Évolution des publications scientifiques

Bibliometry and mathematicsÉtienne GHYS

Académie des Sciences14-15 mai 2007

Colloque de l’Académie des sciences "Évolution des publications scientifiques - Le regard des chercheurs" des 14-15 mai 2007

Mathematics : a small world

• ≃ 2 500 000 papers written since Euclid…

• ≃ 70 000 mathematical papers each year.

Nombre d'articles publiés (par tranches de 5 ans)

16268 2163536492

4898170043

89893

138291

177062

213605

259002279976

320375

364100

0

50000

100000

150000

200000

250000

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350000

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40-44 45-49 50-54 55-59 60-64 65-69 70-74 75-79 80-84 85-89 90-94 95-99 00-04

Mathematicians don’t write too much

• Typically, 1 or 2 published papers per year (averaged over the career) is considered as a good activity.

• A mathematical paper has usually 1 or 2 authors, sometimes 3.

• Usually, the bibliography of a paper contains 10 to 20 items.

but they read a lot !

Number of Citations : a useless tool in mathematics

• Highly depends on the subdomain• Example : 27 mathematicians from

the Académie des Sciences !• From 5850 to• 60 …

Mathematical « time scale » is long !

• Typically a paper is published 1 to 2 years after submission (sometimes more):

• Referee procedure is fundamental (and long!)• « Half life » of a maths paper is 10 to 20

years. Longer for some very good papers.

The « Impact factor » is not appropriate for mathematicians

Citations 2004

43869

31649

21172

15663

11583

9058

65514553

32532032 1344 640 483 117 60 37 28 19 21 25 14

0

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20000

25000

30000

35000

40000

45000

50000

99-03 94-98 89-93 84-88 79-83 74-78 69-73 64-68 59-63 54-58 49-53 44-48 39-43 34-38 29-33 24-28 19-23 14-18 09--13

04--08

99-03

Example : the Comptes Rendus :

Mathématique• Among the mathematical papers

published between 2000 and 2004• 3 469 contain a citation to a Compte

Rendu Note published in the 90’s• 1 600 in the 80’s• 871 in the 70’s• 465 in the 60’s• 190 in the 50’s• 123 in the 19th century !

How to evaluate a mathematician ?

• Only good method : read his/her papers !• Acceptable method : trust somebody who

read his/her papers.• Prizes, Awards, Invitation to Congresses, etc.• Comité National des Universités, Comité

National d’évaluation de la recherche scientifique, etc.

The mathematical world is small enough

to allow a « personalized » evaluation.

Read Condorcet !

Essai sur l’application de l’analyse à la probabilité des décisions rendues à la pluralité

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