Mathematical proofs at a crossroad?
Identifieur interne : 000F01 ( Main/Exploration ); précédent : 000F00; suivant : 000F02Mathematical proofs at a crossroad?
Auteurs : Cristian S. Calude [Nouvelle-Zélande] ; Solomon Marcus [Roumanie]Source :
- Lecture notes in computer science [ 0302-9743 ] ; 2004.
Descripteurs français
- Pascal (Inist)
- Wicri :
- topic : Sociologie.
English descriptors
- KwdEn :
Abstract
For more than 2000 years, from Pythagoras and Euclid to Hilbert and Bourbaki, mathematical proofs were essentially based on axiomatic-deductive reasoning. In the last decades, the increasing length and complexity of many mathematical proofs led to the expansion of some empirical, experimental, psychological and social aspects, yesterday only marginal, but now changing radically the very essence of proof. In this paper, we try to organize this evolution, to distinguish its different steps and aspects, and to evaluate its advantages and shortcomings. Axiomatic-deductive proofs are not a posteriori work, a luxury we can marginalize nor are computer-assisted proofs bad mathematics. There is hope for integration!
Affiliations:
Links toward previous steps (curation, corpus...)
- to stream PascalFrancis, to step Corpus: 000033
- to stream PascalFrancis, to step Curation: 000066
- to stream PascalFrancis, to step Checkpoint: 000032
- to stream Main, to step Merge: 000F12
- to stream Main, to step Curation: 000F01
Le document en format XML
<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en" level="a">Mathematical proofs at a crossroad?</title><author><name sortKey="Calude, Cristian S" sort="Calude, Cristian S" uniqKey="Calude C" first="Cristian S." last="Calude">Cristian S. Calude</name><affiliation wicri:level="1"><inist:fA14 i1="01"><s1>University of Auckland</s1><s3>NZL</s3><sZ>1 aut.</sZ></inist:fA14><country>Nouvelle-Zélande</country><wicri:noRegion>University of Auckland</wicri:noRegion></affiliation></author><author><name sortKey="Marcus, Solomon" sort="Marcus, Solomon" uniqKey="Marcus S" first="Solomon" last="Marcus">Solomon Marcus</name><affiliation wicri:level="1"><inist:fA14 i1="02"><s1>Romanian Academy</s1><s3>ROM</s3><sZ>2 aut.</sZ></inist:fA14><country wicri:auto="ROM">Roumanie</country><wicri:noRegion>Romanian Academy</wicri:noRegion></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">INIST</idno><idno type="inist">04-0437916</idno><date when="2004">2004</date><idno type="stanalyst">PASCAL 04-0437916 INIST</idno><idno type="RBID">Pascal:04-0437916</idno><idno type="wicri:Area/PascalFrancis/Corpus">000033</idno><idno type="wicri:Area/PascalFrancis/Curation">000066</idno><idno type="wicri:Area/PascalFrancis/Checkpoint">000032</idno><idno type="wicri:explorRef" wicri:stream="PascalFrancis" wicri:step="Checkpoint">000032</idno><idno type="wicri:doubleKey">0302-9743:2004:Calude C:mathematical:proofs:at</idno><idno type="wicri:Area/Main/Merge">000F12</idno><idno type="wicri:Area/Main/Curation">000F01</idno><idno type="wicri:Area/Main/Exploration">000F01</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a">Mathematical proofs at a crossroad?</title><author><name sortKey="Calude, Cristian S" sort="Calude, Cristian S" uniqKey="Calude C" first="Cristian S." last="Calude">Cristian S. Calude</name><affiliation wicri:level="1"><inist:fA14 i1="01"><s1>University of Auckland</s1><s3>NZL</s3><sZ>1 aut.</sZ></inist:fA14><country>Nouvelle-Zélande</country><wicri:noRegion>University of Auckland</wicri:noRegion></affiliation></author><author><name sortKey="Marcus, Solomon" sort="Marcus, Solomon" uniqKey="Marcus S" first="Solomon" last="Marcus">Solomon Marcus</name><affiliation wicri:level="1"><inist:fA14 i1="02"><s1>Romanian Academy</s1><s3>ROM</s3><sZ>2 aut.</sZ></inist:fA14><country wicri:auto="ROM">Roumanie</country><wicri:noRegion>Romanian Academy</wicri:noRegion></affiliation></author></analytic><series><title level="j" type="main">Lecture notes in computer science</title><idno type="ISSN">0302-9743</idno><imprint><date when="2004">2004</date></imprint></series></biblStruct></sourceDesc><seriesStmt><title level="j" type="main">Lecture notes in computer science</title><idno type="ISSN">0302-9743</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Axiomatic</term><term>Sociology</term><term>Theorem proving</term></keywords><keywords scheme="Pascal" xml:lang="fr"><term>Démonstration théorème</term><term>Sociologie</term><term>Axiomatique</term></keywords><keywords scheme="Wicri" type="topic" xml:lang="fr"><term>Sociologie</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">For more than 2000 years, from Pythagoras and Euclid to Hilbert and Bourbaki, mathematical proofs were essentially based on axiomatic-deductive reasoning. In the last decades, the increasing length and complexity of many mathematical proofs led to the expansion of some empirical, experimental, psychological and social aspects, yesterday only marginal, but now changing radically the very essence of proof. In this paper, we try to organize this evolution, to distinguish its different steps and aspects, and to evaluate its advantages and shortcomings. Axiomatic-deductive proofs are not a posteriori work, a luxury we can marginalize nor are computer-assisted proofs bad mathematics. There is hope for integration!</div></front></TEI><affiliations><list><country><li>Nouvelle-Zélande</li><li>Roumanie</li></country></list><tree><country name="Nouvelle-Zélande"><noRegion><name sortKey="Calude, Cristian S" sort="Calude, Cristian S" uniqKey="Calude C" first="Cristian S." last="Calude">Cristian S. Calude</name></noRegion></country><country name="Roumanie"><noRegion><name sortKey="Marcus, Solomon" sort="Marcus, Solomon" uniqKey="Marcus S" first="Solomon" last="Marcus">Solomon Marcus</name></noRegion></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Mathematiques/explor/BourbakiV1/Data/Main/Exploration
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000F01 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 000F01 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Wicri/Mathematiques
|area= BourbakiV1
|flux= Main
|étape= Exploration
|type= RBID
|clé= Pascal:04-0437916
|texte= Mathematical proofs at a crossroad?
}}
| This area was generated with Dilib version V0.6.33. |  |