PL EN


Journal
2013 | 21 | 1(81) | 7-22
Article title

Kilka słów o dowodzie w matematyce

Authors
Title variants
EN
Some words on a proof in mathematics
Languages of publication
PL
Abstracts
EN
The aim of the paper is to study the role and features of proofs in mathematics. Formal and informal proofs are distinguished. It is stressed that the main roles played by proofs in mathematical research are verification and explanation. The problem of the methods acceptable in informal proofs, in particular of the usage of computers, is considered with regard to the proof of the Four-Color Theorem. The features of informal and formal proofs are compared and contrasted. It is stressed that the concept of an informal proof is not precisely defined, it is simply practised and any attempts to define it fail. It is − so to speak − a practical notion, psychological, sociological and cultural in character. The second one is precisely defined in terms of logical concepts. Hence it is a logical concept which is rather theoretical than practical in character. The first one is − in part at least − semantical in nature, the second is entirely syntactical. A proof-theoretical thesis, similar to the Turing-Church Thesis in the recursion theory, is formulated. It says that both concepts of a proof in mathematics are equivalent. Arguments for and against it are formulated.
Keywords
Journal
Year
Volume
21
Issue
Pages
7-22
Physical description
Contributors
  • Uniwersytet im. Adama Mickiewicza, Wydział Matematyki i Informatyki, ul. Umultowska 87, 61−614 Poznań, Poland
References
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.cejsh-c647bab9-e4c5-4e25-bb3f-033a422c254e
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