Posted by: Alexandre Borovik | June 17, 2021

The Azat Miftakhov Day: Videos are on Youtube.

Videos are on Youtube,

Fantastic mathematics lectures, and very powerful speeches from Cedric Villani and Ilia Kapovich.

Posted by: Alexandre Borovik | June 16, 2021

The Azat Miftakhov Day: Speech by Cédric Villani

The Azat Miftakhov Day  is now on and on the Youtube channel DayAzatMiftakhov
Text of the opening speech just given by Cédric Villani:
Dear friends and colleagues,
It is an honour — although a sad honour — for me to introduce this day of lectures, dedicated to our Russian colleague Azat Miftakhov. I thank the Azat Miftakhov Committee for their trust in inviting me to introduce this jade
Just a few days ago, I was among the group of mathematicians and officials who welcomed our Turkish colleague Tuna Altinel. For 2 years he had to endure persecution by the Turkish institutions, forbidding him to come back to his University in Lyon. A whole international community was mobilized in France and in Turkey. From the University to the city of Villeurbanne to the Parliament, to raise voice and accompany Tuna throughout each step of the kafka-style maze.
This was not the first time that I was involved in a team work to help the light shine again in the darkness. For years I have been one of those calling for a memory work in favour of the mathematician Maurice Audin, arbitrarily captured, tortured and killed in the Algeria war. It took more than sixty years between the moment when Audin was arrested, 11 June 1957 and the historical declaration of President Macron on 13 September 2018. Some of our mathematician colleagues such as Laurent Schwartz, Michel Broué, Gérard Tronel and many others have been quite active, starting with the public PhD defence of Audin, organised by Laurent Schwartz in the absence of Audin himself.
Today we are gathered for another one of these cases in which a fellow human is being prosecuted by an administration. It may look like an endless pit to go through all these individual cases! After all, it is estimated that there are more than 100 000 prisoners of opinion around the world. So why focus so much energy on individual cases? First, because each of them, as a fellow human, deserves our wholehearted support. As they say, “He who saves a single life, saves the world entire. » But also, some individual cases become emblematic of the cause, and have repercussions for many other cases. And, in the case today, this is one of our colleagues, member of our community, with whom we have shared work and mathematical dreams.
And so this is the fate of Azat Miftakhov today. 28-year old, originally from Tatarstan, pursuing studies of mathematics at Moscow State University, and now persecuted for more than 2 years. First arrested for « explosive manufacturing », with no proof, case dismissed, then re-arrested for breaking a window, one year ago, at an office of the United Russia Party, under the testimony of two secret witnesses, one of whom was already dead during the trial. Does it not sound like a joke?! No joke, Miftakhov was beaten by the police, Miftakhov was sentenced to 6 years of prison. It is heartbreaking to see Russia, with its glorious scientific tradition, still fighting with the demons of political persecution which broke the careers and lives of so many people.
It is my conviction that mathematicians and scientists always have to stand up against absurdity and unfairness and re-expose their faith in the power of daring thought, free speech and the combination of logics and imagination which is so important for us. In this very special day, we shall not only hear words from our very respected colleagues Anatoli Vershik and Tuna Atlinel, but also hear great mathematics by world-renowned experts. Maryna Viazovska rom the École Polytechnique Fédérale de Lausanne, Alexander Bufetov from CNRS, Institut de Mathématiques de Marseille, and Steklov Institute, and last but not least our young colleague from Bonn, Peter Scholze, who as you know received the Fields Medal in Rio 3 years ago. It is a pleasure to thank the French Mathematical Society for their support of this outstanding event.

The Azat Miftakhov committee:

Posted by: Alexandre Borovik | June 16, 2021

The Azat Miftakhov Day – Live broadcast

The Azat Miftakhov Day will take place this Wednesday June 16, 2021 starting at 4pm Central European Summer Time (UTC+2)*
It will be broadcast live on our website ( and on the youtube channel DayAzatMiftakhov.

It will be organized online by the Azat Miftakhov committee in solidarity with Azat Miftakhov, a graduate student from Moscow State University who was sentenced to six years in a medium-security penal colony and has already been arbitrarily detained by Russian state authorities for almost two years and half.

The Azat Miftakhov Day is sponsored by Société Mathématique de France (SMF). 

Here is the program:

4pm Cédric Villani (Member of the French National Assembly)

Opening speech

4:15 pm Maryna Viazovska (École Polytechnique Fédérale de Lausanne, Switzerland)

Sphere packings, universal optimality, and Fourier interpolation (abstract)

5:15 pm Alexander Bufetov (CNRS & Institut de Mathématiques de Marseille, France & Steklov, IITP RAS, Russia)

Determinantal point processes: quasi-symmetries, minimality and interpolation (abstract)

6:15 pm Peter Scholze (Universität Bonn, Germany)

Condensed Mathematics (abstract)

On Wednesday, June 16, please join the international mathematical community in showing solidarity with Azat.

The webinar will be broadcast live on our website and on the youtube channel DayAzatMiftakhov.


The Azat Miftakhov committee

* Tokyo at 11pm, Moscow at 5pm, Bonn, Paris and Warsaw at 4pm, London at 3pm, New York at 10am, San Francisco at 7am

Posted by: Alexandre Borovik | June 9, 2021

A white horse is not a horse

My attention was brought to this two millennia old paradox:

Horse can be black.

White horse cannot be black.

So white horse not horse.

See Wikipedia,  When a white horse is not a horse for a discussion.

This paradox is of interest to me because I started to think that one of the reasons of collapse of the New Math reforms in the 1960s and 1970s was introduction of sets and not predicates;  in my view, children appear to be more perceptive to the concept of unary predicate, or property. Properties are closely related to sets, but they are not sets. I was unaware that the universe of properties also has its share of paradoxes.

A colleague wrote to me as a comment on my paper

A. Borovik, A mathematician’s view of the unreasonable ineffectiveness of mathematics in biology. Biosystems 205, July 2021, 104410, :

On the subject of unreasonable ineffectiveness, here’s a hilarious problem that might have a mathematical solution, but seems well outside the scope of current mathematics. […]

The Centipede Segmentation Problem: Prove that it is impossible to have a centipede that has an even number of pairs of legs, or 17 or 19 pairs of legs.

Apparently, there are fairly good datasets in biology which suggest that this is the case:

This reminds me one of the greatest mysteries of the Forest in Strugatsky Brothers‘ novel “The snail on the slope” from 1960s: the number of pups in a brood is always a prime number.

Their novel is admittedly the greatest book of Russian sci-fi, fantastically multifaceted; in particular, it is a vicious satire of the Soviet system, Soviet society, and Soviet science. The Forest is a symbol of many things, and one of them is unreasonable ineffectiveness  of not only mathematics, but also any kind of science in comprehension of Life.

You may skip most of the fragment from the novel that I included — I highlighted a few key lines at the end of the fragment.

The pups had already gone quite a way, but Stoyan, driving with great skill, keeping the offside wheels on the path and the nearside on the dusty moss, soon overtook them and crawled slowly behind carefully using the clutch to adjust his speed. […]

Pepper stroked his swollen finger and looked at the pups. The children of the forest. Or perhaps its servants. Or maybe its experiments. They were proceeding slowly and tirelessly one after the other in line ahead, as if flowing along the ground; they oozed across rotting tree stumps, crossed ruts, pools of stagnant water in the tall grass, through prickly bushes. The track kept disappearing, diving into evil-smelling mud, hiding itself under layers of tough gray mushrooms that crunched under the wheels, then again appearing, while the pups held their direction and stayed white, clean, smooth; not a blade of grass stuck to them, not a thorn wounded them, they were unstained by the sticky black mud. They oozed along with a kind of stupid unthinking confidence, as if along a road long-known and habitual. There were forty-three of them.

I was dying to get here and now I’ve arrived, at least I’m seeing theforest from inside and I’m seeing nothing. I could have imagined all this sitting in my bare hostel room with its three empty bunks; late night insomnia, everything quiet all about, then right on midnight the piledriver starts thumping on the construction site. I could have thought it all up: mermaids, walking trees and these pups, turning into pathfinder Selivan–the most absurd things, the holiest. And everything there is in the Directorate I can imagine and bring to mind. I could have stayed at home and dreamed this all up, lying on my sofa listening to symphojazz or voices talking unfamiliar languages on the radio. […] But that doesn’t mean a thing. To see and not understand is the same as making it up. I’m alive, I can see and I don’t understand. I’m living in a world someone has thought up without bothering to tell me, or maybe even himself. A yearning for understanding–that’s my sickness, thought Pepper suddenly, a yearning for understanding.

He stuck his hand out of the window and held his aching finger against the cool car-body. The pups were paying the landrover no attention. They probably had no suspicion of its existence. They gave off a sharp unpleasant smell; their membrane now seemed transparent and it was as if wave-like shadows moved beneath.

“Let’s catch one,” suggested Quentin. “It’s simple enough, we’ll wrap it in my jerkin and take it to the lab.”

“Not worth it,” said Stoyan.

“Why not?” Quentin asked. “We’ll have to catch one sooner or later.”

“Doesn’t seem right, somehow,” Stoyan said. “In the first place, God help us, the thing’ll die on us and I’ll have to write a report for Hausbotcher.”

“We’ve had them boiled,” Acey announced suddenly. “I didn’t like the taste, but the boys said it was all right. Bit like rabbit, I can’t touch rabbit, to me a cat and a rabbit’s just the same; can’t bear the stuff… .”

“I’ve noticed one thing,” said Quentin. “the number of pups is always asimple number: thirteen, forty-three, forty-seven… .”

“Nonsense,” objected Stoyan. “I’ve come across groups of six or twelve.”

“That’s in the forest,” said Quentin, “after that groups scatter in different directions. the cesspit always produces a simple number, you can check the log, I’ve put all my conclusions down.”


“Well all right, write an article then,” said Stoyan.

“I already have,” said Quentin.

Translation from Russian by by Alan Meyers, 1980.

Posted by: Alexandre Borovik | April 13, 2021

Help Leicester Pure Maths fund Legal Support

Sibylle Schroll would like you to support Help Leicester Pure Maths fund Legal Support by making a donation and spreading the word.

About this fundraiserThe faculty of pure mathematics at Leicester needs your help. They would like to hire legal counsel in relation to the circumstances described in the links below:

What is GoFundMe?

GoFundMe is the world’s largest free social fundraising platform and has helped millions raise over $5 billion for the people and causes they care about.

Posted by: Alexandre Borovik | April 13, 2021

Tuna Altinel: detained in Turkey for two years now

Istanbul, April 12, 2021

Friends in solidarity,

Today is April 12, 2021. I have been detained in Turkey for two years.

It was two years ago today that my passport was confiscated in Istanbul, as a way to punish me for
exercising my freedom of speech in France. Since that day I had to confront the stubborn silence of
an autocracy, imprisonment, unfounded prosecutions, the obstinate recalcitrance in the face of my
acquittals, the constant refusal to return my passport. The State that put me through this ordeal did
not hesitate to violate its own laws.

During these two years, an international movement of solidarity has grown up around me. I wish to
thank all those who have taken part. Before such a massive support of democratic values, the dykes
of autocracy have crumbled: unlike most political prisoners in Turkey, I was quickly released from
jail; I was acquitted; the Regional Court ruled promptly on the appeals. Finally, on April 2, the
administrative court to which I had submitted an appeal of the refusal to return my passport has
ruled in my favor.

Friends in solidarity, do not be abused! This is not the end. Before us stands a lawless and arbitrary
power. The administrative court actually reached its decision as early as January 25, 2021, that is
two months and a half before I was notified. Such a delay has no legal grounds. The State, which
forced its own judges to this outrageous deferral, will not neglect to submit its appeal within 30
days (the legal deadline).

I call on all democratic forces in France. A new phase, hopefully the last, of this race of indefinite
duration has just begun. We must remain mobilised.

Tuna Altınel


There was a much advertised (at least in the UK)  high level UN Security Council meeting on Climate Change on 23 February 2021 (online, chaired by Boris Johnson, UK Prime Minister). It appears  that the meeting has been hastily downgraded to  a non-event after Sir David Attenborough, addressing the Security Council in a short speech, said  something unspeakable:
“We have left the stable and secure climatic period that gave birth to our civilisations. There is no going back – no matter what we do now, it’s too late to avoid climate change and the poorest, the most vulnerable, those with the least security, are now certain to suffer.”
This segment of Sir David’s speech was not included in the BBC video clip  “Attenborough gives stark warning on climate change to UN – BBC News”A,, and reports about the meeting (and Attenborough’s video) almost instantly disappeared from the BBC front page. However, the segment can be found on Sky News,  The entire 8 minute video of Attenborough’s speech  is on the UN site:
On the optimistic note,  Sir David said
“I do believe if we act fast enough we can reach a new stable state. It will compel us to question our economic models and where we place value; invent entirely new industries; recognise the moral responsibility that wealthy nations have to the rest of the world and put the value on nature that goes far beyond money.”
It appears that there is a coherent, and well supported by archaeological and geological evidence, theory behind Sir David’s words; his speech cannot be easily dismissed as fantasy.
I summarise some points of this theory which I happened to learn from various sources  over the last 20 or maybe even 30 years. I am not an expert, and I would much appreciate corrections and further details.
  1. The current period of stable climate which allowed the human civilisation to develop, was about 11 thousand years long, and it was abnormally long on the scale of the last 50 or 100 thousand pretty turbulent years.
  2. The last violent episode which preceded our  golden era was a circulation event triggered by a flood of fresh water from the melting glaciers in North America which directed the Gulf Stream to Africa rather than Europe, correspondingly directing the jet streams in atmosphere over North Atlantic to south of Europe. This meant that temperatures at what now is London were like in nowadays Irkutsk. But Sahara got abundant rain and was covered by forests and lakes with hippos and crocodiles, and flamingos — immortalised in cave paintings (made by us, humans, who happened to migrate there at that time).
  3. All that is dated with surprising precisions by pollen from flowering plants preserved in sea sediments. The most interesting bit  is the length of transitional period between the two climate regimes — just about 10 years.
  4. A similar event can be triggered by collapse of glaciers in Greenland as the result of  melting water accumulating  in under  ice lakes and eventually finding its way to the ocean.  I would not claim, however, that this is to happen tomorrow. But something like that has already happened once.
  5. Of course, climate can mutate in many other directions, including Britain becoming, in hte new stable state of climate,  a subtropical country and Scotland replacing thistle, as its national symbol, by artichoke (Wiki:  a variety of a species of thistle cultivated as a food).  I’ve seen plantations of artichoke in Turkey, they look hilarious.
  6. The Gulf Stream example suggests that switching to the new stable period could be short, but interesting.
  7. My last comment is on artichokes and jet streams. The most poignant artichokes I have seen in Turkey were on what was, two millennia ago, the river bed of Meander, the great river of Asia Minor, now almost dry. The history of glorious civilisations of Mediterranean and Middle East was the history of ecological disasters created by people. It is hard to believe now that North Africa and Turkey were covered by  subtropic forests. Well, England not long ago was covered by mighty oaks, and Scotland — by pines, and the famous heather moors is a secondary landscape, an ecological system which replaced forests destroyed by people, and which is much more fragile than forest.
  8. Meander became a verb  (with the meaning `follow a winding course’)  because the river was bending, creating loops, etc. Last time I’ve seen this word — to meander — was  in relation to jet streams over North Atlantic which started to meander. Water flows against the gradient of altitude of the surface and starts to meander, that is, the flow is becoming unstable, if the gradient is too small. It is claimed that the same happens with jet steams: they flow against the gradient of temperature, and are destabilised by warming up of Arctic which is decreasing the gradient.  There is a possibility that the climate of British Isles can change even without dramatic events in Greenland.
The reasons or triggers for climate change — a becoming a scholastic issue now.  What matters is
A. Ecological systems around the world are weakened and under stress, and their ability  to cope with changes in climate is compromised.
B. The ability of humans, as species, to cope with the change  is also compromised. On one hand, we reached a fantastic level of technological development  (which,  of course, helps) — but on the other, this technology is not equally shared, and, on the top of that:
C. This is the greatest unspeakable issue — the Earth is overpopulated by humans beyond sustainable levels.
D. In point C, the words “beyond sustainable levels” should of course be understood as “at levels unsustainable under the current socio-economic systems prevalent in the world and interconnected within the single global economy”.  However, any  change of the socio-economic systems on that scale is a task perhaps even more challenging than dealing with the climate change itself. It is likely that the number of people killed in the process will be comparable with loss of life in all natural disasters and pandemics triggered by the climate change.
 I do not claim that I am right or correct in every detail. But my message is:
The problems of the Earth and of the human civilisation on the Earth reached the level when they can no longer be entrusted to politicians and journalists — and neither can be left to the social media. The readers of my blog are a few but they tend to be educated people with proven skills of analytic thinking — if you read this, please allocate some of your time to analysis of all that mess.
The 21st century starts now, in 2021 — the same way as the 20th century started in 1914 with World War I.
Posted by: Alexandre Borovik | February 21, 2021

How do illogical proofs or answers “feel” to mathematicians?

My answer to a question on Quora: My high school math teacher often made rudimentary mistakes in her equations. What does that say about her?

This could be turned into a good learning experience for you: watch your teacher and try instantly identify her mistakes and correct them – for yourself. I had this experience in my school days, and remember it fondly. It really helps to start mastering mathematics.

It is up to you to decide whether to try to correct your teacher in front of the class, but remember, it could be very cruel to her, you may regret that later. It would be much more useful to quietly provide your classmates with correct solutions.

And maths teachers in schools are frequently overworked. And what do you know about her home life? She could simply suffer from long term sleep deprivation. Especially in the present crazy times…

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