Search Results for Borel

Biographies

1. Borel biography
   
   • Felix Edouard Justin Emile Borel .
     
   • Emile Borel's father was Honore Borel who was a Protestant minister.
     
   • Honore Borel himself was the son of a craftsman from Montauben, the capital of Tarn-et-Garonne in the Midi-Pyrenees region.
     
   • At the time Emile was born, his parents were living in a fine eighteenth century house in which Honore Borel had a school for the children of Protestant families in the neighbourhood.
     
   • Honore Borel was an intelligent man and for the first years of his son's life he educated him at home.
     
   • Family friends urged Borel to enter the Ecole Polytechnique, which was considered the more prestigious establishment, but he had other ideas.
     
   • Borel was advised that a degree from the Ecole Polytechnique would give him the best opportunities for a job in industry or business.
     
   • The two became firm friends and through the Darboux family Borel came to know leading mathematicians of the day, in particular Emile Picard who he later remarked was a major influence on him at this time.
     
   • the theory of measure, Borel's theory of divergent series, his theory of non-analytic continuation and the theory of quasi-analytic functions all derive from ideas which make their first appearance in this paper.
     
   • And it contained the explicit statement and proof of the famous covering theorem which, quite inappropriately, acquired the name of the Heine-Borel theorem ..
     
   • Later Borel spoke about the mathematicians who had influenced him most in his early years mentioning, among others, Camille Jordan, Emile Picard, Paul Appell, Edouard Goursat, Paul Painleve and Marcel Brillouin.
     
   • At almost exactly the same time that he was receiving his doctorate, when still only 22 years of age, Borel was appointed Maitre de Conference at the University of Lille.
     
   • Borel achieved much over the next years, both in his career and in the outstanding mathematics which he produced.
     
   • They had no children but adopted one of Borel's nephews, Fernand Lebeau, the son of his eldest sister who he had lived with while a pupil at the Lycee at Montauben.
     
   • Marguerite Borel was an outstanding author, writing under the pen name Camille Marbo (Marbo being the first three letters of Marguerite and the first two of Borel), and received the distinction of being awarded the Prix Femina in 1913 for La Statue voilee.
     
   • In 1909 Borel was appointed to a chair of Theory of Functions created specially for him at the Sorbonne and he went on to hold this professorship until 1941.
     
   • On the fall of Painleve in 1917, Borel returned for a time to the front ..
     
   • In 1928, with financial support from Rockefeller and Rothschild, he set up the Institut Henri Poincare (the Centre Emile Borel is now part of the Institute) and he ran the Institute for thirty years.
     
   • In [Enseignement mathematique 11 (1965), 1-95.',8)">8] Borel's mathematical work is divided into the following topics: Arithmetic; Numerical series; Set theory; Measure of sets; Rarefaction of a set of measure zero; Real functions of real variables; Complex functions of complex variables; Differential equations; Geometry; Calculus of probabilities; and Mathematical physics.
     
   • Borel created the first effective theory of the measure of sets of points.
     
   • Borel, although not the first to define the sum of a divergent series, was the first to develop a systematic theory for a divergent series which he did in 1899.
     
   • In addition to many textbooks, Borel published more than fifty papers between 1905 and 1950 on the calculus of probability.
     
   • In addition, between 1921 and 1927, Borel published a series of papers on game theory and became the first to define games of strategy.
     
   • After 1924, Borel became active in the French government serving in the French Chamber of Deputies (1924-36) and as Minister of the Navy (1925-40).
     
   • In 1946, when he was 75 years old, Borel published the fascinating book Les paradoxes de l'infini.
     
   • Honours awarded to Emile Borel .
     
   • Lunar featuresCrater Borel .
     
   • Paris street namesRue Borel and Square Borel (17th Arrondissement) .
     
   • http://www-history.mcs.st-andrews.ac.uk/Biographies/Borel.html .
     

2. Borel Armand biography
   
   • Armand Borel .
     
   • Armand Borel attended secondary school in Geneva but was also educated at a number of private schools.
     
   • As well as Stiefel, Borel had attended lectures at the Ecole Polytechnique Federale by Hopf who played an important role in influencing Borel's mathematical tastes.
     
   • Following his graduation, Borel was appointed as a teaching assistant at the Ecole Polytechnique Federale in Zurich.
     
   • Jean Leray became Borel's thesis supervisor and he attended courses which he gave at the College de France.
     
   • Borel wrote [Notices Amer.
     
   • After his year in Paris, Borel went to Geneva where he substituted for the professor of algebra from 1950 to 1952.
     
   • In 1952 Borel married Gabrielle Aline Pittet; they had two daughters Dominique Odette Susan and Anne Christine.
     
   • In the autumn of 1952 Borel, and his new wife Gaby (as she was always known) set off for the United States.
     
   • Borel had been invited to spend a year at the Institute for Advanced Study at Princeton and this was extended to a second year.
     
   • This was an opportunity for Borel to learn a great deal about algebraic geometry and number theory from Weil.
     
   • We should note at this point the major contribution that Borel made to Bourbaki.
     
   • Borel writes in [Notices Amer.
     
   • I think this was basically the influence of one person, Armand Borel.
     
   • Borel's work, apart from a dozen books, lecture notes ..
     
   • Among his books are Topics in the homology theory of fibre bundles (1967), which is based on lectures Borel gave at the University of Chicago in 1954 in which he described the state of the topic at that time adopting the same methods and points of view as in his thesis.
     
   • Also in 1969 Linear algebraic groups was published based on a graduate course given by Borel at Columbia University in the spring of 1968.
     
   • One book which does not seem to be based on a lecture course is Automorphic forms on SL(R) which Borel himself says would have been better titled "Introduction to some aspects of the analytic theory of automorphic forms on SL(R) and the upper half-plane X." .
     
   • Borel received many honours for his outstanding contributions to mathematics.
     
   • The citation states that Borel's results:- .
     
   • Borel also received the Balzan prize in 1992:- .
     
   • In fact we learn much of Borel's view of mathematics in the reply he made on receiving the Balzan prize:- .
     
   • Borel was an astute observer: he had an uncanny eye for artistic detail and would reflect on the influence of literature and culture on human outlook.
     
   • Borel loved to travel and made visits to many countries including India, Mexico and China.
     
   • Honours awarded to Armand Borel .
     
   • Other Web sitesZhejiang University (Pictures of Armand Borel) .
     
   • http://www-history.mcs.st-andrews.ac.uk/Biographies/Borel_Armand.html .
     

3. Heine biography
   
   • He is best remembered for the Heine-Borel theorem:- .
     
   • The second part of this paper covers the history of the Heine-Borel theorem and is summarised in the following review:- .
     
   • The last half of the paper is devoted to a more systematic account of the gradual discovery and formulation of the so-called Heine-Borel theorem.
     
   • Borel formulated his theorem for countable coverings in 1895 and Schonflies and Lebesgue generalized it to any type of covering in 1900 and 1898 (published 1904), respectively.
     
   • The priority questions are nicely illustrated with quotes from the correspondence between Lebesgue and Borel and other letters.
     

4. Gateaux biography
   
   • Volterra himself, invited by Borel and Hadamard, came to Paris to give a series of lectures on functional analysis, published in 1913 ([Lecons sur les fonctions de lignes (Gauthier-Villars, Paris, 1913).',23)">23]) and whose redaction was precisely made by Peres.
     
   • On 18 April 1913, Emile Borel wrote to Volterra that:- .
     
   • Moreover, on the postcard sent by Borel to Volterra on 1 January 1914 with his best wishes for the new 1914 year (a sentence which sounds strange to the ears of one knowing what was going to happen soon ..
     
   • .), Borel mentioned how he was glad to learn that Volterra was absolutely satisfied with Gateaux in Rome.
     

5. Van Vleck biography
   
   • It is argued that Van Vleck proved the first zero-one law, anticipating the zero-one law of Borel and, more strikingly, that of Kolmogorov.
     
   • By following Van Vleck's own steps in deriving consequences of his zero-one law, a result ("the extended Van Vleck theorem") is given which is directly comparable to Borel's law of normal numbers.
     
   • Finally, it is shown that the Van Vleck zero-one law, which in generality falls between that of Borel and that of Kolmogorov, is further distinguished in that it provides the key step in establishing what may be the earliest example in ergodic theory of a metrically transitive transformation.
     

6. Bachelier biography
   
   • It is known, however, that he received occasional scholarships to continue his studies (on the recommendation of Emile Borel (1871-1956)) and he gave lectures as a 'free professor' at the Sorbonne between 1909 and 1914.
     
   • Borel, however, must have known Bachelier (he had approved the scholarships to Bachelier).
     
   • It seems that Bachelier, was regarded as being of lesser importance in the eyes of the French mathematical elite (Hadamard, Borel, Lebesgue, Levy, Baire).
     

7. Feldman biography
   
   • This result was strengthened by Borel in 1899 when he proved a lower bound for P(e), where P is a polynomial with integer coefficients, depending on the maximum modulus of the integer coefficients of P.
     
   • Gelfond, Feldman's supervisor, had extended Borel's result to numbers of the form αβ, where α, β are algebraic numbers.
     
   • Feldman proved in his thesis Borel type results (called the measure of transcendence) for logarithms of algebraic numbers, obtaining estimates for the lower bound depending (as did Gelfond) on both the degree of P and the maximum modulus of its coefficients.
     

8. Cantelli biography
   
   • Although his name is frequently connected with the name of E Borel, Cantelli's approach to probability is very different from that of Borel.
     
   • Around the time that Cantelli worked on the law of large numbers, Borel was also interested in the topic.
     

9. Stoilow biography
   
   • He was able to attend lectures by Picard, Poincare, Goursat, Hadamard, Borel and Lebesgue.
     
   • Later in his career he wrote articles on some of these outstanding French mathematicians (for example Mathematical work of Henri Lebesgue (Romanian) (1942) and Emile Borel and modern mathematical analysis (Romanian) (1956)).
     
   • His book Lecons sur les principes topologiques de la theorie des fonctions analytiques, published in the prestigious Collection Borel (Paris, 1937), became a classical reference in the 1940s.
     

10. Harish-Chandra biography
    
    • Armand Borel describes some of Harish-Chandra's contributions in [The mathematical legacy of Harish-Chandra, Baltimore, MD, January 9-10, 1998 (Amer.
      
    • In October 1983 a conference in honour of Armand Borel was held in Princeton [Biographical Memoirs of Fellows of the Royal Society of London 31 (1985), 199-225.',14)">14]:- .
      

11. Neyman biography
    
    • He arrived in Paris in the summer of 1926 to visit Borel.
      
    • In Paris for session 1926-27 Neyman attended lectures by Borel, Lebesgue (whose lectures he particularly enjoyed) and Hadamard and his interests began to move back towards sets, measure and integration.
      

12. Frechet biography
    
    • Another task undertaken by Frechet around this time was writing up Borel's lectures for publication.
      
    • It was Borel who encouraged Frechet to seek positions in Paris and he supported his candidacy.
      

13. Menshov biography
    
    • Menshov attended Luzin's lecture course, and when Luzin posed the open problem of whether the Denjoy integral and the Borel integral were equivalent, he was able to solve the problem.
      
    • It appeared as the paper The relationship between the definitions of the Denjoy and Borel integrals in 1916.
      

14. Montgomery biography
    
    • I was especially interested in Borel sets, analytic sets, and projective sets ..
      
    • Armand Borel expresses similar views in [Notices Amer.
      

15. Pade biography
    
    • In this post he succeeded Emile Borel who had just left Lille to take up an appointment at the Ecole Normale Superieure in Paris.
      
    • Although the theory of Pade approximants which he had developed in his thesis, and in many later papers, was not quick to be taken up by many other mathematicians, it did become well known after Borel presented Pade approximants in his 1901 book on divergent series.
      

16. Denjoy biography
    
    • In 1902 Denjoy entered the Ecole Normale Superieure where he studied under Borel, Painleve and Emile Picard.
      
    • Denjoy worked on functions of a real variable in the same areas as Borel, Baire and Lebesgue.
      

17. Lebesgue biography
    
    • Building on the work of others, including that of Emile Borel and Camille Jordan, Lebesgue formulated the theory of measure in 1901 and in his famous paper Sur une generalisation de l'integrale definie, which appeared in the Comptes Rendus on 29 April 1901, he gave the definition of the Lebesgue integral that generalises the notion of the Riemann integral by extending the concept of the area below a curve to include many discontinuous functions.
      
    • During the first world war he worked for the defence of France, and at this time he fell out with Borel who was doing a similar task.
      

18. Bernstein Felix biography
    
    • When Cantor saw Bernstein's proof he was so impressed that he communicated it to Emile Borel and it was published in Borel's Lecons sur la theorie des fonctions in 1898.
      

19. Hirzebruch biography
    
    • After serving as a Scientific Assistant at the University of Erlangen during 1951-52, he spent the two years 1952-54 at the Institute for Advanced Study in Princeton in the United States working with Armand Borel, Kunihiko Kodaira, and D C Spencer on topics such as sheaf theory, vector bundles, characteristic classes and Thom cobordism.
      
    • the proportionality theorem for complex homogeneous manifolds and (with Armand Borel) the general theory of characteristic classes of homogeneous spaces of compact Lie groups, .
      

20. Vallee Poussin biography
    
    • Further important texts published by him were his Borel tract on the Lebesgue integral (1916), approximation theory (1919), mechanics (1924), and potential theory (1937).
      

21. Rogers biography
    
    • His later work covered a wide range of different topics in geomery and analysis including Borel functions, Hausdorff measure and local measure, topological properties of Banach spaces and upper semicontinuous functions.
      

22. Geocze biography
    
    • He spent 1908 in Paris where he learnt of the effective theory of the measure of sets of points being developed by Borel, Baire and Lebesgue.
      

23. Von Neumann biography
    
    • Early in his work, a paper by Borel on the minimax property led him to develop ..
      

24. Calugareanu biography
    
    • His investigations on Picard's fundamental theorem, on theorems of Borel and Nevanlinna in connection with the study of exceptional values of meromorphic functions of finite genus, made him already in the third and fourth decades of this century one of the first important Romanian mathematicians as well as a mathematician of European stature and distinguished member of the Romanian school of complex analysis founded by David Emmanuel and Dimitrie Pompeiu.
      

25. Dieudonne biography
    
    • Armand Borel writes in [Notices Amer.
      

26. Burkill biography
    
    • This was a particularly active area of research in the early decades of this century after the pioneering work of Lebesgue, Borel and their contemporaries in establishing the concepts of measure and the Lebesgue integral associated with it.
      

27. Wazewski biography
    
    • His doctoral dissertation, on topological results relating to dendrites, was examined in 1923 by the powerful examining committee consisting of Borel, Denjoy and Montel.
      

28. Tannery Jules biography
    
    • Through his lectures and supervisory duties at the Ecole Normale this gifted teacher gave valuable guidance to many students and inspired a number of them to seek careers in science (for example, Paul Painleve, Jules Drach, and Emile Borel).
      

29. Rey Pastor biography
    
    • He also brought important foreign mathematicians to the university to give short courses, including: Frederigo Enriques (1925), Francesco Severi (1930), Tullio Levi-Civita (1937), Emile Borel (1928) and Jacques Hadamard (1930).
      

30. Hobson biography
    
    • His book Theory of Functions of a Real Variable published in 1907 was the first English book on the measure and integration developed by Baire, Borel and Lebesgue.
      

31. Aleksandrov biography
    
    • Aleksandrov proved his first important result in 1915, namely that every non-denumerable Borel set contains a perfect subset.
      

32. Hunt biography
    
    • In the last section potential theory is reached and some important results are proved: the completed maximum principle for potentials, balayage, and the almost-Borel measurability of excessive functions.
      

33. Kurepa biography
    
    • Chapter 4 is on topological and metric spaces, with the fifth and final chapter on limiting processes in analysis, measure theory, Borel and Souslin sets.
      

34. Blumenthal biography
    
    • After this he went to Paris where he spent the winter of 1899-1900 studying under Borel and Jordan.
      

35. Baire biography
    
    • While on the topic of letters, we should remark that [L\'enseignement mathematique 31 (1932), 5-13.',4)">4] contains fifty letters written by Baire to Emile Borel.
      

36. Brouwer biography
    
    • A couple of months later he made an important visit to Paris, around Christmas 1909, and there met Poincare, Hadamard and Borel.
      

37. Peres biography
    
    • He was awarded a scholarship to support him while he undertook research for his doctorate, and Borel introduced him to Volterra who made many journeys to France to promote scientific collaboration.
      

38. Appell biography
    
    • One of his three daughters was to marry Borel.
      

39. Hausdorff biography
    
    • Hausdorff proved further results on the cardinality of Borel sets in 1916.
      

40. Titeica biography
    
    • Among his lecturers were a whole host of leading mathematicians including Darboux, Picard, Poincare, Appell, Goursat, Hadamard, and Borel.
      

41. Hahn biography
    
    • In this area he studied a construction of the Lebesgue integral as a limit of Riemann sums, an integral proposed by Borel around 1910, and worked on the theory of abstract measures, in particular product measures.
      

42. Moore Eliakim biography
    
    • He brought to culmination the study of improper integrals before the appearance of the more effective integration theories of Borel and Lebesgue.
      

43. Paley biography
    
    • Zygmund discovered Paley's extraordinary talent and the two worked jointly on existence proofs, brilliantly applying ideas from Borel's Calcul des probabilites denombrables.
      

44. Sierpinski biography
    
    • Borel had proved such numbers exist but Sierpinski was the first to give an example.
      

45. Drach biography
    
    • Drach was a friend of Borel, and together they published lectures by Poincare Lecons sur la theorie de l'elasticite (1892) and by Jules Tannery Introduction a l'etude de la theorie des nombres et de l'algebre superieure (1895) while Drach was a student at the Ecole Normale Superieure.
      

46. Bruhat biography
    
    • Finally we should mention that Bruhat was a member of Bourbaki being a third generation member along with Armand Borel, Alexandre Grothendieck, Pierre Cartier, Serge Lang, and John Tate.
      

47. Khinchin biography
    
    • With these ideas he also strengthened the law of large numbers due to Borel.
      

48. Luzin biography
    
    • Luzin proceeded from the point of view of the French school (Borel, Lebesgue), which greatly influenced him.
      

History Topics

1. Real numbers 3
   
   • Emile Borel introduced the concept of a normal real number in 1909.
     
   • Borel called a number normal (in base 10) if every k-digit number occurred among all the k digit blocks about 1/10k of the time.
     
   • Now Borel was able to prove that, in one sense, almost every real number was normal.
     
   • However despite proving these facts, Borel couldn't show that any specific number was absolutely normal.
     
   • In 1927 Borel came up with his "know-it-all" number.
     
   • Borel describes k as an unnatural real number, or an "unreal" real.
     
   • Borel devotes a whole book [Les nombre inaccessible (Gauthier-Villiars, Paris, 1952).',1)" onmouseover="window.status='Click to see reference';return true">1], which he published in 1952, to discuss another idea, namely that of an "inaccessible number".
     
   • An accessible number, to Borel, is a number which can be described as a mathematical object.
     
   • However, as Borel pointed out, there are a countable number of such descriptions.
     

2. Bourbaki 2
   
   • Armand Borel first became acquainted with the Bourbaki team in 1949.
     
   • Armand Borel, Francois Bruhat, Pierre Cartier, Alexander Grothendieck, Serge Lang, and John Tate are considered the younger members of this third generation.
     
   • Armand Borel explains in [Notices Amer.
     
   • For this Armand Borel must take the bulk of the credit for he was the main driving force behind the style and content of this part.
     

3. Bourbaki 2 references
   
   • A Borel, Twenty-Five Years with Nicolas Bourbaki, (1949-1973), Notices Amer.
     
   • A Borel, Twenty-Five Years with Nicolas Bourbaki, (1949-1973), Mitt.
     
   • K Krickeberg, Comment: "Twenty-five years with Nicolas Bourbaki 1949-1973" by A Borel, Mitt.
     

4. Bourbaki 1 references
   
   • A Borel, Twenty-Five Years with Nicolas Bourbaki, (1949-1973), Notices Amer.
     
   • A Borel, Twenty-Five Years with Nicolas Bourbaki, (1949-1973), Mitt.
     
   • K Krickeberg, Comment: "Twenty-five years with Nicolas Bourbaki 1949-1973" by A Borel, Mitt.
     

5. Bourbaki 2 references
   
   • A Borel, Twenty-Five Years with Nicolas Bourbaki, (1949-1973), Notices Amer.
     
   • A Borel, Twenty-Five Years with Nicolas Bourbaki, (1949-1973), Mitt.
     
   • K Krickeberg, Comment: "Twenty-five years with Nicolas Bourbaki 1949-1973" by A Borel, Mitt.
     

6. Bourbaki 1 references
   
   • A Borel, Twenty-Five Years with Nicolas Bourbaki, (1949-1973), Notices Amer.
     
   • A Borel, Twenty-Five Years with Nicolas Bourbaki, (1949-1973), Mitt.
     
   • K Krickeberg, Comment: "Twenty-five years with Nicolas Bourbaki 1949-1973" by A Borel, Mitt.
     

7. Set theory references
   
   • H Gispert, La theorie des ensembles en France avant la crise de 1905 : Baire, Borel, Lebesgue ..
     

8. Pi history
   
   • Is π normal ? That is does every block of digits of a given length appear equally often in the expansion in every base in an asymptotic sense? The concept was introduced by Borel in 1909.
     

9. Mathematical games references
   
   • R W Dimand and M A Dimand, The early history of the theory of strategic games from Waldegrave to Borel, in Toward a history of game theory (Durham, NC, 1992), 15-27.
     

10. Real numbers 3 references
    
    • E Borel, Les nombre inaccessible (Gauthier-Villiars, Paris, 1952).
      

11. Bourbaki 1
    
    • Armand Borel explains the subtle title that was chosen for the whole work [Notices Amer.
      

12. Set theory
    
    • Emile Borel pointed out that the Axiom of Choice is in fact equivalent to Zermelo's Theorem.
      Go directly to this paragraph
      

13. Mathematical games references
    
    • R W Dimand and M A Dimand, The early history of the theory of strategic games from Waldegrave to Borel, in Toward a history of game theory (Durham, NC, 1992), 15-27.
      

14. Real numbers 3 references
    
    • E Borel, Les nombre inaccessible (Gauthier-Villiars, Paris, 1952).
      

15. Set theory references
    
    • H Gispert, La theorie des ensembles en France avant la crise de 1905 : Baire, Borel, Lebesgue ..
      

Famous Curves

Societies etc

1. International Congress Speakers
   
   • Emile Borel, Definition et domaine d'existence des fonctions monogenes uniformes.
     
   • Emile Borel, Le calcul des probabilites et les sciences exactes.
     
   • Georges Valiron, Le theoreme de Borel-Julia dans la theorie des fonctions meromorphes.
     
   • Armand Borel, Arithmetic Properties of Linear Algebraic Groups.
     

2. Paris street names
   
   • Rue Emile Borel (17th Arrondissement)nnnnn M .
     
   • Square Borel (17th Arrondissement)nnnnnnnnn .
     

3. Lunar features
   
   • (W) (L) Borel .
     

4. Lunar features
   
   • Borel .
     

5. LMS Honorary Member
   
   • 1939 E Borel .
     

6. AMS Colloquium Lecturers
   
   • 1971 Armand Borel .
     

7. Lunar features
   

8. French Mathematical Society
   
   • 1905 E Borel .
     

9. MAA Chauvenet Prize
   
   • The Borel Theorem and Its Generalizations, Bull.
     

10. Dutch Mathematical Society Brouwer Medal
    
    • 1978 A Borel .
      

11. AMS Steele Prize
    
    • 1991 Armand Borel .
      

12. Times Obituaries
    
    • Borel's biographyThe obituary (1956) .
      

References

1. References for Borel Armand
   
   • References for Armand Borel .
     
   • A Borel, Oeuvres : collected papers, Vol.
     
   • A Borel, Oeuvres : collected papers, Vol.
     
   • A Borel, Oeuvres : collected papers, Vol.
     
   • A Borel, Oeuvres : collected papers, Vol.
     
   • J Arthur, E Bombieri, K Chandrasekharan, F Hirzebruch, G Prasad, J-P Serre, T A Springer, J Tits, Armand Borel (1923-2003), Notices Amer.
     
   • A Borel, Twenty-Five Years with Nicolas Bourbaki, (1949-1973), Notices Amer.
     
   • B Casselman, Some of my memories of Armand Borel, Asian J.
     
   • A Haefliger, Armand Borel (1923-2003) (French), Gaz.
     
   • A Haefliger, Armand Borel (1923-2003), European Math.
     
   • L Ji, Armand Borel as a mentor, Asian J.
     
   • A W Knapp, J-P Serre, K Chandrasekharan, E Bombieri, F Hirzebruch, T A Springer, J Tits, J Arthur, G Prasad and M Goresky, Armand Borel, Asian J.
     
   • N Mok, Armand Borel in Hong Kong, Asian J.
     
   • J-P Serre, Discours prononce en seance publique le 30 septembre 2003 en hommage a Armand Borel (1923-2003), Gaz.
     
   • N R Wallach, Armand Borel: A reminiscence, Asian J.
     
   • http://www-history.mcs.st-andrews.ac.uk/References/Borel_Armand.html .
     

2. References for Borel
   
   • References for Emile Borel .
     
   • S Callens, Ensemble, mesure et probabilite selon Emile Borel, Math.
     
   • E F Collingwood, Emile Borel, J.
     
   • E F Collingwood, Addendum: Emile Borel, J.
     
   • L de Broglie, Notice sur la vie et l'oeuvre de Emile Borel, Academie des Sciences (9 December 1957).
     
   • M Frechet, La vie et l'oeuvre d'Emile Borel, Enseignement mathematique 11 (1965), 1-95.
     
   • E Knobloch, Emile Borel as a probabilist, in The probabilist revolution Vol 1 (Cambridge Mass., 1987), 215-233.
     
   • Lettres de Rene Baire a Emile Borel, Cahiers du Seminaire d'Histoire des Mathematiques 11 (Univ.
     
   • B Maurey and J-P Tacchi, La genese du theoreme de recouvrement de Borel, Rev.
     
   • F A Medvedev, The Du Bois-Reymond theorem and ordinal transfinite numbers in the investigations of E Borel (Russian), Istor.-Mat.
     
   • P Montel, Notice necrologique sur Emile Borel, C.
     
   • P Montel, Necrologie: Emile Borel, Rev.
     
   • O Onicescu, Emile Borel (1871-1956), the creator of the theory of measure (Romanian), Gaz.
     
   • B Penkov, Emile Borel (1871-1956) (on the occasion of the 100th anniversary of his birth) (Bulgarian), Fiz.-Mat.
     
   • S Stoilow, Emile Borel and modern mathematical analysis (Romanian), Gaz.
     
   • http://www-history.mcs.st-andrews.ac.uk/References/Borel.html .
     

3. References for Bourbaki
   
   • A Borel, Twenty-Five Years with Nicolas Bourbaki, (1949-1973), Notices Amer.
     
   • A Borel, Twenty-Five Years with Nicolas Bourbaki, (1949-1973), Mitt.
     
   • K Krickeberg, Comment: "Twenty-five years with Nicolas Bourbaki 1949-1973" by A Borel, Mitt.
     

4. References for Gateaux
   
   • Emile Borel, Introduction geometrique a quelques theories physiques (Gauthier-Villars, 1914).
     
   • Emile Borel, Sur les principes de la theorie cinetique des gaz, Ann.
     
   • Emile Borel, Mecanique statistique, d'apres l'article allemand the P Ehrenfest et T Ehrenfest, Encyclopedie des Sciences Mathematiques, Tome IV, Vol.
     

5. References for Harish-Chandra
   
   • A Borel, Some recollections of Harish-Chandra, in The mathematical legacy of Harish-Chandra, Baltimore, MD, January 9-10, 1998 (Amer.
     
   • A Borel, Some recollections of Harish-Chandra, Current Sci.
     

6. References for Baire
   
   • R Baire, Lettres de Rene Baire a emile Borel, Cahiers du Seminaire d'Histoire des Mathematiques 11 (Paris, 1990), 33-120.
     
   • H Gispert, La theorie des ensembles en France avant la crise de 1905 : Baire, Borel, Lebesgue ..
     

7. References for Van Vleck
   
   • A Novikoff and J Barone, The Borel law of normal numbers, the Borel zero-one law, and the work of Van Vleck, Historia Math.
     

8. References for Poincare
   
   • A Borel, Henri Poincare and special relativity, Enseign.
     
   • A Chatelet, G Valiron, E LeRoy and E Borel, Hommage a Henri Poincare, Congres International de Philosophie des Sciences, Paris, 1949 Vol I (Paris, 1951), 37-64.
     

9. References for Heine
   
   • P Dugac, Sur la correspondance de Borel et le theoreme de Dirichlet- Heine- Weierstrass- Borel- Schoenflies- Lebesgue, Arch.
     

10. References for Weil
    
    • A Borel, Adre Weil and Algebraic Topology, Notices Amer.
      
    • http://www.ams.org/notices/199904/borel.pdf .
      
    • A Borel et al, Adre Weil (1906-1998), Notices Amer.
      

11. References for Montel
    
    • S Domoradzki, Among the teachers of Tadeusz Wazewski were E Borel, A Denjoy and P Montel (Polish), in School of the history of mathematics (Polish) (Miedzyzdroje, 1996), Zesz.
      

12. References for Hadamard
    
    • J D Gray, Comments on collected works, in particular those of Emile Borel and Jacques Hadamard, Historia Mathematica 3 (2) (1976), 203-206.
      

13. References for Lebesgue
    
    • B Bru and P Dugac (eds.), Lettres d'Henri Lebesgue a Emile Borel, in Cahiers du Seminaire d'Histoire des Mathematiques 12 (Paris, 1991), 1-511.
      

14. References for Humbert Georges
    
    • E Borel, Notice sur la vie et les travaux de Georges Humbert (Paris, 1922).
      

15. References for Weyl
    
    • A Borel, Hermann Weyl and Lie groups, Hermann Weyl, 1885-1985 (Eidgenossische Tech.
      

16. References for Leray
    
    • A Borel, G M Henkin and P D Lax, Jean Leray (1906-1998), Notices Amer.
      

17. References for Eisenhart
    
    • A Borel, The School of Mathematics at the Institute for Advanced Study, in A century of mathematics in America II (Amer.
      

18. References for Chevalley
    
    • A Borel, The work of Chevalley in Lie groups and algebraic groups, in Proceedings of the Hyderabad Conference on Algebraic Groups, Hyderabad, 1989 (Manoj Prakashan, Madras, 1991), 1-22.
      

19. References for Dieudonne
    
    • A Borel, Twenty-Five Years with Nicolas Bourbaki, (1949-1973), Notices Amer.
      

20. References for Montgomery
    
    • A Borel, Deane Montgomery (1909-1992), Notices Amer.
      

Additional material

1. Stäckel's contribution to Mathematics Teaching
   
   • A similar reform movement was taking place in France at around the same time, largely due to Emile Borel, who had written several books in French on the subject.
     
   • Having, as he did, a good command of French, Stackel read, and was impressed by, Borel's books and wanted to make [Leben und Werk des Mathematikers Paul Stackel (Staatsexamensarbeit, Karlsruhe University, 1993).',2)" onmouseover="window.status='Click to see reference';return true">2]:- .
     
   • He was, however, not content simply to translate Borel's work into German and instead set about reworking the French version into a textbook suitable for a German-speaking audience and for the German education system.
     

2. Mathematics in France during World War II
   
   • This man could see in the list of names Borel, Montel, de Broglie, Valery, Brunschvicg, only a group of prisoners who wanted to give him the slip.
     

3. Oswald Veblen Publications
   
   • 1904 (a) "The Heine-Borel Theorem", Bull.
     

4. The Brouwer Medal
   
   • 1978 A Borel .
     

5. W H Young addresses ICM 1928
   
   • The main invited lectures were by D Hilbert, J Hadamard, U Puppini, E Borel, O Veblen, G Castelnuovo, W H Young, V Volterra, H Weyl, T von Karman, L Tonelli, L Amoroso, M Frechet, R Marcolongo, N Luzin, F Enriques, G D Birkhoff.
     

Quotations

1. Quotations by Borel
   
   • Quotations by Emile Borel .
     
   • http://www-history.mcs.st-andrews.ac.uk/Quotations/Borel.html .
     

Chronology

1. Mathematical Chronology
   
   • Heine publishes a paper which contains the theorem now known as the "Heine-Borel theorem".
     
   • Borel introduces "Borel measure".
     
   • Borel publishes the first in a series of papers on game theory and becomes the first to define games of strategy.
     

2. Chronology for 1890 to 1900
   
   • Borel introduces "Borel measure".
     

3. Chronology for 1870 to 1880
   
   • Heine publishes a paper which contains the theorem now known as the "Heine-Borel theorem".
     

4. Chronology for 1920 to 1930
   
   • Borel publishes the first in a series of papers on game theory and becomes the first to define games of strategy.