30 December 2008

Prayer for the Riemann Hypothesis

In October 2008, I submitted a prayer at the Prayer Request Site asking for a zero of the zeta function with real part different from 1/2. I gave to whomever fulfills these prayers (let's call it god) a deadline of a month. As the deadline is well over, I can now safely declare that

god told me that there all zeros of the zeta function have real part equal to 1/2; in other words, god told me that the Riemann Hypothesis is true.

An unsolved problem in Mathematics has been solved by the mere intervention of the owner of the Prayer Request Site, i.e. god. Isn't it amazing how prayer works?

Not being ungrateful, I submitted a thank you note at the Prayer Request Site:

Thank you for showing me that the Riemann Hypothesis is true: all zeros of the zeta function have real part equal to 1/2. Can you please help me write a paper now? Or is it sufficient to simply declare that you told me so?

29 December 2008

Saint Joseph Stalin

A couple of years ago, a certain Aleksandr Filippov wrote a history textbook, titled “Russian History, 1945-2007”, for Russian schoolchildren. In it, he returns to an almost Soviet view of Stalin's legacy, claiming that there were "rational reasons behind the use of violence [by Stalin] in order to ensure maximum efficiency". Stalin is being hailed as an efficient manager who [merely] had to resort to extreme measures to modernize the lumbering of Soviet agrarian economy.

In a review of the textbook by Irina Karatsuba, historian and associate professor in the Department of Regional Studies at Moscow State University, we read that "this was without doubt a paid-for textbook, written on someone’s orders, phony all the way through", that "Putin is the second most effective leader the country has ever had, after Stalin".

There is, indeed, a movement in Russia aiming towards the rehabilitation of Stalin. Putin himself is, certainly, behind it. Recall that Putin's dream is to be buried next to Stalin. In the revisionist scheme, the Orthodox Church cannot remain indifferent. Indeed, icons of Stalin have already appeared:

The icon on the left shows Stalin standing before the Blessed Matrona of Moscow, a 20th-century saint. According to legend, Stalin would frequently talk to the woman who gave him advice on how to defeat Nazi Germany in World War II.

The icon on the right depicts Stalin himself as a Saint.

Absurdities? Stupidities? Irrational acts? Indeed, all of the above and more. Revising history happens all the time in all countries. Even if we now, most of us, see the aforementioned revision as totally irrational, it may, in the end, become the norm: if a lie keeps being propagated by an official source for long time then it persists; people forget and the next generation is brought up starting from different initial conditions. And we all know that getting rid of (bad) initial conditions is tough.


1.Irina Karatsuba's review:
This past summer I read this textbook in detail and took part in a round table discussion organized by the journal “Bolshoi Gorod” in which the textbook was discussed. After studying Filippov’s textbook and discussing it with the authors, I came to the inescapable conclusion that this was without doubt a paid-for textbook, written on someone’s orders, phony all the way through. It is based on one very dangerous idea, which can be summed up succinctly as, “The State is everything, the individual nothing.” Regarding the current regime, the textbook is absolutely servile, stating simply that Putin is the second most effective leader the country has ever had, after Stalin. And this is the crowning glory - there is nowhere higher to go. For this reason, of course, its introduction into schools in any capacity (and I think it will be introduced, as the leading textbook) can bring only harm.

The textbook automatically brings to mind how we all once studied. Soviet textbooks contained not a word of truth, of course, and no one took them seriously, nor did they expect to learn anything from the subject of history, but searched for the truth instead on their own. I recall how a textbook I was once studying (I graduated from high school in 1977) said that “the careerist Ezhov and the political adventurist Beria, using some of Stalin’s personal marks, fabricated accusations that resulted in the deaths of tens of thousands of Communists.” Reading this, at age 16, I thought to myself: But how could these two people, with the help of a third, kill tens of thousands of people… What kind of regime was this? I think this is about the line of thought that will be followed by those who study from Filippov’s textbook.

But for me, as a professional, this is of course sad, because it is not just a step backward, but ten steps backward in comparison with the textbooks that were written at the end of the 1990’s and the beginning of this decade. And I am very bitter about how the textbooks of Dolutskiy and other authors are being replaced with nonsense like this.

This event is not, of course, unique. It is part of a general process of searching for a new Russian identity. A reconsideration of the Soviet period is taking place, expelling the odious waste of “the terrible 1990s” (although the current occupants of the our political Mount Olympus during the same 1990s all occupied high-profile posts) - this is all part of the creation of a myth about ourselves. But this myth is phony through and through, and worse than that it is immoral, because it sanctifies the spilling of blood and use of violence. It just perpetuates a falsehood. All of which brings to mind the words of the 16-th century Russian essayist Ivan Peresvetov, who wrote to Ivan the Terrible, “In Russian czarism there is belief, but no truth. But God does not love belief. He loves the truth.” Immortal words.

I would also recall the words of Petr Chaadaev, who wrote in 1837 that “The era of blind belief has passed. I think that now the truth is our greatest obligation to the Motherland.” Alas, this was such a premature hope, because even today this “now” has not yet arrived. But what will become of our Motherland, and of the truth, if this “now” never arrives?

Of course, the universities cannot be separated from society as a whole, and this false conception of history is beginning to penetrate them as well. One of the authors of the textbook, Leonid Polyakov, is professor of at the Higher School of Economics. This is a person who has said the most incredible things lately, such as that “we really never know what happened in the past”, and we need a positive myth about ourselves… In other words, we should just make ourselves look good, tell ourselves falsehoods - that this will help us. I do not understand how it is we can build something on falsehoods that will help us. But beyond this it becomes an issue of individual honesty, and I cannot believe that the majority of my colleagues, in either the universities or schools, will be inclined to teach according to the Filippov textbook. On the contrary, I have seen only shock, deep shock, in reaction to this textbook. The academic and teaching communities will oppose this textbook; they are already opposing it.

2. Another example of history revisionism: Almost every Greek will now tell you that the revolution against the Ottomans has started from within the Church and that the Bishop Germanos of Patras (Georgios Gotzias 1771-1826) proclaimed the national uprising on 25 March 1821 (national day of Greece). This is a mere myth. The truth is that the Greek Church did not want any uprising at all because the priests had a special status in the Ottoman Empire as tax collectors and hence benefiting themselves from the money deals with the Turks. In fact, when Patriarch Gregory V (Georgios Angelopoulos 1746-1821) failed to suppress the revolution, the Turks hung him. The Greek State revised the history, and now this Patriarch is now a Saint of the Orthodox Church. (To be fair, it is true that the hanging of the Patriarch was, indeed, perceived as an atrocious act amongst Greeks and did help in creating a national sentiment, so, indirectly, it did help the uprising. But it seems that the Patriarch himself had no intention of supporting a revolution against the Turks.)

24 December 2008


Gallica is the Interner digital library of the National Library of France. It was established more than 10 years ago. To-date, it hosts about one hundred thousand books, most in scanned form. Everything is available for free. It is a treasure for those who do not have direct access to the original sources, such as the works of Henri Poincare (see e.g. `La Valeur de la Science'). There is a lot of information out there, but verylittle time. A few thoughts come in mind: (1) How can we use the information efficiently? (2) It is, after all, true that our hours are minutes when we wait to learn and centuries when we know what is to be learnt, as António Machado says.

Incidentally, Newton's birthday (the image above is from one of his major works) is tomorrow, 25 December.

17 December 2008

New high tech game

A new family game has just made its appearance on the Internet. It's a perfect Christmas activity for the whole family:

As of 17 December 2008, 13:30, more than 7 million shoes have successfully hit Dubya.

15 December 2008

The h factor

Academic and research administrators have an interest in reducing one's work into a single number. Ideally, they claim, they could use a single number to decide whether researcher A is better than researcher B. The actual reasons behind such claims are that the majority of administrators (academic department chairmen, directors funding agencies, heads of laboratories, etc) cannot understand each researcher's work, and also want to minimize their time in giving a judgment: they can, with the click of a button, order researchers in a line a button and finish their work in five minutes.

In fact, there is a "science" being developed, called "bibliometrics" (see here, here, here and here) aiming at producing such indices. The most (in)famous of these indices is the h factor (not the x factor--this is a TV programme--see below). The h factor is defined as follows: If a researcher has n papers cited n times each then his or her h factor is at least n. In fact the h factor is the largest such n.

For example, if a researcher has written one paper which is cited 1000 times and 9 other papers which are cited once each then his h factor is 1. If researcher B has written 3 papers, each cited twice, then her h factor is 2. Hence B is better than A (an administrator would conclude).

A recent report by Robert Adler (Probabilist of the Technion–Israel Institute of Technology), John Ewing (Executive Director, American Mathematical Society, and Peter Taylor (Probabilist, University of Melbourne) show that "citation data provide only a limited and incomplete view of research quality, and the statistics derived from citation data are sometimes poorly understood and misused; [r]esearch is too important to measure its value with only a single coarse tool". It's an interesting read.

However, I admit that the report may not be as much fun as an x factor episode:

Just to make things clear, the guy in this video is not looking for an h factor, but an x factor. (Some colleagues tell me it's more or less the same thing though.)

4 December 2008

Happy Newtonmas cards

I designed some cards for the season. Please feel free to copy, print on hard paper, and send them around. There is a front side and a back side which should be glued together. Depending on taste, you may pick any of the front side versions.


What measure theory is about

It's about counting, but when things get too large.
Put otherwise, it's about addition of positive numbers, but when these numbers are far too many.

The principle of dynamic programming

max_{x,y} [f(x) + g(x,y)] = max_x [f(x) + max_y g(x,y)]

The bottom line

Nuestras horas son minutos cuando esperamos saber y siglos cuando sabemos lo que se puede aprender.
(Our hours are minutes when we wait to learn and centuries when we know what is to be learnt.) --António Machado

Αγεωμέτρητος μηδείς εισίτω.
(Those who do not know geometry may not enter.) --Plato

Sapere Aude! Habe Muth, dich deines eigenen Verstandes zu bedienen!
(Dare to know! Have courage to use your own reason!) --Kant