Anti-research-advisorship statement
Oct. 19th, 2025 11:52 am![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
posicThe aim of the following declaration is to explain my position and the reasons why I generally decline, and with rarest improbable exceptions, will continue to decline any requests for scientific advisorship. The statement explains why I am not taking students.
Short summary: The incentives are perverse. It has become all too easy to be a bad or mediocre mathematician while having a nice career and a pleasant life. Being a really good mathematician is way harder, and the lives of really good mathematicians may tend to be more difficult. The students are not interested in becoming really good mathematicians. They want to go the easy way and be bad or mediocre mathematicians with a pleasant life. I am not interested in producing mediocre mathematicians. (The "bad" and "good" here are understood in the sense of the genuine value, as opposed to the social recognition value. I do not care about the social recognition value.)
A longer explanation: I do not dwell here on the more glaring and primitive issues, such as lack of the basic politeness and respect towards the advisor on the part of the students. The students refusing to pay due respect to the people whose advice they seek. Such issues, while indicative of the general state of affairs and representing an insurmountable obstacle in themselves, do not yet lie at the root of the problem. They are the symptom, not the cause.
The main reason is that my mathematics teaching philosophy and research ethos stand in complete contradiction to the prevailing thinking and the spirit of the day. I do not believe in the popular misconception that everyone can become a good mathematician if he wants to. An extraordinary and rare talent is required. I also do not believe in another popular misconception, viz., that a good teacher can teach anyone anything. An extraordinary and rare internal motivation on the part of the student is required.
Doing research in mathematics requires great dedication. The best way to make this point is to state it in terms of the risks involved. Scientific research is supposed to be a highly risky enterprise.
I would compare mathematics to theology, as it was practiced in the medieval Europe. If I wrote a treatise in theology and somebody disagreed with me, they could declare me a heretic and have me burned at the stake.
I would also compare mathematics to experimental science as it was practiced at the dawn of scientific knowledge. Doing an experiment in physics or chemistry also could make me burned alive, because the unknown substance might turn out to be flammable and ignite in my hands or to my face. Or the substance could explode, etc. As the saying goes, "if we knew what we were doing, it would not be called research". The scientist could get poisoned by a chemical, or electrocuted by an atmospheric lightning, or infected with a deadly pathogen, or die of radiation sickness, etc.
Mathematics, if approached seriously, involves its own specific set of risks. Here I do not mean minor career inconveniences such as being unable to prepare one's thesis in due time, or not finding the next postdoc, etc. The real risk known to be consistently empirically associated with doing mathematics is the risk of going to a mental institution. One tries to prove a theorem real hard, gets exhausted, and needs time and medication to recover. There is also the accompanying risk of being driven to suicide, either from inability to achieve a breakthrough in one's research, or from career troubles and lack of funds to support oneself.
From my perspective, a student who is serious about doing research in mathematics is supposed to accept such risks and be ready to take them. Mathematics is not here to serve as an entertainment for you or a means to achieve your career objectives. If you are a mathematician, then the purpose of your existence is to advance the mathematical knowledge of humanity. You are not supposed to play it safe; certainly not under my watch. If anything, the opposite is expected: you are supposed to hurt yourself again and again until you discover what you can really do and how much you can contribute.
Simply put, from my perspective, an aspiring research mathematician is someone who is prepared to endanger his health and his life in exchange for a chance of achieving an important breakthrough in his understanding of the subject. If you are not ready to put your health and your life on the line, then what you are doing is not mathematical research. It is an imitation of mathematical research.
So, I would not encourage a student of mine to prepare his thesis by the deadline required by the administration. I would encourage him to bang his head against a wall until he breaks through the wall or breaks his head.
Unfortunately, decades of irresponsible governmental funding of education and science created a completely opposite mentality, in which people who enjoyed their math. lectures in college and could do homework exercises have come to perceive themselves to be entitled to a safe and pleasant entertainment in the form of years of watered-down math. "research" at the hapless taxpayer's expense. Nowadays, young mathematicians speak of their research as being driven by two competing goals of "having fun" versus "building a career".
Let me repeat. From my perspective, you as a mathematician are not supposed to have fun. You are not supposed to have much of a career, either. You are supposed to sacrifice your well-being, by any conceivable objective parameters of well-being, for a chance to advance human knowledge of mathematics in an important way.
If that is not what you are interested in, then I am not a suitable advisor for you. If your talent and preparation are not sufficient to make any level of risk and sacrifice enough for a reasonable probability of making an important contribution to mathematics, then I am not a suitable advisor for you, either.
The discussion above emphasizes the risks. The risks are an important aspect. The risks for an aspiring research mathematician are supposed to be high. Another way to look at the problem is to average out the risks and consider the expected, most probable outcome.
In the Russian language and culture, there is this concept of "Hamburg accounting", гамбургский счет. The Hamburg accounting represents the genuine value of things, as opposed to their socially recognized value. In my own life, I strove to maximize the genuine value of my total lifetime contribution to mathematics and other worthy human endeavors, at the expense of almost all other concerns.
Any advice I might offer you would be aimed at making you the very best mathematician you could possibly become; the "very best" being understood in the sense of the genuine value and not the social appraisal value; at the expense of you having a difficult and painful life. That is what I chose for myself in my own life, after all. I am not interested in helping you make your life any more pleasant than you deserve, from the point of view of the genuine value of your contribution.
This makes my aims completely opposite and contradictory to the life goals of about every student I could advise, setting the stage for a conflict. I have had more than enough sharp conflicts in my life. I do not shy away from conflict when I believe that there are important values at stake that need to be defended. Nobody needs or wants unnecessary conflicts.
The cowardly present-day world wants conformity and blame avoidance, not a breakthrough to the unknown. The pragmatic-minded present-day student wants a pleasant life and a comfortable career, not dangers and self-sacrifice for the sake of realizing one's talents in creative pursuit. I am a deeply marginal figure in this environment.
My own career was a bad joke for more than 15 years, and only improved when I was closer to the age of 50. I am not really interested in advancing anybody's careers, or in careerism generally.
Realistically speaking, this means that I am not a suitable advisor for anybody. That is why I am not taking students.
Leonid Positselski
Short summary: The incentives are perverse. It has become all too easy to be a bad or mediocre mathematician while having a nice career and a pleasant life. Being a really good mathematician is way harder, and the lives of really good mathematicians may tend to be more difficult. The students are not interested in becoming really good mathematicians. They want to go the easy way and be bad or mediocre mathematicians with a pleasant life. I am not interested in producing mediocre mathematicians. (The "bad" and "good" here are understood in the sense of the genuine value, as opposed to the social recognition value. I do not care about the social recognition value.)
A longer explanation: I do not dwell here on the more glaring and primitive issues, such as lack of the basic politeness and respect towards the advisor on the part of the students. The students refusing to pay due respect to the people whose advice they seek. Such issues, while indicative of the general state of affairs and representing an insurmountable obstacle in themselves, do not yet lie at the root of the problem. They are the symptom, not the cause.
The main reason is that my mathematics teaching philosophy and research ethos stand in complete contradiction to the prevailing thinking and the spirit of the day. I do not believe in the popular misconception that everyone can become a good mathematician if he wants to. An extraordinary and rare talent is required. I also do not believe in another popular misconception, viz., that a good teacher can teach anyone anything. An extraordinary and rare internal motivation on the part of the student is required.
Doing research in mathematics requires great dedication. The best way to make this point is to state it in terms of the risks involved. Scientific research is supposed to be a highly risky enterprise.
I would compare mathematics to theology, as it was practiced in the medieval Europe. If I wrote a treatise in theology and somebody disagreed with me, they could declare me a heretic and have me burned at the stake.
I would also compare mathematics to experimental science as it was practiced at the dawn of scientific knowledge. Doing an experiment in physics or chemistry also could make me burned alive, because the unknown substance might turn out to be flammable and ignite in my hands or to my face. Or the substance could explode, etc. As the saying goes, "if we knew what we were doing, it would not be called research". The scientist could get poisoned by a chemical, or electrocuted by an atmospheric lightning, or infected with a deadly pathogen, or die of radiation sickness, etc.
Mathematics, if approached seriously, involves its own specific set of risks. Here I do not mean minor career inconveniences such as being unable to prepare one's thesis in due time, or not finding the next postdoc, etc. The real risk known to be consistently empirically associated with doing mathematics is the risk of going to a mental institution. One tries to prove a theorem real hard, gets exhausted, and needs time and medication to recover. There is also the accompanying risk of being driven to suicide, either from inability to achieve a breakthrough in one's research, or from career troubles and lack of funds to support oneself.
From my perspective, a student who is serious about doing research in mathematics is supposed to accept such risks and be ready to take them. Mathematics is not here to serve as an entertainment for you or a means to achieve your career objectives. If you are a mathematician, then the purpose of your existence is to advance the mathematical knowledge of humanity. You are not supposed to play it safe; certainly not under my watch. If anything, the opposite is expected: you are supposed to hurt yourself again and again until you discover what you can really do and how much you can contribute.
Simply put, from my perspective, an aspiring research mathematician is someone who is prepared to endanger his health and his life in exchange for a chance of achieving an important breakthrough in his understanding of the subject. If you are not ready to put your health and your life on the line, then what you are doing is not mathematical research. It is an imitation of mathematical research.
So, I would not encourage a student of mine to prepare his thesis by the deadline required by the administration. I would encourage him to bang his head against a wall until he breaks through the wall or breaks his head.
Unfortunately, decades of irresponsible governmental funding of education and science created a completely opposite mentality, in which people who enjoyed their math. lectures in college and could do homework exercises have come to perceive themselves to be entitled to a safe and pleasant entertainment in the form of years of watered-down math. "research" at the hapless taxpayer's expense. Nowadays, young mathematicians speak of their research as being driven by two competing goals of "having fun" versus "building a career".
Let me repeat. From my perspective, you as a mathematician are not supposed to have fun. You are not supposed to have much of a career, either. You are supposed to sacrifice your well-being, by any conceivable objective parameters of well-being, for a chance to advance human knowledge of mathematics in an important way.
If that is not what you are interested in, then I am not a suitable advisor for you. If your talent and preparation are not sufficient to make any level of risk and sacrifice enough for a reasonable probability of making an important contribution to mathematics, then I am not a suitable advisor for you, either.
The discussion above emphasizes the risks. The risks are an important aspect. The risks for an aspiring research mathematician are supposed to be high. Another way to look at the problem is to average out the risks and consider the expected, most probable outcome.
In the Russian language and culture, there is this concept of "Hamburg accounting", гамбургский счет. The Hamburg accounting represents the genuine value of things, as opposed to their socially recognized value. In my own life, I strove to maximize the genuine value of my total lifetime contribution to mathematics and other worthy human endeavors, at the expense of almost all other concerns.
Any advice I might offer you would be aimed at making you the very best mathematician you could possibly become; the "very best" being understood in the sense of the genuine value and not the social appraisal value; at the expense of you having a difficult and painful life. That is what I chose for myself in my own life, after all. I am not interested in helping you make your life any more pleasant than you deserve, from the point of view of the genuine value of your contribution.
This makes my aims completely opposite and contradictory to the life goals of about every student I could advise, setting the stage for a conflict. I have had more than enough sharp conflicts in my life. I do not shy away from conflict when I believe that there are important values at stake that need to be defended. Nobody needs or wants unnecessary conflicts.
The cowardly present-day world wants conformity and blame avoidance, not a breakthrough to the unknown. The pragmatic-minded present-day student wants a pleasant life and a comfortable career, not dangers and self-sacrifice for the sake of realizing one's talents in creative pursuit. I am a deeply marginal figure in this environment.
My own career was a bad joke for more than 15 years, and only improved when I was closer to the age of 50. I am not really interested in advancing anybody's careers, or in careerism generally.
Realistically speaking, this means that I am not a suitable advisor for anybody. That is why I am not taking students.
Leonid Positselski
