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https://www.informit.com/articles/article.aspx?p=2213858

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  • Every problem whose solution can be efficiently verified can also be efficiently solved (P equals NP).

    Without evidence. Knuth presents his position as a personal conviction resting on two heuristics he himself calls naive: that so many able people have failed to prove inequality, and that among the enormous number of algorithms running in n to a huge power it is hard to believe all fail. The Robertson-Seymour graph minor theorem, which guarantees polynomial-time algorithms nobody can write down, is what he says tipped him. It is the best-known dissent from the field's majority view and is offered as intuition rather than evidence. Sep 16, 2026

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Art of Computer Programming, The: Volume 1: Fundamental Algorithms, 3rd Edition130 passages · 1 marked

Don Knuth: As you say, I've come to believe that P = N P , namely that there does exist an integer M and an algorithm that will solve every n -bit problem belonging to the class N P in n M elementary steps.

Every problem whose solution can be efficiently verified can also be efficiently solved (P equals NP).UnknownReading · this claim’s Steward

Without evidence. Knuth presents his position as a personal conviction resting on two heuristics he himself calls naive: that so many able people have failed to prove inequality, and that among the enormous number of algorithms running in n to a huge power it is hard to believe all fail. The Robertson-Seymour graph minor theorem, which guarantees polynomial-time algorithms nobody can write down, is what he says tipped him. It is the best-known dissent from the field's majority view and is offered as intuition rather than evidence.

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https://www.informit.com/articles/article.aspx?p=2213858
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https://web.archive.org/web/20260822202021/https://www.informit.com/articles/article.aspx?p=2213858
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44,018 characters, retrieved Sep 16, 2026 · 88 sections, 146 passages
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History 4

  1. Nov 9, 2026DividedSegmenter · Divided into 233 parts by its own structure
  2. Nov 9, 2026FactsFacts fetcher · Facts looked up
  3. Sep 16, 2026ReadingSteward of “Every problem whose solution can be efficiently…” · asserts without evidence, read whole
  4. Sep 16, 2026Entered the graphEntered the graph; copy stored