Take a ball in four dimensions. Get as many balls of the same size to touch it without overlapping. The most you can do is 24.
We believe - though it hasn't been proved yet - that you're forced to put 16 of these balls at the corners of a hypercube and the other 8 at the corners of a hyperoctahedron.
If you look hard, you can see the red balls here are at the corners of a hypercube, drawn in perspective. The green ones are at the corners of a hyperoctahedron.
All this is just the tip of the iceberg! To hear the whole story, come to my online talk about the numbers 8 and 24:
You can attend on Zoom 10:00 am- 11:30 am Eastern Time, Thursday August 24, 2023. You can already see the slides now if you're the sort who prefers that. And the talk will be on YouTube eventually, if you're the sort who prefers that. I aim to please everyone.
@johncarlosbaez not sure if there is time for contributions but I expect you include the integer solutions of the alternate sum n^2= (+-) (1-4+9-...+ m^2)
It is interesting watching #Twitter (from afar) sheepishly backtrack on the #LK99 hype.
There were three, maybe four ringleaders as far as I could tell - which included some that are competent in science and physics that should have known better.
But whipping up useless hype gets people paid by Twitter at the moment.
It all really underscores my position on how unsuitable Twitter is for actual science and public education - and that was fairly true even in the pre-#Musk Twitter Era.
@adamjcook a problem with the "good science" take is that it took two weeks to get into the arxiv paper telling that the claimed phase transitions was a well known hallmark of Cu2 S. And nobody told it before in twitter.
The Koide formula is a mysterious relation between the 3 charged leptons:
the electron,
the muon (like an electron but ~206.768 times heavier),
the tau (like an electron but ~3477 times heavier).
Nobody knows whether it's really true or just a coincidence.
For the most part, serious physicists have given up seeking relations between masses of elementary particles, because it's so hard to explain any such relations.