634:
42:
164:
as an auditor. From age eleven to seventeen, he obtained two bachelor's degrees, a license and a PhD with a thesis concerning the mathematical theory of electricity, and was admitted to the 1839 entrance examination of the École
Polytechnique. Bertrand was a professor at the
506:
An incommensurable number can be defined only by indicating how the magnitude it expresses can be formed by means of unity. In what follows, we suppose that this definition consists of indicating which are the commensurable numbers smaller or larger than it
160:. His father died when Joseph was only nine years old; by that time he had learned a substantial amount of mathematics and could speak Latin fluently. At eleven years old he attended the course of the
923:
948:
262:(1883) argued that Cournot had reached a very misleading conclusion, and he reworked it using prices rather than quantities as the strategic variables, thus showing that the
943:
674:
933:
918:
608:
913:
686:
614:
397: – situation in which two players (firms) reach a state of Nash equilibrium where both firms charge a price equal to marginal cost ("MC")
938:
667:
888:
660:
561:
893:
928:
153:
908:
536:
463:
953:
274:
454:
499:
281:
903:
898:
883:
388:
205:
746:
427:
424: – Theorem that gives the probability that an election winner will lead the loser throughout the count
421:
394:
217:
20:
433:
754:
738:
174:
403:
209:
24:
620:
818:
762:
255:
643:
683:
409:
236:
197:
438:
730:
166:
161:
415:
129:
878:
873:
331:
318:
263:
259:
228:
698:
603:
170:
8:
794:
778:
714:
251:
842:
306:(Paris: Imprimerie Impériale, 1867) (report on recent progress in mathematical analysis)
542:
273:
states in
Chapter XII, that thermodynamic entropy and temperature are only defined for
157:
133:
834:
770:
375:
Les fondateurs de l'astronomie moderne: Copernic, Tycho Brahé, Képler, Galilée, Newton
826:
722:
647:
629:
546:
532:
486:
459:
343:
Leçons sur la théorie mathématique de l'électricité / professées au Collège de France
193:
585:
638:
580:
524:
232:
802:
706:
116:
625:
374:
366:
358:
350:
342:
326:
310:
302:
294:
270:
141:
528:
220:. In 1849, he was the first to define real numbers using what is now termed a
867:
850:
652:
335:
125:
121:
810:
298:(Paris : Gauthier-Villars, 1864–1870) (2 volumes treatise on calculus)
221:
213:
201:
180:
He conjectured, in 1845, that there is at least one prime number between
96:
412: – Existence of a prime number between any number and its double
247:
243:
137:
458:. Vol. 2. New York: Charles Scribner's Sons. pp. 87–89.
303:
Rapport sur les progrès les plus récents de l'analyse mathématique
924:
Corresponding members of the Saint
Petersburg Academy of Sciences
177:
of which he was the permanent secretary for twenty-six years.
487:Éloge historique de Joseph Bertrand par Gaston Darboux (1902)
452:
Struik, D.J. (1970–1980). "Bertrand, Joseph Louis
Francois".
62:
949:
Honorary members of the Saint
Petersburg Academy of Sciences
41:
277:. He was one of the first people to state this publicly.
399:
Pages displaying wikidata descriptions as a fallback
362:(Paris : J. Hetzel, 1865) (biography of Arago)
295:
Traité de calcul différentiel et de calcul intégral
200:, in 1850. He was also famous for two paradoxes of
944:Members of the Royal Swedish Academy of Sciences
865:
559:
280:In 1858 he was elected a foreign member of the
682:
668:
354:(Paris : Gauthier-Villars et fils, 1889)
346:(Paris : Gauthier-Villars et fils, 1890)
120:; 11 March 1822 – 5 April 1900) was a French
604:Bertrand, Joseph Louis Francois (1822–1900)
451:
675:
661:
40:
919:Members of the French Academy of Sciences
584:
330:(Mallet-Bachelier, 1855) (translation of
152:Joseph Bertrand was the son of physician
497:
370:(Paris : C. Lévy, 1891) (biography)
266:price was simply the competitive price.
934:Academic staff of the Collège de France
441: – Theorem in dimensional analysis
866:
378:(Paris: J. Hetzel, 1865) (biographies)
212:. There is another paradox concerning
656:
518:
322:(Paris : Gauthier-Villars, 1887)
115:
939:Foreign members of the Royal Society
287:
216:that is named for him, known as the
196:proved this conjecture, now termed
154:Alexandre Jacques François Bertrand
13:
889:19th-century French mathematicians
521:Eine kurze Geschichte der Analysis
455:Dictionary of Scientific Biography
445:
391: – Probability theory paradox
14:
965:
914:Members of the Académie Française
635:Works by or about Joseph Bertrand
597:
314:(L. Hachette, 1849) (arithmetics)
282:Royal Swedish Academy of Sciences
156:and the brother of archaeologist
227:Bertrand translated into French
117:[ʒozɛflwifʁɑ̃swabɛʁtʁɑ̃]
586:10.1090/s0002-9904-1891-00020-6
254:(1838) of French mathematician
23:. For the Olympic swimmer, see
19:For the basketball player, see
894:19th-century French economists
621:Joseph Louis François Bertrand
615:References for Joseph Bertrand
609:Joseph Louis François Bertrand
553:
512:
491:
480:
389:Bertrand paradox (probability)
109:Joseph Louis François Bertrand
34:Joseph Louis François Bertrand
1:
473:
909:French probability theorists
406: – Mathematical paradox
395:Bertrand paradox (economics)
359:Arago et sa vie scientifique
147:
21:Joseph Bertrand (basketball)
7:
755:Pierre Jean Georges Cabanis
747:Claude-Carloman de Rulhière
382:
327:Méthode des moindres carrés
10:
970:
929:École Polytechnique alumni
739:Nicolas Thyrel de Boismont
260:Bertrand Competition Model
246:, he reviewed the work on
173:, and was a member of the
18:
693:
560:Davis, Ellery W. (1891).
529:10.1007/978-3-662-57816-2
498:Bertrand, Joseph (1849).
422:Bertrand's ballot theorem
252:Cournot Competition Model
250:theory, specifically the
188: − 2 for every
175:Paris Academy of Sciences
102:
92:
85:
69:
48:
39:
32:
25:Joseph Bertrand (swimmer)
954:Lycée Saint-Louis alumni
819:Marie-Jean-Lucien Lacaze
763:Antoine Destutt de Tracy
626:Works by Joseph Bertrand
428:Bertrand–Edgeworth model
351:Calcul des probabilités
256:Antoine Augustin Cournot
904:French number theorists
617:(archived 3 March 2016)
611:(archived 4 April 2004)
564:Calcul des Probabilités
418: – Physics theorem
237:method of least squares
231:'s work concerning the
899:Differential geometers
519:Spalt, Detlef (2019).
501:Trait'e d'Arithmetique
430: – Economic Model
404:Bertrand's box paradox
124:whose work emphasized
884:Scientists from Paris
573:Bull. Amer. Math. Soc
311:Traité d'arithmétique
130:differential geometry
113:French pronunciation:
439:Buckingham π theorem
410:Bertrand's postulate
275:reversible processes
229:Carl Friedrich Gauss
198:Bertrand's postulate
16:French mathematician
795:Marcellin Berthelot
779:Jean-Baptiste Dumas
731:Jean-François Boyer
715:Jacques de Tourreil
208:and the Paradox of
192: > 3.
167:École Polytechnique
162:École Polytechnique
684:Académie française
566:, par J. Bertrand"
416:Bertrand's theorem
206:Bertrand's Paradox
158:Alexandre Bertrand
134:probability theory
861:
860:
827:Jacques Chastenet
723:Jean-Roland Malet
699:Daniel de Priézac
630:Project Gutenberg
538:978-3-662-57815-5
465:978-0-684-10114-9
288:Works by Bertrand
171:Collège de France
106:
105:
87:Scientific career
961:
854:
846:
843:Pierre-Jean Rémy
838:
830:
822:
814:
806:
798:
790:
782:
774:
766:
758:
750:
742:
734:
726:
718:
710:
702:
677:
670:
663:
654:
653:
646:in the database
639:Internet Archive
591:
590:
588:
570:
557:
551:
550:
516:
510:
509:
495:
489:
484:
469:
400:
233:theory of errors
218:Bertrand Paradox
119:
114:
76:
58:
56:
44:
30:
29:
969:
968:
964:
963:
962:
960:
959:
958:
864:
863:
862:
857:
849:
841:
835:Georges Dumézil
833:
825:
817:
809:
803:Francis Charmes
801:
793:
787:Joseph Bertrand
785:
777:
771:François Guizot
769:
761:
753:
745:
737:
729:
721:
713:
707:Michel Le Clerc
705:
697:
689:
681:
600:
595:
594:
568:
558:
554:
539:
517:
513:
496:
492:
485:
481:
476:
466:
448:
446:Further reading
398:
385:
319:Thermodynamique
290:
271:Thermodynamique
204:, known now as
150:
112:
81:
78:
74:
65:
60:
54:
52:
35:
28:
17:
12:
11:
5:
967:
957:
956:
951:
946:
941:
936:
931:
926:
921:
916:
911:
906:
901:
896:
891:
886:
881:
876:
859:
858:
856:
855:
847:
839:
831:
823:
815:
807:
799:
791:
783:
775:
767:
759:
751:
743:
735:
727:
719:
711:
703:
694:
691:
690:
680:
679:
672:
665:
657:
651:
650:
644:Author profile
641:
632:
623:
618:
612:
606:
599:
598:External links
596:
593:
592:
552:
537:
511:
490:
478:
477:
475:
472:
471:
470:
464:
447:
444:
443:
442:
436:
434:Bertrand curve
431:
425:
419:
413:
407:
401:
392:
384:
381:
380:
379:
371:
363:
355:
347:
339:
323:
315:
307:
299:
289:
286:
210:Bertrand's box
149:
146:
142:thermodynamics
104:
103:
100:
99:
94:
90:
89:
83:
82:
79:
77:(aged 78)
71:
67:
66:
61:
50:
46:
45:
37:
36:
33:
15:
9:
6:
4:
3:
2:
966:
955:
952:
950:
947:
945:
942:
940:
937:
935:
932:
930:
927:
925:
922:
920:
917:
915:
912:
910:
907:
905:
902:
900:
897:
895:
892:
890:
887:
885:
882:
880:
877:
875:
872:
871:
869:
852:
851:Xavier Darcos
848:
844:
840:
836:
832:
828:
824:
820:
816:
812:
808:
804:
800:
796:
792:
788:
784:
780:
776:
772:
768:
764:
760:
756:
752:
748:
744:
740:
736:
732:
728:
724:
720:
716:
712:
708:
704:
700:
696:
695:
692:
688:
685:
678:
673:
671:
666:
664:
659:
658:
655:
649:
645:
642:
640:
636:
633:
631:
627:
624:
622:
619:
616:
613:
610:
607:
605:
602:
601:
587:
582:
578:
574:
567:
565:
556:
548:
544:
540:
534:
530:
526:
522:
515:
508:
503:
502:
494:
488:
483:
479:
467:
461:
457:
456:
450:
449:
440:
437:
435:
432:
429:
426:
423:
420:
417:
414:
411:
408:
405:
402:
396:
393:
390:
387:
386:
377:
376:
372:
369:
368:
367:Blaise Pascal
364:
361:
360:
356:
353:
352:
348:
345:
344:
340:
337:
336:least squares
333:
329:
328:
324:
321:
320:
316:
313:
312:
308:
305:
304:
300:
297:
296:
292:
291:
285:
283:
278:
276:
272:
267:
265:
261:
257:
253:
249:
245:
240:
238:
234:
230:
225:
223:
219:
215:
211:
207:
203:
199:
195:
191:
187:
183:
178:
176:
172:
168:
163:
159:
155:
145:
143:
139:
135:
131:
127:
126:number theory
123:
122:mathematician
118:
110:
101:
98:
95:
91:
88:
84:
80:Paris, France
72:
68:
64:
63:Paris, France
59:11 March 1822
51:
47:
43:
38:
31:
26:
22:
811:Jules Cambon
786:
579:(1): 16–25.
576:
572:
563:
555:
523:. Springer.
520:
514:
505:
504:. page 203.
500:
493:
482:
453:
373:
365:
357:
349:
341:
325:
317:
309:
301:
293:
279:
268:
241:
226:
222:Dedekind cut
189:
185:
181:
179:
151:
108:
107:
86:
75:(1900-04-05)
73:5 April 1900
879:1900 deaths
874:1822 births
334:'s work on
264:equilibrium
242:Concerning
214:game theory
202:probability
97:Mathematics
868:Categories
474:References
55:1822-03-11
562:"Review:
547:186745152
269:His book
248:oligopoly
244:economics
194:Chebyshev
148:Biography
138:economics
383:See also
235:and the
687:seat 40
637:at the
853:(2013)
845:(1988)
837:(1978)
829:(1956)
821:(1936)
813:(1918)
805:(1908)
797:(1900)
789:(1884)
781:(1875)
773:(1836)
765:(1808)
757:(1803)
749:(1787)
741:(1755)
733:(1736)
725:(1714)
717:(1692)
709:(1662)
701:(1639)
648:zbMATH
545:
535:
462:
258:. His
93:Fields
569:(PDF)
543:S2CID
332:Gauss
184:and 2
533:ISBN
507:....
460:ISBN
169:and
140:and
70:Died
49:Born
628:at
581:doi
525:doi
870::
575:.
571:.
541:.
531:.
284:.
239:.
224:.
144:.
136:,
132:,
128:,
676:e
669:t
662:v
589:.
583::
577:1
549:.
527::
468:.
338:)
190:n
186:n
182:n
111:(
57:)
53:(
27:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
