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Explanation
The Joke
A mathematician comes before an audience to propose "a new branch of mathematics." His goal is to find the "least elegant proof" -- that is, the proof that requires the most effort for the shallowest understanding. He demonstrates by considering the game of Go: the number of possible games on a 19x19 Go board can be found in the OEIS (the Online Encyclopedia of Integer Sequences), and by setting up some elaborate formula relating Go board configurations to a trivially simple mathematical fact, one could construct a maximally inelegant proof.
However, another mathematician objects that this is "too ugly" even by the standards of this proposed discipline. Before the proposer can respond, the audience erupts into a violent mob, screaming "GAS HIM! GAS HIM!" as the scene turns to red-tinted chaos.
The Humor
The comic satirizes the mathematical community's deep aesthetic attachment to elegance in proofs. Mathematicians famously prize beautiful, concise proofs (Paul Erdos spoke of "The Book" containing God's most elegant proofs) and viscerally recoil from ugly, brute-force ones. The joke inverts this value system by proposing a field dedicated to finding the least elegant proofs, which is inherently self-defeating -- pursuing ugliness with rigor is itself a kind of perverse elegance.
The violent overreaction in the final panels is a classic SMBC escalation gag. The mathematicians respond to a bad proof the way a mob would respond to genuine villainy, treating aesthetic offense as a capital crime. The reference to the OEIS is a nod to the real mathematical resource that SMBC's mathematically literate audience would recognize. The comic also plays on the idea that within mathematics, aesthetics function almost as moral principles, so an intentionally ugly proof is treated as a kind of moral atrocity worthy of mob justice.