Every mathematician has only a few tricks

Taco Bell math, cheat codes, and memes—geniuses reuse the same few moves

TLDR: A MathOverflow thread argues even top mathematicians rely on a small set of repeatable tricks. Commenters split between praising the “few tricks” playbook, joking about “Taco Bell math,” and defending complexity and randomness as real cheat codes—spotlighting how shared problem-solving patterns drive breakthroughs across math and engineering.

MathOverflow dusted off Gian-Carlo Rota’s claim that even legends like Hilbert reuse just a handful of tricks—and the crowd brought receipts. Mathematicians flexed their favorite moves: swap the order of sums, remember the average beats the min/max, and apply linearity of expectation to everything (yes, even noodles). One camp cheers simplicity—“If you can’t prove it, make it simpler”—while a rival camp cackles: make it more complicated and add parameters until the problem bows. Combinatorics folks joke: shove it into OEIS (an online sequence encyclopedia) and pray. Erdős fans swear by randomness; purists say ditch inclusion–exclusion and let Möbius do the dirty work. Then came drama: is the famous “pigeonhole principle” basic, or is Dijkstra’s average trick the classy version? Nostalgia hit hard when Tricki.org resurfaced—a wiki of tactics, now a relic. The joke that stole the show: eigenman’s “Taco Bell math”—same six ingredients, infinite menu. And the campus legend? ArcHound waking from a nap, whispering “Chinese Remainder Theorem,” and solving 90% of an algebra class. Meanwhile, Atiscant summed up the vibe: get enough structure and do an “abstract nonsense” proof. The big fight: are we all remix artists, or inventors of new tools? Either way, the community’s calling them cheat codes.

Key Points

  • A MathOverflow thread compiles frequently used mathematical problem-solving tricks, inspired by Gian-Carlo Rota’s essay.
  • General strategies include changing the order of summation/integration, simplifying or adding parameters, consulting OEIS, exploiting duality, and using random constructions.
  • Core inequalities and analytic tools cited include triangle inequality, Hölder/Cauchy–Schwarz, integration by parts, and average-based bounds related to the pigeonhole principle.
  • Combinatorial and probabilistic techniques highlighted include Möbius inversion for inclusion–exclusion and linearity of expectation (e.g., in Buffon’s needle).
  • Additional standard methods mentioned include group actions (symmetric group), series expansions for inverses, and commutative algebra routines (localize + complete, hypersurface sections, socle).

Hottest takes

“we’re like Taco Bell. We all use the same six ingredients, mixing them in different ways.” — eigenman
“I woke up, said Chinese remainder theorem and with like 90% success rate” — ArcHound
“do an “abstract nonsense” proof” — Atiscant
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