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Proving theorems is not for the mathematicians anymore: with theorem provers, it’s now a job for the hacker.
Martin Rinard -
…Taking the quotient of M by by w itself, we get the Leech lattice. In this lattice each sphere touches 196560 others, which is the most one can attain, and again this is the only way to get 196560 spheres to touch a central one in 24 dimensions. This should be obvious by visualizing it. :-)
John Baez, Week 20 of This Week’s Finds in Mathematical Physics -
A lot of times when people first hear about topology they get they impression that it’s all about rubber doughnuts, Mobius strips, and other Dali-esque wiggly objects in hyperspace. Then, when they take courses in it, they are confronted with nasty separation axioms and cohomology theories!
John Baez -
If with your alchemy you can make three pounds of gold, why should you stop there?
John T. Graves, in his response to William Rowan Hamilton’s letter describing his discovery/invention of the (4-dimensional) quaternions.
Two months later, Graves wrote to Hamilton describing his own discovery/invention of the (8-dimensional) octonions, the largest normed division algebra.
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Certainly the best times were when I was alone with mathematics, free of ambition and pretense, and indifferent to the world.
Robert Langlands -
Note the remarkable unity of algebra. Algebraists look at mathematics and science and see structure; they study form rather than content.
Terry Gannon, Moonshine Beyond the Monster -
things I have been thinking a lot about lately include all of the following
Spin groupsClifford algebras
algebraic K-theory
the Serre-Swan theorem
Z2-graded everything (i.e. supersymmetry)
how to parallelize training a multilayer neural net
wtf is a monad in programming and why isn’t it just a monad
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(via onalighternote)
Posted on April 12, 2012 via plot summary with 2,442 notes
Source: plotsummary
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It kinda sucks that it took me so long to get around to learning about homology and cohomology, because they’re probably the most interesting mathematical ideas I’ve encountered in months.
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732 symmetry in the Poincaré disk
note that the disk is tessellated by regular heptagons here
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