Analysis of mathematical flights on the Hirsch index

Interviews of Natalia Demina , published in TRV No. 218, RAS academician Vasiliev and laureate of the Prize, Fields Stanislav Smirnov, caused a great discussion, both from those who support the choice of wound mathematics and those who believe that serious mistakes were made.

One of the opponents, A. D. Polyanin from the Institute of Problems of the RAS mechanics, previously feared to call his name, and the TRV editors welcomes the fact that he now openly publishes his note under his name. It is interesting that earlier in his notes, who were sent by e-mail, there were claims to the size of the Hirsch Member of the Russian Academy of Sciences A. G. Kuznetsov, but after checking the data conducted by academician Vasilyev, these claims were removed.

Open letter to the editorial office of "Trinity Option"

Chief editor B. I. Stern

Deeply beloved Boris Evgenievich!

In the Triv-Hunger No. 24 (218), a selection of materials was published about the recently held elections to the Russian Academy of Sciences. In particular, they consider elections in the department of mathematical sciences in which I participated. In connection with the disease of the Academician-Secretary of the OMN RAS L. D. Faddeev, I was instructed to conduct meetings of the section "Mathematics" of the department. So I have all the information about the elections and I would like to comment on your publications, since they give a distorted idea of ​​both the process and the results of these elections.

Both in your newspaper and in many other responses were criticized by the non -removal of the winner of the Field Prize S. K. Smirnov as an academician. At the same time, nowhere is it said about the true situation that has developed in his election. In fact, S. K. Smirnov was elected academician of the present part of the Mathematics section. He received 11 votes of the possible 15, i.e., more than two -thirds of the votes participating in the vote, which is a decisive condition for the election. However, the charter of the Russian Academy of Sciences has an additional condition under which the number of votes should be at least half the number of the list of the section (23 academicians).

This condition was always executed with more than, but not in this case. In the past elections, there were no 8 academicians, 6 due to illness, two, professors of American universities, and semester held at their universities. I think that many of them would support Smirnov's candidacy. So it is difficult for me to agree with the opinion of my colleague in the department of V. A. Vasiliev about the collective insanity of our community. I am sure that if the elections in the Russian Academy of Sciences take place in two years, the outstanding mathematician S.K. Smirnov will take his place in the OMN RAS.

In these elections, we elected many talented young mathematicians. Previously, the media and officials reproached us for the expanded reproduction of the "jam". Now, it would seem, you can even mention such a shift with a line. But no, a new argument was found, their Hirsch is not the same, not the same value. In their interviews in this issue, both Smirnov and Vasiliev explained why mathematicians consider the use of leakometric indicators (such as Hirsch index and others) unlawful to evaluate the results in our science.

At the same time, the report of the International Mathematical Union quoted by Smirnov has long been translated into Russian and several years, along with other critical materials of our Western colleagues, available on the website of an independent Moscow University ( www.mcme.ru/free-books/bibliometric.pdf ). The harmfulness of these indices for the development of science has been manifested with all the last years when they became decisive to obtain grants and compile reports on scientific research. In order for the number of work to become larger, you can divide the whole work into a few, you can, choosing the task, take one that is simpler and, therefore, “more reliable”, but for the mass of middle peasants, every morning on the computer appears a sea of ​​proposals to be published in such a way as to enter WOS, Scopus and other places designed by the authorities.

The works of the young young people were reported at the most prestigious international conferences, including international (ICM) and European (ECM) Congresses, received well -known prizes in a tough struggle, that is, they passed the real competition that was always in our science, and not the “chicken” that officials are imposed on us.

Unfortunately, it is necessary to note the low level of journalistic professionalism, which manifested in an interview. Instead of asking ridiculous questions about the number of publications of A. G. Kuznetsov, one could ask about the results of those who were chosen. Let's say the work of A. A. Gaifullin about the bending of polyhedra, the proof of the hypothesis of “blacksmiths”, its physical meaning would be so easy to explain very briefly. Here we need the simple law of Boyle-Mariott from the school course of physics.

Speaking of any “chicken”, the journalistic community could be inquired by research and other sciences, for example, psychology, and sociology. Thus, in Anglo-American sociology, there have long been work that shows the harmfulness of the use of formal numerical indicators in matters where the human factor is really present, the human psychology is played (the so-called laws of Gudhart and Campbell, see Links to these research in my article in the Socrates magazine, http://socrat-online.ru/uploads/socrat-special-2016.pdf ).

In the context of a new attack on the Russian Academy of Sciences, according to techniques resembling the attack of summer and autumn 2013, your publication, which positions itself as objective and independent, did not show, in my opinion, neither one nor the other.

December 8, 2016

A.N. Parshin,
Academician, head. Department of the Mathematical Institute. V.A. Steklov RAS

From the editorial office:

Academician Parshin for some reason breaks the open door. He distributed his letter to URBI et orbi, it seems, simultaneously with his reference to the editor. Usually they do this when they fear that the letter will not be published. Did Alexei Nikolayevich have the grounds for such fears?

Alexey Nikolaevich writes (and distinguishes with fat font) that S.K. Smirnov was elected academician. There is a funny substitution: the result of voting in the mathematics section of the department of mathematical sciences, in which S.K. Smirnov received a certain number of votes, is declared the election result, and the fact that after this “election” S.K. Smirnov did not become an academician, declared a consequence of the unfortunate combination of circumstances: illness and employment of a large number of members of the section. We note, however, that these circumstances did not prevent the election of S. V. Kislyakov, S. V. Matveev, S. V. Konyagin and D.V. Treeshev. Therefore, these worthy scientists received more votes when voting than S.K. Smirnov. The question of whether to agree in this situation with the diagnosis of V. A. Vasiliev, remains thereby open.

Alexey Nikolaevich devotes most of his open letter to criticism of premiuming indicators, but exactly the same criticism has just sounded in an interview with V. A. Vasiliev and S. K. Smirnov criticized by him. Let us recall that the first was called “Hiresemania and Hirschefobia”, and the second “Hirsch index in mathematics is not an argument”, and it already contained a link to the same translation of the report of the American mathematical society, which is mentioned by Alexei Nikolaevich, only published on another site. He is not satisfied with the fact that the journalist asked the citation of A. G. Kuznetsov and A. A. Gayfullin - apparently, it never occurred to him that the interviewer repeats the common argument just then to get a qualified answer to him; Exactly the way V. A. Vasiliev gave. (By the way, the question so upset by Alexei Nikolaevich was preceded by the words “Critics are surprised that ...”).

In general, it is difficult to resist the conclusion that Alexei Nikolaevich saw several familiar stimuli in the text and answered them with a standard set of arguments without reading the interviews carefully and not paying attention to their context. As for the hints of the “Trinity Option” in the “attack on the Russian Academy of Sciences”, we will leave them on the conscience of academician Parshin. There is nothing new in them: exactly such hints and reproaches we hear all the years of the newspaper.

Viktor Vasiliev, Academician of the Russian Academy of Sciences, President of the Moscow Mathematical Society:

The letter of A. N. Parshin drew my attention to the fact that, speaking of the collective insanity in connection with the vote on the candidacy of S. Smirnov, I would really have to express my thought: otherwise many readers can understand this remark in the same way as Alexei Nikolaevich (which I did not want). Of course, we are not talking about the individual properties of all and each individual member of our community, namely about the properties of the collective, that is, about the ability of all this team as a single thinking organism to make certain decisions in the context of a clash of opinions and interests.

History knows too many examples when a team of distinctive personalities behaves even more unreasonable than the most unreasonable of its members.

I like many of our collective solutions in these elections, but life is arranged in such a way that our team will not be judged by the degree of optimality of good collective solutions, but by the most rude mistakes. Therefore, the inability to avoid such mistakes is also evidence of the collective (in the same sense) loss of self -preservation. However, in my opinion, it was necessary to choose Smirnov not only of these - and first of all not of these - considerations. And yes, I am grateful to the newspaper Trinity Option and Natalia Demina for the opportunity to speak out for accurate acute questions.

Andrey Polyanin , doct. Fiz.-Mat.Saak, professor, professor of the Department of Applied Mathematics, Institute of Problems of Mechanics named after A. Yu. Ishilinsky RAS/ MGTU named after N.E. Bauman:

Any comparisons of the effectiveness of scientists based on citation indices and Hirsch should be carried out very carefully, without going beyond the narrow limits of scientific specialties. However, it is important to note that if the author’s works are very little cited, then they are:

(i) either little -known or uninteresting and nobody needs it,

(II) or not yet in demand (which is extremely rare).

In other words: Low citation is an important indicator of the scientist. At the same time, an additional negative factor is a high level of self -cycling.

It should be noted that some recently selected young corresponding members, in addition to slight citation, have a very high percentage of self-digitability (the RINC data from November 13, 2016 are given below):

Gaifullin Alexander Alexandrovich:

• Hirsch index excluding self -citizenship 1,
• The number of self -cysties is 72.6% (the number of citation by co -authors 80.6%).

Moiseev Tikhon Evgenievich:

• Hirsch index excluding self -citizenship 2,
• The number of self -digitalities is 66.1% (the number of citation by co -authors 79.7%).

Lukoyanov Nikolay Yuryevich:

• Hirsch index excluding self -citizenship 3,
• The number of self -cysties is 64.5% (the number of citation by co -authors 88.7%).

These data are very indicative (pay attention to the unusually high percentage of self -citizenship and quotes by co -authors) and lead to the conclusion: the work of these scientists are focused on the extremely narrow circle of scientists and are not too interesting for colleagues. The figures are unlikely to indicate the outstanding successes of these scientists in the development of science (although there are no doubts in the high qualifications of these scientists).

It is important to emphasize that scientific science indicators, with all their conventions, are more objective indicators of the effectiveness of scientists than their positions, titles and scientific degrees.

PS I expressed my opinion on the use of scientific parameters earlier, see A. Polyanin A. D. Disadvantages of citation indices and Hirsch and the use of other scientific indicators // Mathematical modeling and numerical methods, 2014, No. 1, C. 131-144 ( http://mmcm.bmstu.ru/articles/2/ , there is also an expanded version of this article on the Internet: Polyanin A. D. Disadvantages of citation indices and hirsch. Maximum citation indices, EQWORLD- http://eqworld.ipmnet.ru/ru/info/sci-edu/polyanin_indexh_2014.html ).

Olga Vinogradova, head. IFHE laboratory named after A.N. Frumkin RAS, professor of the Faculty of Physics, Moscow State University, Dokt. physical. sciences, member of Academia Europaea:

The critics of the Hirsch index are mainly those who have low and who is taking into account the scientific indicators is simply disadvantageous, that is, not all mathematicians. It is difficult to agree that mathematicians are much published and poorly quoted. Even biologists will envy the citation of Kolmogorov, Arnold or Samara. Nowadays, mathematicians publish a lot, often with co -authors, and their work is perfectly referred to. The impact factors of the leading mathematical magazines (JAMS, Acta Mathematica, Annals of Math. And others) are quite high and even higher than that of the best magazines in some areas of physics. Fields laureates of Tao, Okunkov, Witten and many other well -known mathematicians have very large Hirsch indices. Hirsch Indexs of Professors “Pure” mathematics at the Faculty of Mathematics MIT, where my co -authors work, are in the range from 20 to 40+, and at applied MIT mathematicians they, of course, are even higher. So to say that quoting indicators in mathematicians are low and do not correlate with their level is wrong. Of course, Viktor Vasiliev is absolutely right that there are work that only specialists can understand and use, and that different sections of mathematics are quoted in different ways. But this is true for any other field of science. For example, if a theoretical physicist is not focused on experimenters, then it is usually cited worse. However, it is also true that the solution of really important and urgent problems (mathematics and physics-theoretics is not an exception here) inevitably leads to high citation. Poor citation always means the narrowness of the theme (circle of communication) and/or the irrelevant task, and often just a low level of work.

Elections for the Mathematics separation became for many a sensation with the Minus sign, as they “rolled” many candidates with a high Hirsch index, but scientists with meager citation were massively elected. In his interview, Viktor Vasiliev gives an example of Alexander Gayfullin, who "solved three famous tasks (more precisely, three cycles of tasks), and all three are perfect classics, and on different topics." According to Web of Science (12/11/2016), Gayfullin's work (excluding self -digitalization) was quoted only 12 times and only in 11 articles. His Hirsch index without self -citing is 1. In the year of election in the Russian Academy of Sciences, Gaifullin did not publish a single article and was not quoted at all. A natural question arises: how did you solve that these tasks, which, judging by the citation, were few interesting to anyone, are classics? This visual example also suggests that the conviction that is widespread among Russian mathematicians that quoting should not be taken into account is fraught with a serious danger. It demotivates talented young mathematicians to work in actively developing and most important areas, encouraging the solution of tasks that are only interesting to the extremely narrow circle of specialists, and sometimes completely unnecessary.

I fully admit that many of the low -circulated winners of the elections in the mathematics department were really the best candidates for their vacancy. However, the election in the Russian Academy of Sciences of a large number of scientists whose scientific achievements have not yet been confirmed by any objective criteria (Hirsch index, citation index, publications in leading mathematical journals), does not help increase its reputation in our country or in the world. Unfortunately, such a result was partially predetermined long before the elections themselves, when RAS allocated a disproportionately large number of vacancies, including many vacancies with a restriction of age.

And the latter - about the next non -removal of Stanislav Smirnov, laureate of the prestigious Fields Prize in the Russian Academy of Sciences. In the Soviet Union, this award was received by Novikov, Margulis and Drinfeld, of which only Novikov was elected a member of the USSR Academy of Sciences. From Russian citizens, Fields medalists became Zelmanov, Kontsevich, Voevodsky, Perelman, Okunkov and Smirnov. None of them are a member of the Russian Academy of Sciences, so in my opinion, the case of Smirnov, in my opinion, became no sensation.

Viktor Vasiliev, Academician of the Russian Academy of Sciences, President of the Moscow Mathematical Society:

I can’t say anything about Moiseev and Lukoyanov, who got out of the section of applied mathematics and computer science.

However, I know the works of A. A. Gaifullin (and evidence of their professional recognition). This knowledge convinces that, before applying biblometric criteria to specific situations and piece researchers (having, like any statistical methods, the more chances they are not too much to evade reality, the more objects they are applied to the greatest array), A. D. Polyanin should be interested in the substantial side of the case among specialists. Which was quite simple, because with the former supervisor of Gaifullin, V. M. Bukhtabar, he regularly meets in the VAK Expert Council.

The very small part of the gyruscous layer is made up of researchers, about which it is easy to say what belongs to them in the building of our science. This can be said about Gaifullin three times: the existence of quite local combinatorial formulas for all Pontryagin classes and such a clear formula for the first class; эффективное решение проблемы Стинрода о реализации гомологий; доказательство многомерной гипотезы «кузнечных мехов». Если Хирш подсказывает вам, что все эти слова — какая-та ерунда и жульничество, в которых не стоит даже разбираться, то помочь тут трудно, ведь спорить с радикальным свидетелем Хирша почти столь же безнадежно, как пытаться логически переубедить последовательного берклеанца. Поэтому я предлагаю отдаться на суд времени, хорошо запомнив, кто что говорил, и обязательно вернуться к вопросу лет через шесть-восемь. Стало быть, запишем для истории: Андрей Полянин — вот как звали человека, в 2016 году атаковавшего А. А. Гайфуллина под библиометрическими знаменами.

Науке необходимы разные ученые: и те, чья работа сразу идет в массы, и покорители суровых высот, где пока что мало кто может встать рядом и пройти дальше, тем более что в некоторых случаях выше идти уже некуда. Первых надо любить, но их существование — не аргумент, чтобы не признавать вторых.

Истинная правда, что на индексы цитирования особенно часто злобятся ученые, у которых они существенно ниже уровня их признания (либо формального, выраженного в степенях и должностях, либо адекватного признания профессиональным сообществом — того самого «Гамбургского счета»). Точно так же неудивительно, когда ярыми поборниками этих индексов становятся те, у кого ситуация противоположная. Поэтому достаточно кисло к диктату этих индексов приходится относиться и тем, кто хорошо видит, что такое их несоответствие реальному уровню бывает, и иногда очень существенно.

И последнее замечание — в предвкушении возможной дискуссии (даже выходящее за рамки этой темы). Для соблюдения полемической гигиены давайте не забывать про кванторы. Делая утверждение о большом множестве (например, о математиках или об ученых вообще), тем более цитируя кого-то, давайте обязательно уточнять: «все» или «некоторые», или «иногда», или «как правило», или «в среднем» и т. п. Иначе очень легко вроде бы и не соврать, а смысл поменять радикально.

Евгений Асмолов , ст. scientific. sore. Лаборатории механики многофазных сред НИИ механики МГУ, докт. physical. Sciences, Vedas. scientific. sore. ЦАГИ им. Prof. Н. Е. Жуковского:

В. А. Васильев описал возможные ужасные последствия учета библиометрических показателей, но действующая система выборов ужаснее. Сам автор признает, что «отделение математики почти что оккупировано тремя институтами, и прежде всего московской Стекловкой». То есть если вы не работаете в МИАНе, то вы «по определению» математик так себе. Приведенные примеры неизбранных как раз подтверждают это правило. И так во всех, особенно в небольших, отделениях. По факту, даже не институт ведь решает, кому быть академиком, а его директор. То есть важна договоренность всего трех директоров. В экономике это называется монополия и картельный сговор. Поэтому реально у нас не Академия Наук, а Академия Начальников Наук, их приближенных, любимых учеников и т. п.

Anatoly Vershik, ch. scientific. sore. Санкт-Петербургского отделения Математического института РАН:

О выборах в РАН я уже писал в ТрВ-Наука и считаю в целом их неприличными, но дело ведь в том, что выборы происходили в прежних советских традициях и по выцветшим советским правилам, и даже более советским, чем прежде. Потому и чиновных лиц столько. Им же плохо объяснили, и они с полным основанием думали, что всё как прежде. Поэтому недовольство этим выглядит лицемерным. Фортов тут ни при чем.

Заодно скажу, что я совершенно не согласен с замечанием, сделанным Аскольдом Иванчиком по этому поводу о том, что В. В. Путин мог критиковать выборы в Академию, в частности, и за неизбрание С. К. Смирнова и А. В. Кабанова. Кто его знает, но полагаю, что нет. У него совсем другие причины для мстительного недовольства Академией и выволочки В. Е. Фортову, а это замечание слишком комплиментарное.

Причина неизбрания этих ученых в том, что команды, разрешающей выбирать тех, кто имеет основную работу за рубежом, за все эти годы не было. А выбирать без высочайшего разрешения в нынешней Академии никто не рискнет. И уверен, что не будет пока такого разрешения, потому что, если его дать, то оно потянет за собой другие «опасные» для системы последствия. Мегагранты дать — пожалуйста, но не больше.

Александр Фрадков, зав. лабораторией «Управление сложными системами» Института проблем машиноведения РАН, сопредседатель Совета Общества научных работников:

Спасибо уважаемому мной А. Н. Паршину за разъяснение итогов выборов в Отделении математических наук. Но вот вторая часть письма с «наездом» на СМИ меня расстроила: перекладывание вины за болезни Академии на тех, кто о них пишет, не добавляет чести академикам. Да и к первой части письма есть вопросы. Так ли хороша «демократическая» процедура выборов, если коллективная болезнь 25% голосующих позволяет им не избирать тех, кого не хочется избирать? Не надо ли что-то подправить в этой консерватории? Обсудим в будущем году.