Husserl wrote a doctoral thesis on calculus of variations. It does not seem to be available on the Göttinger Digitalisierungs-Zentrum and so far as I have found the online collections of his works are only philosophical. Anyway I'd rather not read the original just now and try to figure out how it relates to the level of other work on the subject at the time. I'd like to find out that someone has already done that.

Claire Ortiz Hill and Jairo José da Silva have written well on Husserl's engagement with actual mathematics. See http://rancho.pancho.pagesperso-orange.fr/Writings.htm

But I do not know if she has written on his doctoral work itself.

I'd especially like to find specifically philosophical discussion of this doctoral work on calculus of variations, but an historic overview would also help. Can anyone here help me?

  • It's an interesting question, but why would philosophers try to parse a math dissertation?
    – virmaior
    Jun 10, 2016 at 23:44
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    @virmaior Why would Plato write about Theaetetus's math, or why would Descartes write a philosophical preface to his Geometry? Why would philosophers from Carnap through Putnam want to understand Einstein's actual physics? Jun 11, 2016 at 0:13
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    @virmaior Are you offering excuses for Plato and Descartes? Or are you pointing out a weakness of modern thought? Personally I would not shy away from exploring a philosophically interesting conclusion merely on the grounds that the evidence for it is, as you put it, snazzy. Jun 11, 2016 at 0:36
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    @virmaior Oh. In fact I think Claire Ortiz Hill and Jairo José da Silva have shown that to understand Husserl as he wished to be understood then you have to include his views on math and logic. I would not call those insights hidden, but rather overt, and neglected. As to the dissertation itself, I want to know about it but I don't think all philosophers need to join me in the quest. (Notice this is exactly what I would say if I thought the dissertation had hidden gems and I wanted help finding them without showing my own hand.) Jun 11, 2016 at 6:26
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    "But I do not know if she has written on his doctoral work itself." Well, why don't you ask her? Jun 11, 2016 at 22:26

1 Answer 1


Husserl's dissertation Beiträge zur Variationsrechnung (“Contributions to the Calculus of Variations”) has nothing philosophical in it. The work is based on the lectures by Kronecker and Weierstrass that Husserl attended as a student in Berlin and is entirely technical. Scrimieri has published extracts from it (Giorgio Scrimieri "Analitica matematica e fenomenologica in Edmund Husserl", Bari: Edizioni Levante, 1979). There is a French translation ("Contributions à la Theorie du Calcul des Variations". Ed. by J. Vauthier in Queen’s Papers in Pure and Applied Mathematics 65. Kingston, Ontario: Queen’s University, 1983). I think that Ingeborg Strohmeyer also mentions it in her "Einleitung" to Husserliana XXI. But mostly it only gets mentioned for biographical reasons.

  • There is a pdf of the French translation at sdvigpress.org/dox/108014/108014.pdf it includes extensive logical and historical remarks on the method of infinitesimals in general, and calculus of variations in particular, supporting Weierstrass's views which Kronecker rejected as bad philosophy. The Introduction and the Présentation de la thèse by J. Vauthier both note various issues of philosophic relevance but I have not had time to read the whole thing carefully. Jan 2, 2018 at 1:20
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    Of course not. As you pointed out, the PDF is on-line, check it out, and let me know what you think. The dissertation is a work in mathematics, not on mathematics. As such, it does use concepts (e.g. infinity, space) that Husserl also analyzes later elsewhere in a philosophical respect, but these concepts are not problematized or thematized in the dissertation itself. Scrimieri 1979 has a partial transcription of the original German (with some minor errors), the full German version has never been published as far as I know, but they have a copy and scan at the Husserl-Archives. Jan 4, 2018 at 9:40
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    I already said i think Husserl taking sides in the famous philosophical debate between Weierstrass and Kronecker is of philosophical interest. To put it in your terms, infinitesimals are thematized in gthe dissertation itself. Jan 4, 2018 at 11:41
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    I'm curious to see how you would find support for that claim in the dissertation. Husserl discusses Jacobi's solution to Lagrange's problem of integrating a non-linear differential equation, and brings in Weierstrass' lectures only in the very last pages. He doesn't say at this point (as a twenty-something that slept through Wundt's philosophy classes) whether he thinks that imaginary numbers are real or fictional, the transfinite makes sense, only cardinals or ordinals are meaningful numbers, what the foundations of math are, etc. Maybe he has an opinion in merit, but it's not in this text. Jan 4, 2018 at 14:16
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    True, he does not say whether he thinks imaginary numbers are real or fictional. For one thing, no one talked about imaginary numbers in those terms at that time. And if you can only recognized Weierstrass's influence when his name is used, then of course you will not believe Kronecker had any influence here at all. If you are actually interested in the history of mathematics then contact me by e-mail, you can find my address on Google. Jan 4, 2018 at 14:44

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