Prof. D. C. McCarty recently gave an interesting interview (published in January 2015, and easily found on a large video hosting site), entitled

What are the limits of mathematical explanation?

I think this is the best interview with a philosopher that I have heard or read in a long while, and hope that Prof. McCarty will give more interviews of that quality, and I recommend the interview to anyone.

However, there is one problematic minute during this interview, which is of potential concern to the mathematical community: during that minute an embellishment is made of one the most often retold legends in the lore of modern mathematics: Hilbert's public denial that there are unsolvable mathematical questions, his 1930 radio address to that effect (and Gödel's announcement, co-located and simultaneous, of a theorem contradicting Hilbert's belief).

The problematic minute starts at 12 min 1 sec, and ends at 13 min 10 sec, of the recording that I listened to. I transcribe it here:

Interviewer: Hilbert said that we will know everything in mathematics [...] There is no ignorabimus in mathematics. Prof. McCarty: He did say that, and in fact, he did more than say it: he insisted upon it. He talked about it in his 1901(e1) problems-lecture, and you may have heard this on [...] or in some other way: his last lecture at Königsberg in 1931.(e2) He ends the lecture(e3) by talking about the ridiculous or foolish ignorabimus, and he said that there is no ignorabimus, and they didn't turn off the recording-device early enough. You can hear Hilbert's little hideously laugh after he says 'Es gibt kein ignorabimus.' at the end; and then he goes 'ha ha ha', in a slightly mean way. It seems to me that Hilbert's utterance there was the last gasp of a mathematics, and approach to mathematics, that he represented and was, I think, common in the 19th century. That is, that there aren't any permanent limits to our mathematical cognition.


1.1. Did Hilbert audibly laugh at the end of his 1930 radio address in Königsberg?

1.2. If so, can the laugh justifiably described as 'hideous' and 'mean'?

  1. Is there a more extensive recording of Hilbert's address of 8 September 1930 than what can be found here, here, or here (none of which contains any trace of dishonesty or mockery)? (Not even the file behind the last-mentioned link contains any such trace, which is two seconds longer than e.g. the version which can be found on the largest video hosting service, and still does not contain any laugh? By the way, I did not take the trouble to analyze and compare these audio-files with some specialized software; it is clear that some sort of cutting did occur, but apart from that I don't see what new insight analyzing the available and laughterless recordings would give.)

  2. Independently of what the answer to 1. is, what, if anything, made Prof. McCarty say that Hilbert is on record with a hideous laugh at end of his famous address?


  • I deliberately decided against trying to contact Prof. McCarty privately, because I think that this question is not injurious (quite the contrary) and because the purpose of this question is to publicly set the historical record straight (to the extent that this is at all possible with such a distant historical event).

  • Under the 'usual' assumptions about 'history', 'logic' and 'reality', Questions 1.1, 2 and 3 are defined questions with definite answers; in particular, either Hilbert laughed at the end or he didn't (and I think Hilbert would agree with this, given that around the same time he thought he had found proof of the law of exclude middle...).

  • As regards Question 2, I can think of the following reasons:

    • Prof. McCarty was a victim of the well-known psychological mechanism of confabulation

    • Prof. McCarty had access to an unpublished, uncut version of the radio recording, whereas each publisher of the audio-file either cut the recording to get rid of the 'hideous laugh', or they got an already cut file from some other source

    • Prof. McCarty read some written account of Hilbert's address, in which a statement about Hilbert laughing at the end is made; if that is so, then of course this raises the further question of what the basis for that hypothetical written account was...

  • It may be convenient to readers to have a transcription of Hilbert's address, and a translation; this is what this nice document of J. T. Smith of San Francisco State University offers; I checked the transcription, and found it to be perfect, except for the minuscule detail that "geniesst" must be 'genießt', "grosse" must be 'große', and "heisse" must be 'heiße' (the same orthographical errors are made on the above-mentioned MAA-page, by the way).

  • I don't think this question is unimportant; other sciences (like chemistry or physics) passionately discuss and document their history and legends too---just think about the vibrant research about the history of physics---and the above-mentioned interview casts one of the most well-known legends of 20th-century mathematics in a new and unbecoming light: Hilbert, against his better knowledge, gleefully giving false hopes to the general public.


(e1) By the way, that's a secondary, unimportant mistake in the interview: Hilbert's famous talk at the second ICM in Paris was given in on 8 August 1900, not in 1901. Even the subsequent publication of the talk, both in German and in French traslation, happened already in 1900, so the date 1901 seems completely wrong.

(e2) This is another slight mistake on the part of the interviewee: all sources I know agree that Hilbert's radio address was recorded (and presumably also broadcast---the sources remain silent about that detail) on 8 September 1930, not 1931.

(e3) Presumably, what is meant by 'lecture' here is just the radio address.

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    $\begingroup$ It may be a difference of style, but I think the current presentation does not fit MathOverflow. Something that would be better would be to open with: "I am looking for an uncut recording of an address given by David Hilbert, where oddly enough laughter has a historico-mathematical significance. Can someone tell me where such an accessible recording is?", then follow with most of your characterization, but mute the emotional context and instead emphasize the mathematical ramifications. As it currently reads, it smells of gossip to me. Gerhard "Not Much To Say Here" Paseman, 2018.03.01 $\endgroup$ – Gerhard Paseman Mar 1 '18 at 17:40
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    $\begingroup$ I agree with Gerhard that the question should be written in a less loaded way, but I would also suggest that it might be a better fit for hsm.SE. $\endgroup$ – Emil Jeřábek Mar 1 '18 at 18:12
  • $\begingroup$ By the way, is there a particular reason you want readers to locate the interview themselves, instead of directly linking to the “large video hosting site”? $\endgroup$ – Emil Jeřábek Mar 1 '18 at 18:16
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    $\begingroup$ @EmilJeřábek: thanks for the feeback; regarding the linking: no, there is no particular reason, I am not sure what is more appropriate. $\endgroup$ – Peter Heinig Mar 1 '18 at 18:21
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    $\begingroup$ I'm impressed by the quantity of upvotes that such highly off-topic questions can get. $\endgroup$ – YCor Mar 1 '18 at 22:12

Constance Reid describes the recording on page 196 of her book Hilbert (1969).

The recording was not made directly from the live address. Instead, Hilbert was asked to repeat the conclusion of his speech in the broadcasting studio of a local radio station. This is significant, Hilbert was not speaking in front of an audience, he was speaking into an unfamiliar recording device in the presence of a technician. The faint$^*$ laugh when the technician turned off the machine might just have been a laugh of relief that this was over and had gone well. Hilbert's final sentence was a bit "heavy", if I would be asked to repeat this in front of a recording device I might have felt slightly silly, without the audience, and I might well have laughed to remove the tension.

As reported by Laurent Siebenmann, the laugh was erased in the 1971 restoration process by Springer that transferred the original 1930 recording from a wax cylinder onto vinyl. Attempts to locate the original recording for a CD edition of the speech failed --- it seems the laugh is lost.

$^*$ Reid says the laugh is audible if one listens very carefully.

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    $\begingroup$ Since common sense seems to imply that Reid will no have made that up, I think that this, amazingly, already more or less answers all the questions. I see no reason not to accept this as answer. $\endgroup$ – Peter Heinig Mar 1 '18 at 18:33
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    $\begingroup$ It looks more and more like a Cheshire Cat laugh :) $\endgroup$ – Qfwfq Mar 1 '18 at 21:28
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    $\begingroup$ perhaps the opposite of the Cheshire cat, because there the "laugh" persisted: ... the cat vanished quite slowly, beginning with the end of the tail, and ending with the grin, which remained some time after the rest of it had gone. $\endgroup$ – Carlo Beenakker Mar 1 '18 at 22:09

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