The top 10 mathematical achievements of the last 5ish years, maybe

Just another top ten list.

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I have recently been going through my book Maths 1001 making updates for a forthcoming foreign edition (of which more in future). So I have been looking over mathematical developments since approximately 2009. Thus, I present ten major developments in the subject since around then, arranged arbitrarily in ascending order of top-ness.

"Socolar-Taylor tile" by Parcly Taxel - Own work. Licensed under CC BY-SA 4.0 via Wikimedia Commons - https://commons.wikimedia.org/wiki/File:Socolar-Taylor_tile.svg#/media/File:Socolar-Taylor_tile.svg “Socolar-Taylor tile” by Parcly Taxel – Own work. Licensed under CC BY-SA 4.0 via Wikimedia Commons – https://commons.wikimedia.org/wiki/File:Socolar-Taylor_tile.svg#/media/File:Socolar-Taylor_tile.svg

10. Mochizuki’s claimed proof of the abc conjecture.   The countdown kicks off on an awkward note. If Shinichi Mochizuki’s 2012 claimed proof of the abc conjecture had gained widespread acceptance, it would definitely top this list. As it is, it remains in limbo, to the enormous frustration of everyone involved.

9. The weak Goldbach conjecture. “From 7 onwards, every odd number is the sum of three primes.” We have known since 1937 that this holds for all large enough…

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