How to construct the Leech lattice

This lecture describes an astonishingly simple construction of the Leech lattice in 24 dimensions, found by John Conway and Neal Sloane.

[diribigal]

Thanks to Lyam Boylan for the fancy visuals

[uroscolovic]

Professor your work is already amazing, and this new concept for videos is interesting. Today I got highest grade at Mathematical Logic exam, for which I had a huge help from your ZFC videos. I just wanted to express gratitude.

[yamsox]

A pleasure collaborating! Very interesting topic too, as I learned a lot in the process.

[larspos]

When two of your favourite creators collaborate

[alexandersanchez]

@Lyam Boylan I think you have the slash the wrong way around at 6:45. When professor Borcherds says "kill off all copies of rho" he means quotient by the subspace spanned by rho. He doesn't mean deleting rho (or integer multiples of it) because that would still leave us in 25 dimensions.

[Helgabion]

Really cool colab!! I hope you make more videos like this in the future :)

[vert]

I feel like I am just being spoiled with a lecture so good I will dangerously assume all other math lectures are equally as good from this point onwards.

[RickyMud]

This is the highest production video of yours I’ve seen so far, very nice

[oskuh.]

These new animations make these videos even more fantastic! Brilliant.

[asmeurer]

The video replaced forward slash / with backslash \ in the notation, which confused me a bit.

[agustinferrer]

Please continue with the animated videos, great work!

[mbgdemon]

Keep making videos like this and this channel will be huge

[captainsnake]

It’s stuff like this that reminds me why I love math. For reasons we can’t explain, this suddenly works in 24 dimensions. Nothing could be more mysterious.

[Achrononmaster]

@2:00 it is not a "joke played by the universe". It is a consequence of general relativity _with_ non-trivial local topology (so non-classical GR). The 8 and 24 arise naturally from the 4D Dirac spinors, via the Clifford algebra. You will not so easily see this if you use the matrix algebra rep. There are 8 disjoint 24-cells in the Standard Model of particle physics. An automorphism group of the whole lot is CPTt symmetry: CPT plus a triality "reflection".

[henryaudubon]

Wonderful combination of advanced mathematics with helpful visuals. Brilliant video!

[charlieaydin]

Dude i was ready to click away but i thought id give it a chance. About 25 seconds in i was so caught up i thought ‘i should get comfy for this’.

This was so stimulating and well presented. Thank tou

[angryscientist]

This is beautiful. I'd be lying if I said I understood exactly what is going on here, but I am gonna keep coming back to this video until I do.

[aam]

I barely understood any of it - but stayed for the beauty of what you were describing even if my appreciation was superficial at best. I’d love to know how you go about producing the graphics for these presentations.

[杨远-rd]

Professor this work is so amazing I've watched it over and over. Together with the RH video these two might be the best manim video's I've ever seen.

[miguelandrade]

It was not only interesting, but also a great cinematic experince!!! Loved it <3