122
$\begingroup$

Oftentimes in math the manner in which a solution to a problem is announced becomes a significant chapter/part of the lore associated with the problem, almost being remembered more than the manner in which the problem was solved. I think that most mathematicians as a whole, even upon solving major open problems, are an extremely humble lot. But as an outsider I appreciate the understated manner in which some results are dropped.

The very recent example that inspired this question:

  • Andrew Booker's recent solution to $a^3+b^3+c^3=33$ with $(a,b,c)\in\mathbb{Z}^3$ as $$(a,b,c)=(8866128975287528,-8778405442862239,-2736111468807040)$$ was publicized on Tim Browning's homepage. However the homepage had merely a single, austere line, and did not even indicate that this is/was a semi-famous open problem. Nor was there any indication that the cubes actually sum to $33$, apparently leaving it as an exercise for the reader.

Other examples that come to mind include:

  • In 1976 after Appel and Hakken had proved the Four Color Theorem, Appel wrote on the University of Illinois' math department blackboard "Modulo careful checking, it appears that four colors suffice." The statement "Four Colors Suffice" was used as the stamp for the University of Illinois at least around 1976.
  • In 1697 Newton famously offered an "anonymous solution" to the Royal Society to the Brachistochrone problem that took him a mere evening/sleepless night to resolve. I think the story is noteworthy also because Johanne Bernoulli is said "recognized the lion by his paw."
  • As close to a literal "mic-drop" as I can think of, after noting in his 1993 lectures that Fermat's Last Theorem was a mere corollary of the work presented, Andrew Wiles famously ended his lecture by stating "I think I'll stop here."

What are other noteworthy examples of such announcements in math that are, in some sense, memorable for being understated? Say to an outsider in the field?

Watson and Crick's famous ending of their DNA paper, "It has not escaped our notice that the specific pairing we have postulated immediately suggests a possible copying mechanism for the genetic material," has a bit of the same understated feel...

Improve this question
$\endgroup$
21
  • 13
    $\begingroup$ The tale about Cole seems to have no basis in fact and was just a legend propagated by E. T. Bell, who was a former PhD student of Cole. Cole did have a real method of discovering the factorization (the answers to mathoverflow.net/questions/207321/… include a link to Cole's article) and it was not the "three years of Sundays" that Bell wrote. I therefore don't think the Cole story should be among your examples. $\endgroup$
    – KConrad
    Commented Mar 10, 2019 at 20:37
  • 7
    $\begingroup$ Tim Browning announced the three-cubes solution, but it seems that he was reporting on work of Andrew Booker, see gilkalai.wordpress.com/2019/03/09/… and people.maths.bris.ac.uk/~maarb/papers/cubesv1.pdf $\endgroup$
    – Gerry Myerson
    Commented Mar 10, 2019 at 22:02
  • 18
    $\begingroup$ This is perhaps an example of the opposite phenomenon. It's from my own hazy memory, and I don't fully recall the particulars, including how I happened to overhear this. (Maybe I was just walking by at the right time?). But one morning while I was in grad school at Chicago in the 1970s, Yitz Herstein walked into Irving Kaplansky's office and announced that "Last night, I proved a beautiful theorem". To which Kaplanskky replied: "Wouldn't it have been better if you'd waited for me to say that?" $\endgroup$
    – Steven Landsburg
    Commented Mar 11, 2019 at 1:48
  • 10
    $\begingroup$ Even soft questions deserve accurate answers....the answers here are an ahistorical embarassment. $\endgroup$
    – user44143
    Commented Mar 11, 2019 at 14:58
  • 11
    $\begingroup$ This is a truly bizarre use of the phrase "mic drop." $\endgroup$
    – Noah Snyder
    Commented Mar 12, 2019 at 22:13

14 Answers 14

Reset to default
93
$\begingroup$

The best known lower bound for the minimal length of superpermutations was originally posted anonymously to 4chan.

The story is told at Mystery Math Whiz and Novelist Advance Permutation Problem, and a publication with a cleaned-up version of the proof is at A lower bound on the length of the shortest superpattern, with "Anonymous 4chan Poster" as the first author. The original 4chan source is archived here.

Improve this answer
$\endgroup$
9
  • 17
    $\begingroup$ Also: a new superpermutation of 7 symbols, shorter than any that was known at the time (8907 symbols long), was posted as a pseudonymous comment on YouTube in February 2019. $\endgroup$
    – Robin Houston
    Commented Mar 10, 2019 at 22:05
  • 31
    $\begingroup$ "Mainly devoted to anime" is a rather kind way to put it.. ;-) $\endgroup$
    – R.. GitHub STOP HELPING ICE
    Commented Mar 10, 2019 at 22:29
  • 29
    $\begingroup$ @R.., as I understand it, the 4chan poster answered a question in a forum dedicated to a particular anime program. The anime in question was meant to be non-linear, and watched in any order. The question was effectively "what is the most efficient way to watch all $n$ episodes of the anime serially, in any order." So it was answered in a forum really "devoted to anime," rather than the average 4chan forum. $\endgroup$
    – Mark S
    Commented Mar 10, 2019 at 23:32
  • 8
    $\begingroup$ @MarkS More specifically, Suzumiya Haruhi no Yuuutsu, and hence the problem was also named "The Haruhi Problem". $\endgroup$
    – Pedro A
    Commented Mar 11, 2019 at 2:04
  • 14
    $\begingroup$ It’s far too late for me to edit my first comment, but I should say that the superpermutation posted as a YouTube comment is 5907 symbols long, not 8907. Apologies for mistyping, and for not noticing sooner. $\endgroup$
    – Robin Houston
    Commented Mar 12, 2019 at 9:34
68
$\begingroup$

I'll just let below (famous) 1966 article from the Bulletin of the American Mathematical Society speak for itself...

Lander and Parkin, BAMS 1966

COUNTEREXAMPLE TO EULER'S CONJECTURE ON SUMS OF LIKE POWERS
BY L. J. LANDER AND T. R. PARKIN
Communicated by J. D. Swift, June 27, 1966

A direct search on the CDC 6600 yielded

$$ 27^5 + 84^5 + 110^5 + 133^5 = 144^5 $$

as the smallest instance in which four fifth powers sum to a fifth power. This is a counterexample to a conjecture by Euler [1] that at least $ n $ $ n $th powers are required to sum to an $ n $th power, $ n > 2 $.

REFERENCE
1. L. E. Dickson, History of the theory of numbers, Vol. 2, Chelsea, New York, 1952, p. 648.

Improve this answer
$\endgroup$
62
$\begingroup$

Perelman solving the Poincare "conjecture," posting it only on the arXiv, leaving math, and refusing the Clay prize could be interpreted as a kind of "mic drop."

Improve this answer
$\endgroup$
8
  • 21
    $\begingroup$ Let us not mince words: " 'I'm not interested in money or fame,' he is quoted to have said at the time. 'I don't want to be on display like an animal in a zoo. I'm not a hero of mathematics. I'm not even that successful; that is why I don't want to have everybody looking at me.' " $\endgroup$
    – Samantha Y
    Commented Mar 11, 2019 at 2:40
  • 6
    $\begingroup$ The announcement was posting on arxiv (with no buzzword). Refusing prizes occurred several years later hence is not part of the announcement. $\endgroup$
    – YCor
    Commented Mar 11, 2019 at 11:42
  • 15
    $\begingroup$ @SamanthaY Ironically, I think he's succumbed to the Streisand Effect by doing that. A significant fraction of my awareness of Perelman and the results he's credited with is a result of his refusals to be recognized. $\endgroup$
    – zibadawa timmy
    Commented Mar 11, 2019 at 14:31
  • 12
    $\begingroup$ @zibadawatimmy Yes, but Perelman refused to be owned by the public, which is quite a different thing than wanting privacy/anonymity. To that end, I feel he succeeded. $\endgroup$
    – Samantha Y
    Commented Mar 11, 2019 at 18:36
  • 9
    $\begingroup$ @ycor I apologize :( this entire thread strikes me as unproductive, but that doesn't excuse my taking offense at you, especially as we seem to be in agreement. That is (if I may say so), perpetuating mythologizing the Perelman story, or characterising it as a 'mic drop' will only drive a wedge between mathematicians and the general public, by portraying us as either prize-driven or "odd-balls", and even if somewhere between these two, as drama obsessed gossips. After all, (and this is a very general comment) don't we want everyone to be mathematician? Let them see we're human. $\endgroup$
    – Samantha Y
    Commented Mar 11, 2019 at 23:47
41
$\begingroup$

Applications of algebra to a problem in topology (YouTube) at Atiyah80 was a talk by Mike Hopkins. In it he announced the solution to the Kervaire invariant one problem in all but one dimension (arXiv, Annals).

EDIT: The video seems to have been removed from Youtube but is still available as a download in the .mov format at empg.maths.ed.ac.uk/Videos/Atiyah80/Hopkins.mov

Improve this answer
$\endgroup$
8
  • 47
    $\begingroup$ I was in the audience as a second year graduate student, and for me it was just another lecture where I could only understand the first 10-15 minutes. A stranger sitting next to me was very excited afterward, but I remember wondering if he was a nut. So yeah, this qualifies as a mic drop in my book. $\endgroup$
    – Paul Siegel
    Commented Mar 11, 2019 at 14:52
  • 4
    $\begingroup$ @Vincent from memory he's most likely discussing stable homotopy groups, so that really it's $\pi_{n+2}(S^n)$ for large enough $n$ (in this case, $n\geq 4$), but being sloppy with notation. It would be better denoted $\pi_2^s(S^0)$. See eg the pink diagonal in this table starting at $\pi_6(S^4)$. $\endgroup$
    – David Roberts ♦
    Commented Mar 13, 2019 at 10:54
  • 4
    $\begingroup$ @Vincent actually, it's saying the same thing, but I think Hopkins would phrase it as looking at the homotopy groups of the sphere spectrum $\mathbb{S}$, which is cooked up out of $S^0$. Then $\pi_2(\mathbb{S})$ is indeed as he describes. $\endgroup$
    – David Roberts ♦
    Commented Mar 13, 2019 at 11:03
  • 3
    $\begingroup$ @PaulSiegel: I was there; perhaps the stranger was Ian Hambleton. I remember Ian said he was happy to have lived to see the discovery of the solution to the Kervaire problem. $\endgroup$
    – Ben McKay
    Commented Sep 2, 2019 at 9:08
  • 2
    $\begingroup$ Ah, I seem to have found a link: empg.maths.ed.ac.uk/Videos/Atiyah80/Hopkins.mov $\endgroup$
    – Sam Hopkins
    Commented Jan 21, 2021 at 4:08
40
$\begingroup$

Not math but in physics the statistical interpretation of the wave-function was announced by Max Born in a footnote.

From his paper Zur Quantenmechanik der Stoßvorgänge,

(1) Anmerkung bei der Korrektur: Genauere Überlegung zeigt, daß die Wahrscheinlichkeit dem Quadrat der Größe $\Phi_{n_\tau m}$ proportional ist.

This can be translated as

(1) Addition in proof: More careful consideration shows that the probability is proportional to the square of the quantity $\Phi_{n_\tau m}.$

Because of its implications this is probably the most important footnote in the history of physics. Max Born was awarded the Nobel prize "for his fundamental research in quantum mechanics, especially for his statistical interpretation of the wavefunction".

Improve this answer
$\endgroup$
4
  • 6
    $\begingroup$ I think "Anmerkung bei der Korrektur" is better translated as "Remark added in proof". In particular, it would be a remark by the author, not by the editor. Also, "zeigt" is present tense, "shows" not "will show". $\endgroup$
    – Andreas Blass
    Commented Mar 11, 2019 at 1:44
  • 25
    $\begingroup$ The footnote is not the announcement of a probabilistic interpretation, but a correction that the probability is proportional to $\Phi^2$ rather than $\Phi$. Also the paper is not so much understated as preliminary, as indicated right below the title. $\endgroup$
    – user44143
    Commented Mar 11, 2019 at 2:41
  • $\begingroup$ @AndreasBlass you're right. You're welcome to provide a better translation than the one I found online. If I remember correctly Born added that footnote once the paper was already in the review process $\endgroup$
    – lcv
    Commented Mar 11, 2019 at 3:14
  • 5
    $\begingroup$ @MattF. I take it that your comment means that he didn't mean to show understatement with the footnote. I totally agree. This is however, how the statistical interpretation was brought to public attention. De facto so to speak. $\endgroup$
    – lcv
    Commented Mar 11, 2019 at 17:54
40
$\begingroup$

From the Wikipedia article on Frank Nelson Cole:

On October 31, 1903, Cole famously made a presentation to a meeting of the American Mathematical Society where he identified the factors of the Mersenne number $2^{67}- 1,$ or M67.[5] Édouard Lucas had demonstrated in 1876 that M67 must have factors (i.e., is not prime), but he was unable to determine what those factors were. During Cole's so-called "lecture", he approached the chalkboard and in complete silence proceeded to calculate the value of M67, with the result being 147,573,952,589,676,412,927. Cole then moved to the other side of the board and wrote 193,707,721 × 761,838,257,287, and worked through the tedious calculations by hand. Upon completing the multiplication and demonstrating that the result equaled M67, Cole returned to his seat, not having uttered a word during the hour-long presentation. His audience greeted the presentation with a standing ovation.

Improve this answer
$\endgroup$
11
  • 17
    $\begingroup$ I'm interested in the historiography of this urban legend. Is the only source for the above E. T. Bell? If so, must it be considered suspect, because E. T. Bell was a much better mythmaker than a biographer? I'd like to believe it to be true - a broken clock is still right twice a day... $\endgroup$
    – Mark S
    Commented Mar 11, 2019 at 0:41
  • 14
    $\begingroup$ Maybe things were different in 1903, but I would not give a standing ovation for an hour of silent arithmetic. Also I’m sorry but those calculations don’t seem like they would take an hour. None of it seems believable. Still a fun story though. $\endgroup$
    – Zach Teitler
    Commented Mar 11, 2019 at 1:18
  • 6
    $\begingroup$ $M_{67}$ would be a big deal any time and finding those factors would have certainly been worthy of acclaim. I just meant that there would be far better ways to present the factorization than grinding through the arithmetic. As an audience member I would be far, far more interested in how Cole found those factors, than in whether he remembered to carry the $3$ or whatever. An hour of that would have been tough to sit through. Although... maybe at one of those 20-minute AMS special sessions, perhaps.... :-) $\endgroup$
    – Zach Teitler
    Commented Mar 11, 2019 at 5:32
  • 5
    $\begingroup$ @MarkS I can't comment on the absolute validity of the claims but did some looking out of curiosity; here is a 1963 article which seems to be the source of the wikipedia claims. The article is "The search for perfect numbers" by Gridgeman: books.google.com/books?id=0Dta7OkNhyoC&lpg=PA87 $\endgroup$
    – TomGrubb
    Commented Mar 11, 2019 at 16:22
  • 11
    $\begingroup$ Given the content of Cole's paper (see projecteuclid.org/download/pdf_1/euclid.bams/1183417760 ), I would think it very unlikely that he would say nothing about his techniques. Perhaps what happened was that he started off his talk by silently writing down the factorization for dramatic effect, and then proceeded to give a "normal" talk. Later, people may have only remembered the dramatic opening. $\endgroup$
    – Timothy Chow
    Commented Mar 18, 2019 at 16:00
33
$\begingroup$

I consider this manner as a mark of a professional mathematician: let others convey the excitement of a discovery. A good recent example was the submission of a paper on bounded gaps between primes. Much of the public excitement was generated by people other than the author, Yitang Zhang.

Gerhard "Can Be Excited In Private" Paseman, 2019.03.10.

Improve this answer
$\endgroup$
3
  • 6
    $\begingroup$ I especially like his understated comment that "I believe one could make it sharper" when asked if he thought $k<70,000,000$ could be reduced. $\endgroup$
    – Mark S
    Commented Mar 10, 2019 at 23:17
  • 7
    $\begingroup$ Well, a distinction can be drawn between the most professional approach, which I guess is to submit the work to the Annals or another top journal, accept invitations to speak about it, etc. followed by Yitang Zhang and the more dramatic (and fun) approach where you post it only to your personal website, refuse to tell people what your talk announcing the result is about in advance, leave math immediately afterwards, etc. It seems that the "mic drop" refers to examples that go above and beyond what you'd do for a usual strong result. $\endgroup$
    – Will Sawin
    Commented Mar 11, 2019 at 1:34
  • 1
    $\begingroup$ And then there is of course Grothendieck who let Borel & Serre publish his proof of the GRR theorem... $\endgroup$
    – ssx
    Commented Mar 12, 2019 at 19:16
32
$\begingroup$

Kurt Gödel, only a few days before Hilbert gives his famous "We must know – We will know!" quote, had just proven that we cannot know.

Namely, any reasonably strong foundation of mathematics, if it has a finitary proof verification process, cannot decide all the true statements. Mathematics, in its essence, is incomplete.

Philosophically speaking, perhaps one of the biggest mic drop moments. Metaphorically, this virtual coinciding with Hilbert's lecture just makes the room even more silent afterwards.

Improve this answer
$\endgroup$
5
  • 23
    $\begingroup$ This took place in 1930 in Koenigsberg, which was Hilbert's hometown. Goedel's talk was a day or two before Hilbert's talk, not at the same conference, and Hilbert may not have even been at that talk. For more, see hsm.stackexchange.com/questions/29/… and maa.org/book/export/html/326610. $\endgroup$
    – KConrad
    Commented Mar 11, 2019 at 15:35
  • $\begingroup$ @KConrad: The silent room is a metaphor here. Because the usual reaction to a mic drop is that the room goes silent for a moment. :-) $\endgroup$
    – Asaf Karagila ♦
    Commented Mar 11, 2019 at 16:02
  • 4
    $\begingroup$ Apparently von Neumann, in the audience, remarked at the end of Gödel's lecture "It's all over". Unfortunately I do not have a good source for this. $\endgroup$
    – David Roberts ♦
    Commented Mar 13, 2019 at 12:46
  • 4
    $\begingroup$ I recall reading somewhere that nobody really grasped the full import of Gödel's lecture in real time, with the exception of von Neumann, whose nearly superhuman ability to understand new mathematical ideas quickly is well known. If true, this would be a good argument for calling this a "mic drop." $\endgroup$
    – Timothy Chow
    Commented Mar 17, 2019 at 16:32
  • 7
    $\begingroup$ @TimothyChow When I was a grad student (closer to 1930 than to now), I was told, probably by Burton Dreben, that Gödel's lecture included some polite words to the effect that his results didn't mess up Hilbert's program because there could be finitistic methods not covered by the theorem, but that von Neumann immediately realized that this was not the case --- finitistic methods are covered with room to spare. $\endgroup$
    – Andreas Blass
    Commented Sep 2, 2019 at 14:37
21
$\begingroup$

I think the following anecdote fits well in this category. Note however, that other participants may have experienced these things differently, since they will have had a better background knowledge of the topic.

At a conference in Uppsala in September 2012, Geordie Williamson was scheduled to give a talk. I can unfortunately not recall the precise topic, as I can no longer find the program for the conference.

He starts his talk by apologizing that he is in fact going to talk about a completely different topic, since he had very recently finished some work on this with his collaborator Ben Elias.
He then goes on to describe Soergel's conjecture and some of the ideas that he and Ben have been working on, hoping to make progress on the conjecture.

The talk is quite technical, involving a lot of quite deep ideas and descriptions of how certain geometrical ideas, such as Hodge theory, can be given more algebraic analogues and how these may be put together to make progress on the conjecture.

As is typical of any technical talk, it is very hard to keep track of all the details and how they fit together along the way, so he provides a nice summary in the end:

"In conclusion, Soergel's conjecture is true".

Improve this answer
$\endgroup$
3
  • 13
    $\begingroup$ Well isn’t he lucky that nobody asked him any questions to make him run out of time. To students on MathOverflow: please don’t plan talks like this (with the result at the very end). $\endgroup$
    – Zach Teitler
    Commented Mar 13, 2019 at 13:14
  • 2
    $\begingroup$ The paper is arxiv.org/abs/1212.0791 $\endgroup$
    – user44143
    Commented Mar 13, 2019 at 13:30
  • 7
    $\begingroup$ @ZachTeitler While I agree that it is usually not a good idea to save the main result until the end, going over time should not be an issue for an experienced speaker with an eye on the time and the ability to adapt the talk on the fly, especially when the statement of the main result takes 10 seconds. $\endgroup$
    – Tobias Kildetoft
    Commented Mar 13, 2019 at 14:18
18
$\begingroup$

Russell and Whitehead's Principia Mathematica has a long and complicated proof that 1+1=2, given after spending 80+ pages defining arithmetic in terms of logical primitives. The proof is accompanied by the famous comment "The above proposition is occasionally useful."

Improve this answer
$\endgroup$
17
$\begingroup$

The first "announcement" of the Green–Tao theorem on arbitrarily long arithmetic progressions of primes was the appearance of their preprint on the arXiv. When I saw that preprint, I posted an article to the USENET newsgroup sci.math, somewhat incredulously asking whether this was the first public announcement, and Tao replied:

It is our first public announcement, yes. Given the track record for announcements for well-known conjectures in number theory, it seems a low key approach is appropriate. :-)

Improve this answer
$\endgroup$
1
  • 1
    $\begingroup$ Tao posted an announcement on his blog soon after the arxiv upload: see entry for April 9, 2004. $\endgroup$
    – none
    Commented Mar 18, 2019 at 6:20
10
$\begingroup$

My favorite is non-mathematician Marjorie Rice challenging the proof of "No other pentagon tilings exist" with multiple new pentagon tilings. Schattschneider's article was the primary announcement of the results.

Improve this answer
$\endgroup$
1
  • 11
    $\begingroup$ While an excellent result, how was this a "mic drop"? $\endgroup$
    – Noah Schweber
    Commented Mar 11, 2019 at 17:38
6
$\begingroup$

Onsager announced in 1948 (see the reconstruction by Baxter) that he and Kaufman had found a proof for the fact that the spontaneous magnetization of the Ising model on the square lattice with couplings $J_1$ and $J_2$ is given by $$ M = \left(1 - \left[\sinh (2\beta J_1) \sinh (2\beta J_2)\right]^{-2}\right)^{\frac{1}{8}}, $$ but he kept the proof a secret as a challenge to the physics community. The proof was obtained by Yang in 1951.

Improve this answer
$\endgroup$
1
  • 23
    $\begingroup$ Why do you say “he” when there were two authors? Why do you say “kept the proof a secret” rather than “considered the argument too messy and unrigorous to publish”? $\endgroup$
    – user44143
    Commented Mar 11, 2019 at 11:05
5
$\begingroup$

In 1978 Roger Apéry proved the irrationality of $\zeta(3)$, giving a talk named "Sur l'irrationalité de $\zeta(3)$" which is known for being unusual. There don't seem to be many accounts of the talk, but from some claims that do exist, while his claims were unbelievable, his presentation was quite droll, and it wasn't until after the talk that it was seriously considered that he was correct. (1)

A possible recent second example is the proof that for every positive integer $n$, there exists a pattern in Conway's Game of Life which oscillates after exactly $n$ generations (since $n$ is called the "period" of such a pattern, this conjecture is known as omniperiodicity.) By 1996 it was known (2) that an oscillator exists for every period $n\geq 61$, by constructing an infinite family of similar patterns based on shuttling active regions around various kinds of looping tracks. This left a list (2) of eighteen periods less than $61$ with no known oscillators - the website LifeWiki gives a short timeline of the last twelve periods to be discovered, and some witnessing patterns. (3)

The final construction was of an oscillator with period $41$, which was first posted without much fanfare into a LifeWiki-associated Discord chat room by Nico Brown in July 2023. It was soon after copied over to the the ConwayLife.com Forums by the same author. The resolution was soon after catalogued on Adam P. Goucher's blog Complex Projective 4-Space in the post "Miscellaneous discoveries".

Edit December 2023: The paper "Conway's Game of Life is Omniperiodic" now posted on arXiv contains more details about the chronology of the result and the constructions, with clickable diagrams that show the evolution of the pattern (run on a third-party site).

(1): A. van der Poorten, "A Proof that Euler Missed ...", The Mathematical Intelligencer vol. 1, 1978.

(2): D. Buckingham, "My Experience with B-heptominos in Oscillators", October 1996. Hosted on conwaylife.com, accessed 25 October 2023.

(3): LifeWiki, "Omniperiodic". Wiki article, accessed 25 October 2023.

Improve this answer
$\endgroup$
1

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .