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Quoted from Wikipedia:

In 1888 Alfred Nobel's brother Ludvig died while visiting Cannes and a French newspaper erroneously published Alfred's obituary. It condemned him for his invention of dynamite and is said to have brought about his decision to leave a better legacy after his death. The obituary stated, Le marchand de la mort est mort ("The merchant of death is dead") and went on to say, "Dr. Alfred Nobel, who became rich by finding ways to kill more people faster than ever before, died yesterday." Alfred was disappointed with what he read and concerned with how he would be remembered.

Alfred Nobel felt guilty for invention of dynamite. He shares this emotion with many other scientists of the human history who became disappointed when they realized that their discoveries make the world a worse place to live. But what about mathematicians? We know almost all scientific discoveries are based on mathematical theorems and concepts but it seems feeling guilty is much more epidemic amongst physicists, chemists and biologists rather than mathematicians.

Question: Is there any mathematician who felt guilty for one of his math discoveries ever? If yes, what was that particular theorem or concept? Please introduce historical references and other quotations which confirm existence of such an emotion.

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    $\begingroup$ Godel probably felt guilty of crushing Hilbert's hopes and dreams. (He better have) $\endgroup$
    – Milo Brandt
    Commented Dec 10, 2014 at 1:17
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    $\begingroup$ Pretty sure Cantor would have felt like that. Read his life story on Wikipedia. $\endgroup$
    – user122283
    Commented Dec 10, 2014 at 1:21
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    $\begingroup$ Dynamite itself is not useful in military applications. However, Nobel also invented other explosives such as gelignite and ballistite, which led to cordite. He also invested heavily in the Swedish arms industry. His purchase of Bofors came a few years after the obituary incident, which might lead one to question just how guilty he felt... $\endgroup$
    – Robert Israel
    Commented Dec 10, 2014 at 1:36
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    $\begingroup$ I think if Hardy came back today he'd be appalled that number theorists are employed by the government to spy on people. $\endgroup$
    – user4894
    Commented Dec 10, 2014 at 2:00
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    $\begingroup$ Grothendieck perhaps. $\endgroup$
    – MJD
    Commented Dec 11, 2014 at 15:19

3 Answers 3

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Einstein, while not strictly a mathematician, expressed profound regrets later in his life when he pondered on the possibility of an atomic war. In 1939, he wrote to Roosevelt to urge the Americans to develop the atomic bomb before Germany, and Roosevelt took action as a direct result of this letter. In 1954, in an interview to The Reporter, Einstein said:

If I would be a young man again and had to decide how to make my living, I would not try to become a scientist or scholar or teacher. I would rather choose to be a plumber or a peddler in the hope to find that modest degree of independence still available under present circumstances.

(He is often credited to have said: "If only I had known, I should have become a watch-maker." But it appears that he never said those exact words.)

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Here are a few comments:

  1. One of the dialogues in Rényi's Dialogues on Mathematics (available at https://archive.org/details/dialoguesonmathe00reny) is quite relevant to the question. More specifically, the second dialog titled "A Dialogue on the Applications of Mathematics" is between Archimedes as Hieron. In it, among other things, Archimedes discusses/comes to terms with why he helped Hieron in war with applications of mathematics. Guilt in this case is balanced by a desire to outreach (I am not doing justice to the dialogue here.). This is not quite an answer to the question, as the dialog is made up by Rényi; still I believe it is worthy of mention (in accordance with the first dialogue in the book, incidentally). Further, it is not clear to me if Archimedes is classified as a mathematician.

  2. A slight generalization of the question could make it more relevant to contemporary research: "Are there any mathematicians who expressed guilt for their choices for patrons?". This is based on the assumption that some, if not all, mathematical research today is funded by bodies that see the potential applicability of the outcomes, and some, if not all, applicabilities are detrimental to some, if not all, humans, or more general beings and things. (If need be, I'm using the word "choice" is a weak sense.)

  3. A variant of the previous item is being/feeling guilty for not knowing who one's patrons are. This type of guilt is more spread out, and easier to ignore, compared to the guilt mentioned in the previous item. It is not improbable that this is by design. (Again, "design" in a weak sense if necessary, e.g. see the last sentence of the first item.)

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I've heard apocryphal stories that Newton was reticent to publish his calculus, concerned that the human race couldn't handle the power. He only begin publicizing it when Leibniz started publishing prolifically, about 20 years later. Perhaps somebody has a citation; I don't, hence I consider it apocryphal.

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