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Surely someone has collected these papers and translations and has them in a single location for download? For music there is musipedia. Surely there is a mathepedia equivalent?

If I search gauss euler riemann jacobi I get nothing of significance.

If people post answers to sources (that are not already posted) I will collect them all in one resource that can be downloaded and post a link as the answer.

As an update I've downloaded most, except the Euler Archive, of the papers in the links given. This was 168 pdf's/etc.

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    $\begingroup$ Conifold has a nice answer giving many sources. hsm.stackexchange.com/questions/5361/… $\endgroup$
    – Ben McKay
    Commented Nov 16, 2022 at 16:46
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    $\begingroup$ Do you really mean musipedia, not imslp? I thought musipedia was just a melody search engine that doesn't actually contain full sheet music. $\endgroup$
    – R. van Dobben de Bruyn
    Commented Nov 16, 2022 at 19:47
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    $\begingroup$ I'd appreciate "the masters" changed in the title to a more factual wording, e.g., "famous mathematicians" (or "famous mathematicians until the XIXth century" if you want to avoid too recent ones)... $\endgroup$
    – YCor
    Commented Nov 17, 2022 at 16:29
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    $\begingroup$ If there is a need for a resource of that kind (which I am not sure about), it should not be hosted by a private person. $\endgroup$
    – Vladimir Dotsenko
    Commented Nov 17, 2022 at 18:05
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    $\begingroup$ Keep in mind that a translation can be copyrighted independently of the original. So even though the works of these folks are long since out of copyright, their modern translations may not be. As such, it wouldn't be legal for someone to collect and make them all freely available in one place. $\endgroup$
    – Nate Eldredge
    Commented Nov 18, 2022 at 20:03

9 Answers 9

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Most of the famous 19th century mathematicians have their collected works published and some of them have been digitized. But they are all in the original language. Translations into English are rare. And sometimes they are of poor quality. For example, this translation of Riemann collected papers, or recent translations of Klein and Fricke.

Few works of Gauss have been translated into English. His diaries are translated in Expositiones Mathematicae, 2 (2) (1984) 97–130, but not freely available.

Concerning Euler, there are translation of many mathematical papers, with some of them placed on the arXiv, and there is a web site which collects his original papers and translations.

Nothing or almost nothing has been translated of Jacobi.

Complete works of Chebyshev are available in Russian and French. Weierstrass's lectures on elliptic functions are available in German and French.

There is no single source where you can find all or most of these translations. One has to search for individual books and papers.

High quality translation of mathematical papers is extremely difficult and requires a very high qualification of the translator and editors. And many mathematicians can read several European languages. So this business is unprofitable, which explains why there are so few translations into English. Those which exist are frequently done by volunteers/amateurs, and are sometimes of poor quality.

Remark. There are many more high quality translations of old mathematics into Russian, which can be explained by certain peculiarities of the Soviet economy, where high quality labor was available at a negligible price.

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    $\begingroup$ For Russian papers, math-net.ru has almost every Russian paper ever written (only a slight exaggeration), at least after 1950-ish, with high quality scans. It also includes links to official English translations (often of quite poor quality, as you say). I have some translations of Russian papers on semigroup and group theory via my website, too, in a slowly growing list. $\endgroup$
    – Carl-Fredrik Nyberg Brodda
    Commented Nov 17, 2022 at 8:38
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    $\begingroup$ @Carl-FredrikNybergBrodda it is more than a slight exaggeration. Basically, there is a selection of good Russian language journals for which all papers were digitized. For quite a few others, nothing was digitized, unfortunately. $\endgroup$
    – Vladimir Dotsenko
    Commented Nov 17, 2022 at 12:52
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    $\begingroup$ @VladimirDotsenko Yes, you're right, I suppose my formulation should rather have been that for the subset of journals which it covers, it is very thorough. It covers many top journals, but as you say there are missing ones, too. $\endgroup$
    – Carl-Fredrik Nyberg Brodda
    Commented Nov 17, 2022 at 12:59
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There are sourcebooks which collect translations of (excerpts from) multiple mathematicians:

  • D.E. Smith, ed., A Sourcebook in Mathematics (Dover, 1959).

  • D.J. Struik, ed., A Sourcebook in Mathematics, 1200-1800 (Princeton University Press, 1969)

  • John Fauvel and Jeremy Gray, eds., The History of Mathematics, A Reader (MacMillan Press, 1987)

  • Ronald S. Calinger, ed., Classics of Mathematics (Prentice Hall, 1995)

  • Jacqueline Stedall, ed., Mathematics Emerging: A Sourcebook 1540-1900 (Oxford University Press, 2008)

These are all useful for teaching and good for browsing, though none is comprehensive. They may not have much Jacobi for you, and Struik’s book may end too early for your taste, but I think the rest all have bits of Euler, Gauss and Riemann.

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Quite a few of Euler's papers are available in translation here: https://arxiv.org/search/?query=euler_l&searchtype=author&source=header

In the original, along with many translations, they are mostly here: http://eulerarchive.maa.org/ I am not sure they are all there.

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    $\begingroup$ Maybe we need a list of all the papers that can be found and centralize them(or put them in a torrent)? I'm talking about all the major players since they are referenced the most. $\endgroup$
    – Gupta
    Commented Nov 16, 2022 at 16:38
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    $\begingroup$ I am not so sure they are referenced so frequently today. Researchers mostly reference the current research literature. $\endgroup$
    – Ben McKay
    Commented Nov 16, 2022 at 16:40
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    $\begingroup$ @Gupta, for locating asides which mention a theorem, something like Dickson's History of the Theory of Numbers may be more useful than a repository of the original papers. Or, perhaps more accurately, the repository may not be very useful without a similar History to serve as an organised index of the results. $\endgroup$
    – Peter Taylor
    Commented Nov 16, 2022 at 16:55
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    $\begingroup$ @Gupta I am not sure I believe your claim "these oldies are the most cited/referenced/used". What data did you use to come to this conclusion? $\endgroup$
    – Carl-Fredrik Nyberg Brodda
    Commented Nov 16, 2022 at 19:08
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    $\begingroup$ @Gupta: At some point the "classics" become less cited because they are common knowledge, or because everyone learned them from a later book or other secondary source. For instance we don't cite Newton or Leibniz every time we use the fundamental theorem of calculus. $\endgroup$
    – Nate Eldredge
    Commented Nov 18, 2022 at 20:10
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As the many answers already make clear, there is not one dedicated source that collects or archives the work of all the masters. Of course, from your question you get a vague understanding what you consider the masters and the time frame you have in mind. Euler, Gauss, Jacobi, Lagrange, Galois, Cayley, Jordan etc are all masters, but the discussion focused a lot on pre-19th century mathematics. I guess most would consider Neumann, Hilbert and Gödel masters as well.

But where you draw the line? For example, would you include translations of Yuri Matiyasevich work on Hilbert's 10th problems (originally published in Russian)?

My point is that having the synopsis to include all the masters is not well-defined, apart from a collection of a bunch of people it gets blurry for others. Should your collection include the work of Otto Hölder, for example? I have not seen him mentioned here, or in any of the linked answers. What about Georg Cantor? Dénes Kőnig? Kuratowski? Paul Erdös? Grothendieck? They all have papers written not in English.

Ok, sorry for my ramblings. To contribute anything to your original question I have to mention the one the masters considered their master: Euclid. His Elements is available in many translations, see the links at the end of the wikipedia page.

Furthermore, I often come across single papers that are foundational or were written by, what would I consider, a master. To give a list of some, probably less know, examples:

Two Papers by Kuratowski:

A translation of the original paper written by M. Presburger showing that the first order theory of the natural numbers is decidable.

A translation of G. S. Makanin's 1966 Ph.D. thesis "On the Identity Problem for Finitely Presented Groups and Semigroups" (2021). This work showed the decidability of equations in free groups (the algorithm actually yields decidability in free monoids). EDIT: This is actually not correct, see the comment by Carl-Fredrik Nyberg Brodda for a more detailed history..

I found a translation of the original paper stating and proving the Sylow Theorems from Sylow.

Translation of a paper by Frobenius.

Translation of a paper by Hölder (unfortunately behind a paywall).

Translation of an often cited paper on synchronizing automata originally published in Slovak by Černý.

Papers (or here) by Axel Thue who worked on patters in strings.

Lastly, Learning via Primary Historical Sources does not contain translations of individual classical papers, but documents that help in reading some of them, even for papers that were originally not published in English.

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    $\begingroup$ Makanin's PhD thesis did not show decidability of equations in free groups or monoids (it deals with special monoids and small cancellation theory). The equations in monoids result was instead included in his DSc thesis (no groups yet). The results for free monoids and free groups are proved separately (in 1977 and 1983, respectively). $\endgroup$
    – Carl-Fredrik Nyberg Brodda
    Commented Nov 17, 2022 at 13:05
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    $\begingroup$ Thank you for your comment! I have to admit, I never read the original work and only know about it from secondary sources or people talking about it at conferences (and maybe I have mixed things up here on the way). I am working on different topics, but reading/learning more about Makanin's algorithm is something on my todo list (that is probably why, having found your translation, it somehow sticked in my head). $\endgroup$
    – StefanH
    Commented Nov 17, 2022 at 14:36
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    $\begingroup$ It is a bit reminiscent of Yu. Matiyasevich's solution of Hilbert's 10th problem, which appeared in his DSc thesis, whereas his PhD thesis was, like Makanin's, instead on the word problem for finitely presented semigroups. $\endgroup$
    – Carl-Fredrik Nyberg Brodda
    Commented Nov 17, 2022 at 14:49
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    $\begingroup$ The collection should include everyone. I use the term master loosely but the point is to have a way to easily get at historical results that are mentioned in various books and papers. One would think that there would be a site dedicated to all papers mathematics(and offshoots) that attempts to consolidate all the information for a single entry point while providing a nice interface to search, modify, etc. Basically something analogous to Wikipedia. It takes nothing in space to store such information now days so no need to leave people out. $\endgroup$
    – Gupta
    Commented Nov 21, 2022 at 18:39
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    $\begingroup$ Having a centralized resource can allow people to "edit" information(again, analogous to wiki). E.g., someone can make a translation(and with github like features others can contribute) or convert text to OCR or rewrite in latex. In fact, having such a site for general knowledge should already exist. Music has similar issues. Could have musicians who can work together on converting a manuscript in to musicXML. Similar for other things. Even a massive site that attempts to do most things(from math to music to science) would probably be a few TB's. $\endgroup$
    – Gupta
    Commented Nov 21, 2022 at 18:41
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Riemann's collected works (much shorter than most great mathematicians, because of his early death) are published in German https://www.cambridge.org/core/books/bernard-riemanns-gesammelte-mathematische-werke-und-wissenschaftlicher-nachlass/EAB8B46090AFADB656CE9E5969F0A03B.

Here are the original papers in German: https://www.emis.de/classics/Riemann/index.html

There is famous translation of one paper in Spivak's Comprehensive Introduction to Differential Geometry.

Here is Riemann's famous Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse, a paper on prime numbers: https://www.claymath.org/publications/riemanns-1859-manuscript, with an English translation.

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David Delphenich's site http://www.neo-classical-physics.info/index.html provides "over 20 books and 450 articles on topics in classical mathematics and physics translated from French, German, Italian, and Russian."

The site especially includes translations 19th and 20th century French and German papers and books on algebra, analysis, geometry and topology, as well as translations of physics papers on theoretical mechanics, space-time structure, etc. It has a topic-based selection of papers by a wide range of authors.

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Here are Wayback Machine links to my English translations, all seven of which are related to Kuratowski's closure-complement theorem.

Sur l'Opération Ā de l'Analysis Situs by C. Kuratowski (1922, in French)

Quelques Notions Fondamentales de l'Analysis Situs au Point du Vue de l'Algèbre de la Logique by M. Zarycki (1927, in French)

General Properties of Cantorian Coherences by M. Zarycki (1928, in German)

Some Properties of the Derived Set Operation in Abstract Spaces by M. Zarycki (1947, in Ukrainian)

On Kuratowski's Problem by V. Soltan (1980, in Russian)

Problems of Kuratowski Type by V. Soltan (1982, in Russian)

Kuratowski Numbers by A. Chagrov (1982, in Russian)

To commemorate the hundredth year since the publication of Kuratowski's paper above, six weeks ago I uploaded And Boundary Makes Three: The Closure-Complement-Boundary Theorem in Topological Spaces to arXiv, page 41 of which gives the following graphical summary of the first century of literature related to the closure-complement theorem.

closure-complement literature

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More and more old journals are available online. There are also excellent machine translators, such as DeepL.

The problem, of course, is that the old journals have been scanned, so the text is not machine-readable.

However, the technology that was used in the past for printing mathematics was, compared to \LaTeX, very simple, as described in my answer and references. Therefore, as I suggested there, the modifications needed to an optical character recognition program such as Tesseract would be quite modest.

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    $\begingroup$ Yes, more needs to be done along these lines. NN's need to be trained to recognize equations, integrals, etc so that more information can be extracted from scans. Same needs to be done in music and other areas. $\endgroup$
    – Gupta
    Commented Nov 21, 2022 at 18:42
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I only wrote this as a comment on Alexandre Eremenko's answer, but after finding more information I thought I would promote it to a whole answer.

Math-Net.Ru is described in the abstract to [1] (arXiv link) as follows:

The main goal of the project Math-Net.Ru is to collect scientific publications in Russian and Soviet mathematics journals since their foundation to today and the authors of these publications into a single database and to provide access to full-text articles for broad international mathematical community. Leading Russian mathematics journals have been comprehensively digitized dating back to the first volumes.

In other words, if you are looking for a paper from a Russian master (e.g. S. I. Adian or A. A. Markov*), then it will likely be there; or, at the very least, its bibliographical information will be.

*The page for A. A. Markov had, until recently, only a handful of articles added. After informing Dmitry Tchebukov, one of the administrators of the site, of this, and sending him a .bib-file with a nearly complete bibliography, he was happy to add these to the site; but not before he had checked each of my entries, and made minor corrections, as well as added a few I had not been able to find! The process seems very rigorous indeed.

[1] Chebukov, Dmitry E.; Izaak, Alexander D.; Misyurina, Olga G.; Pupyrev, Yuri A.; Zhizhchenko, Alexey B., Math-Net.Ru as a digital archive of the Russian mathematical knowledge from the XIX century to today, Carette, Jacques (ed.) et al., Intelligent computer mathematics. MKM, Calculemus, DML, and systems and projects 2013, held as part of CICM 2013, Bath, UK, July 8–12, 2013. Proceedings. Berlin: Springer (ISBN 978-3-642-39319-8/pbk). Lecture Notes in Computer Science 7961. Lecture Notes in Artificial Intelligence, 344-348 (2013). ZBL1390.68748.

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    $\begingroup$ @LSpice Strange! The links work fine for me. I'll try changing them to the Russian versions. $\endgroup$
    – Carl-Fredrik Nyberg Brodda
    Commented Nov 28, 2022 at 7:12

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