Theme 1 – Practical relevance of theory
Many commenters argue that theoretical results that lack immediate practical use are of little value.
- “If algorithmic theorists don’t care about practical performance then why should we care about what they’re doing? It’s just a strange game they’re playing, of no interest to anyone else.” — skybrian
- “No, I don’t care. Until there is a real, practical result, I don’t care.” — adastra22
- “Theory with no possible practical relevance is useless… a computational complexity result requiring arbitrary‑precision arithmetic that is impossible to implement using any physical system qualifies.” — modeless
Theme 2 – Critique of big‑O and unrealistic model assumptions
Several participants point out that big‑O notation can hide enormous constants or rely on operations (e.g., exact complex arithmetic) that cannot be performed in constant time on real hardware, making the claimed improvements “galactic.”
- “The argument… is about whether the n in any particular big O is relevant… the result holds only if you don’t include the cost to multiply arbitrarily large complex numbers.” — burpingtree
- “the constants inside a big‑O are not really constant: they depend on what you assume is a constant‑time operation.” — LPisGood
- “> the algorithm requires you to multiply complex numbers whose magnitudes grow superpolynomially with n. Err... doesn't that completely invalidate the big‑O analysis!?” — jiggawatts
Theme 3 – Long‑term value of seemingly impractical theory
Defenders note that many mathematical breakthroughs were initially useless but later enabled major practical advances (e.g., number theory → cryptography, relativity → GPS).
- “You don't need to care. But every so often breakthroughs in theory can be turned into breakthroughs in practice.” — eru
- “Doing theory is what gives you a chance to push the envelope to places you can’t even imagine when you’re knee deep in real world problems… proving something is possible (if impractical) gives an incentive to find a better algorithm.” — cpa (cites Fermat → modern cryptography)
- “Plenty of mathematics was practically useless for long periods of time, waiting for us to invent computers, cryptography, error correcting codes, etc.” — nullc