This is a higher-level paper, but still a survey (so more readable). It ties together disparate areas like Platonic solids (A-D-E), Milnor’s exceptional fibre, and algebra.
It has pictures and you’ll get a better sense of what mathematics is like from skimming it.
In Simons Foundation’s interview by Michael Hartley Freedman of Robion Kirby, Freedman mentions this paper in which MHF applied RK’s “torus trick” to compression via wavelets.
Programmers work with graphs often (file system, greplin, trees, "graph isomorphism problem" (who cares) ). But have you ever tried to construct a simpler building-block (basis) with which graphs could be built? Or at least a different building block to build the same old things.
This <10-page paper also uses 𝔰𝔩₂(ℂ), a simple mathematical object you haven’t heard of, but which is a nice lead-in to an area of real mathematics—rep theory—that (1) contains actual insights (1a) that you aren’t using (2) is simple (3) isn’t pretentious.
I show this paper to college freshmen because
• it’s pictorial
• it’s about an object you mightn’t have considered mathematical
• no calculus, crypto, ML, or pretentious notation
• it’s short
• it’s a classification proof: “How can it be that you know something about _all possible_ X, even the xϵX you haven’t seen yet?’
need, more than ever, for the software we write to work reliably in a
wide range of conditions--even, and especially, in unexpected
conditions. This paper, written by Robert Rasmussen from the Jet
Propulsion Laboratory in 2008, documents and explains some fundamental
principles about designing fault tolerant systems as learned through
the hard-won experience of designing Guidance, Navigation, and Control
(GN&C) systems for spacecraft. This paper is rich in principles,
examples, and advice, and has a lot to offer to our industry
generally--even for those of us who don't actively work on software for
spaceships!
* Fix dead link for "On the resemblance and containment of documents"
* Fix dead link for "The operating system: should there be one?"
* Fix dead link for "Differential Privacy"
* Fix dead link for "A Theoretician's Guide to the Experimental Analysis of Algorithms"
