In 1978 Roger Apéry [proved](https://en.wikipedia.org/wiki/Ap%C3%A9ry%27s_theorem) 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](https://hsm.stackexchange.com/questions/12784), 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)

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A possible recent second example is the proof that for every positive integer $n$, there exists a pattern in [Conway's Game of Life](https://en.wikipedia.org/wiki/Conway%27s_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](https://en.wikipedia.org/wiki/Discord) chat room by Nico Brown in July 2023. It was soon after copied over to the [the ConwayLife.com Forums](https://conwaylife.com/forums/viewtopic.php?&p=163972#p163972) 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](https://cp4space.hatsya.com/2023/07/23/miscellaneous-discoveries/)".

*Edit December 2023*: The paper "[Conway's Game of Life is Omniperiodic](https://arxiv.org/abs/2312.02799)" 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 ...](https://link.springer.com/article/10.1007/BF03028234)", *The Mathematical Intelligencer* vol. 1, 1978.

(2): D. Buckingham, "[My Experience with B-heptominos in Oscillators](https://conwaylife.com/ref/lifepage/patterns/bhept/bhept.html)", October 1996. Hosted on conwaylife.com, accessed 25 October 2023.

(3): LifeWiki, "[Omniperiodic](https://conwaylife.com/wiki/Omniperiodic)". Wiki article, accessed 25 October 2023.