memorial Human Rights Center for allegedly violating “foreign agent” legislation. Founded in 1991, HRC Memorial is one of the most respected human rights organizations in Russia and in the world. The prosecutors claimed that HRC Memorial repeatedly violated the “foreign agents” law by refusing to label their content as produced by a “foreign agent”.  They also claimed that HRC Memorial justified “terrorism and extremism” by keeping a list of people detained for political reasons on its website. The list featured individuals imprisoned following unfair, politically-motivated trials, including Azat Miftakhov. On 28 December 2021, the Supreme Court ordered the liquidation of its sister organization, International Memorial.

The first Azat Miftakhov Day organized last year, attracted over 1600 participants and raised awareness in the mathematical community of the injustice suffered by our young colleague. We are counting on your participation in this second edition to send a strong message of solidarity to Azat and to press for his immediate and unconditional release.

Registration is mandatory both for participation online or in person. The registration form is available here.

Further information will be available on

The Azat Miftakhov Committee



Sponsored by
Posted by: Alexandre Borovik | July 31, 2021

Strong Beard Game

The memorial plaque for John Venn (1834 – 1923) in Drypool, Hull, England, contains a mysterious phrase:


John Venn is, of course, is a mathematician who proposed Venn diagrams, this is clear. But the phrase

Really strong beard game

is more interesting. “Really strong X game” can be found in print media and on the Internet for some other value of X as well. It means that something is impressively done (or, by extension/humor, impressive). Taking into consideration his social class, Englishness, and times of his life, it suggests connections with cricket — in those days, more fanatical cricket  players frequently exhibited very impressive beards. This my conjecture was immediately confirmed by brief glance in the Wikipedia. First of, all John Venn’s beard:

John Venn (1834 – 1923)

Secondly, a quote from Wikipedia:

He built rare machines. A certain machine was meant to bowl cricket balls. The machine was so fascinating that when Australian cricketers were visiting Cambridge, the machines were used to entertain their arrival. The bowl cricket ball machine that Venn built actually bowled out the top ranked player of the team four times consecutively.

Posted by: Alexandre Borovik | June 24, 2021

From Kant, and applicable to mathematics

Attributed to Kant:

We understand nothing so well as that which we could also make, if we were given the necessary material.

Mathematics has its owns means of providing material.

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