On Proof and Progress in Mathematics.

Thurston, W. P. (1994). On Proof and Progress in Mathematics. Bulletin of the American Mathematical Society, 30(2), 161-177.

Type

Journal article

Intellectual base

Primary research

Year

1994

Volume

30

Issue

2

Pages

161-177

ISSN

0273-0979

DOI

10.1090/s0273-0979-1994-00502-6

DOI registrant

American Mathematical Society

Link

https://doi.org/10.1090/S0273-0979-1994-00502-6

Cited from

engineering_design, rhetoric

Cited by

2 citations across 2 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Accidental Vs Essential Complexity
  • In mathematics, a theorem's intrinsic depth is essential while the notational and bookkeeping scaffolding is accidental, which is why a reorganized proof can compress pages to lines without changing the content.

    This sourceArgues that mathematics is "amazingly compressible": once the right conceptual perspective is found there is "tremendous mental compression," so the logical core of a result is intrinsic (essential) while the notational and bookkeeping presentation is streamlined away — the basis for the claim that a reorganized proof can shrink pages to lines without changing content.

• Enthymeme
  • In mathematical exposition, published proofs are nearly always enthymematic — "obviously" and "it is clear that" mark suppressed premises the reader must supply, whereas a proof assistant states them all.

Verification

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