Karatsuba's algorithm for fast multiplication was first published in A. Karatsuba and Yu. Ofman (1962), "Multiplication of Many-Digital Numbers by Automatic Computers", Proceedings of the USSR Academy of Sciences 145: 293–294.

According to Karatsuba (1995, "The complexity of computations", Proc. Steklov Institute of Mathematics 211: 169–183), this paper was actually written by Kolmogorov (and possibly Ofman) without Karatsuba's knowledge. By modern standards this seems a strange and grave breach of ethics.

Why would Kolmogorov have done this? What did he gain?

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    $\begingroup$ I think claiming "false pretences" is a little inflammatory, since the paper is credited to Karatsuba. It's still reasonable to ask the question though, since it's a little unusual. $\endgroup$ Commented Mar 15, 2014 at 22:46
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    $\begingroup$ ?!? cf p173 2nd ref & Karatsuba calls it "the unusual nature of this publication" wrt 1st ref. in other words he asserts the 1st paper was really written by Kolmogorov & credited to Ofman & himself, Karatsuba. maybe this has something to do with Russian publications conventions or an eccentricity of Kolmogorov? immed related question, what did Ofman have to do with the paper... usually it is opposite case where ppl take work that is done by others and published under their own name to "take credit"; this appears to be an opposite case of "giving credit" in a highly unusual circumstance.... $\endgroup$
    – vzn
    Commented Mar 15, 2014 at 23:27
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    $\begingroup$ @SureshVenkat: true, sorry about that. I've removed the phrase. $\endgroup$
    – Max
    Commented Mar 16, 2014 at 8:06

2 Answers 2


This paper, in Russian,

Gricenko, S. A., Karatsuba, E. A., Korolyov, M. A., Rezvyakova, I. S., Tolev, D. I., & Changa, M. E. (2012). Scientific contributions of A. A. Karatsuba / Научные достижения Анатолия Алексеевича Карацубы. Современные проблемы математики, 16(0), 7-30.

states the following (items 1—3).

  1. Karatsuba presented his algorithm at a seminar led by Kolmogorov.
  2. Kolmogorov prepared an article that had two results of his students, Karatsuba and Ofman. One of the results was Karatsuba's algorithm, the other was an unrelated result of Ofman.
  3. The article clearly attributed the results. It stated that the multiplication algorithm is due to Karatsuba and the other result is due to Ofman.

We can only guess why Kolmogorov did that. I am afraid that the only person who could answer the question why Kolmogorov published the paper without Karatsuba's permission or knowledge was Kolmogorov himself. Perhaps he thought that it was a good way to publish the results of his students. Note that the article correctly attributed all results. The article of Karatsuba and Ofman was published in the Proceedings of the USSR Academy of Sciences; it is my understanding that it had to be submitted/presented by a member of the USSR Academy of Sciences.

Here is the relevant quote from the paper of Gricenko et al (in Russian):

Этот результат был доложен Анатолием Карацубой на семинаре А. Н. Колмогорова в МГУ в 1960 г., после чего семинар был Колмогоровым закрыт. Первая статья с описанием этого метода [2] была подготовлена самим Колмогоровым. Там он представил два разных и не связанных друг с другом результата двух своих учеников, и хотя в статье Колмогоров четко отметил, что одна теорема (не связанная с быстрым умножени- ем) принадлежит Ю. Офману, а другая теорема (с первым в истории быстрым умножением) принадлежит А. Карацубе, эта публикация под именами двух авторов надолго сбила с толку читателей, которые полагали, что оба автора внесли вклад в создание быстрого умножения, и даже называли этот метод двумя именами.

English translation:

This result was presented by Anatoly Karatsuba in A. N. Kolmogorov's seminar at the Moscow State University in 1960, after which the seminar was closed by Kolmogorov. The first article with the description of this algorithm [2] was prepared by Kolmogorov himself. In it he presented two different results from his two students that were unrelated to each other, and although Kolmogorov clearly noted in the article that one theorem (unrelated to fast multiplication) belonged to Y. Ofman, and the other theorem (with the first fast multiplication algorithm in history) belonged to A. Karatsuba, this publication on behalf of the two authors for a long time confused readers, who supposed that both authors had stake in the invention of fast multiplication, and even referred to the algorithm using both names.

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    $\begingroup$ Was it a situation where only some people were allowed to 'communicate' results to a journal, so Karatsuba (a student at the time) couldn't have done so ? $\endgroup$ Commented Mar 16, 2014 at 9:04
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    $\begingroup$ @SureshVenkat: That's a good point! The paper was published in the Proc. of the Soviet Academy of Sciences, and I think that it had to be communicated by an Academy member. If that's the case, Karatsuba could not submit the paper himself. $\endgroup$
    – Yury
    Commented Mar 16, 2014 at 13:33
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    $\begingroup$ helpful but feel not a full answer. nevertheless Karatsuba states he was not directly informed by Kolmogorov & did not find out until post publication, apparently upon seeing the published article and an obvious still-unanswered aspect is why did Kolmogorov not simply ask/inform Karatsuba/Ofman prior to publication $\endgroup$
    – vzn
    Commented Mar 16, 2014 at 14:57
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    $\begingroup$ It's hard to imagine today what the culture was like then, but I can imagine Kolmogorov publishing it (as only he could per @Yury) and thinking he did the students a favor and didn't need to inform them ahead of time. Or maybe he wrote it up and was planning to tell them and forgot. $\endgroup$ Commented Mar 17, 2014 at 4:11
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    $\begingroup$ Perhaps Kolmogorov simply wanted to do a nice surprise to Karatsuba ... a kind of "academic gift" :-) $\endgroup$ Commented Mar 17, 2014 at 11:32

It is probably cultural. Karatsuba's discovery took place only 7 years after the death of Stalin. I do not believe it was an environment in which subjects questioned authority, and authority did not ask permission from subjects. As a professor and member of NAUK, Kolmogorov was definitely authority. No complaints about Kolmogorov, he left us a lot of good stuff!

  • $\begingroup$ This answer is wrong as Stalin died 1953, the discovery by Karatsuba was in 1960 and it was published 1962. By Karatsuba's own memorial, he learned of the paper only having got proofs for publication. $\endgroup$ Commented Oct 28, 2018 at 18:14

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