Marshall Stone and the internationalization of the American mathematical research community.

*(English)*Zbl 1170.01007The article is quite appealing due to the fact that the author had access to archive material. The year 1938 came fifty years after R. Archibald’s A semicentennial History of the American Mathemtical Society during which had flourished already the Bulletin started in 1891 and the Transactions, after 1900. George David Birkhoff may be considered to have been the mid-century doyen of American mathematics, at times the latter became fully competitive with its European counterparts. Under Birkhoff, Marshal M. Stone earned his PhD at Harvard in 1926 and then spent years at that place before he became head of the Mathematics Department of the University of Chicago. He made a major step in 1932 publishing his volume on “Transformations in Hilbert space and their Applications” [American Mathematical Society Colloquium Publ., 15. New York: American Mathematical Society (AMS) (1932; Zbl 0005.40003; JFM 58.0420.02)], deemed ‘one of great classics of the twentieth-century mathematics’ by George Mackey. In 1948 Stone proved the so-called Stone-Weierstrass theorem, considered as one of the most frequently quoted references all over in mathematics. By the end of 1940 the American mathematical community had recieved only two answers concerning the invitations to attend the ICM congress to be held in Boston. On behalf of the Deutsche Mathematiker-Vereinigung Wilhelm Süss expressed the hope that despite the emphatic wishes for war of our former enemy, England, the war can soon be brought to an end without too much injury to the scientific standards or to the savants in the war zone’. Sophie Piccard could only inform that the Swiss would provide visas only to persons possessing already a visa from other countries. Stone felt frustrated by that issue. Yet he now became more willing to invest much more efforts to bringing together mathematicians from all over the world. This decision was taken during the period 1943-1945 when Stone had succeeded to Marston Morse as president of the AMS. The author of the article then investigates in detail the difficulty of the task to advance during the critical post-war epoch. In 1949 Stone embarked on an around-the-world trip starting in Asia and ending in Nancy, France, where he participated in an evening of food and mathematics conversation with members ‘of the elite mathematical collective, Bourbaki’. He was successful to hire in Chicago outstanding mathematicians: Saunders MacLane, John von Neumann, André Weil, Hassler Whitney, Oscar Zariski, Paul Halmos, Irving Segal, Albert Calderon and others. The ICM congress finally held in 1950 in Cambridge MA was a big event with over 1700 mathematicians although only 290 from outside of North America. Stone became President of the IMU for the period 1952-1954. The first vice-president was Emile Borel.

The reviewer would like to recall a supplementary information concerning the topics quoted at the beginning of the article. Norbert Wiener writes about mathematics in the USA after World War One: “George Birkhoff was determined to become and to remain the first American mathematician in those classical branches of mathematics known as analysis, which constitute the extension and the elaboration of Newton’s calculus and physics.” Veblen was interested in topology and believed that it was his destiny to introduce this abstract field as a new American mathematics, in contrast to what he considered the effect and dying European mathematics of analysis, of the differential and integral calculus. He contributed to the birth of a valuable mathematical subject, but his concern with the health of analysis has proved to be at least premature’. We quote the concluding remark of the article: ‘The Cambridge ICM in 1950, but more importantly the beginning of the work of the new IMU in 1952 with Stone as President marked the self-conscious transformation of the American mathematical research community from a national community oriented toward fostering mathematics at home to an international one sensitive to the vicissitudes of world politics and focusd not only on participating actively in but also influencing the mathematical endeavor worldwide.’

The reviewer would like to recall a supplementary information concerning the topics quoted at the beginning of the article. Norbert Wiener writes about mathematics in the USA after World War One: “George Birkhoff was determined to become and to remain the first American mathematician in those classical branches of mathematics known as analysis, which constitute the extension and the elaboration of Newton’s calculus and physics.” Veblen was interested in topology and believed that it was his destiny to introduce this abstract field as a new American mathematics, in contrast to what he considered the effect and dying European mathematics of analysis, of the differential and integral calculus. He contributed to the birth of a valuable mathematical subject, but his concern with the health of analysis has proved to be at least premature’. We quote the concluding remark of the article: ‘The Cambridge ICM in 1950, but more importantly the beginning of the work of the new IMU in 1952 with Stone as President marked the self-conscious transformation of the American mathematical research community from a national community oriented toward fostering mathematics at home to an international one sensitive to the vicissitudes of world politics and focusd not only on participating actively in but also influencing the mathematical endeavor worldwide.’

Reviewer: Jean-Paul Pier (Luxembourg)

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\textit{K. H. Parshall}, Bull. Am. Math. Soc., New Ser. 46, No. 3, 459--482 (2009; Zbl 1170.01007)

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##### References:

[1] | W. Adams, The History of the International Astronomical Union, Publications of the Astronomical Society of the Pacific 61 (February 1949), 5-12. |

[2] | Donald J. Albers, G. L. Alexanderson, and Constance Reid, International mathematical congresses, Springer-Verlag, New York, 1987. An illustrated history, 1893 – 1986. · Zbl 0611.01014 |

[3] | Raymond Clare Archibald, American Mathematical Society semicentennial publications. Vol. I, Three Centuries of Science in America, Arno Press, New York, 1980. A semicentennial history of the American Mathematical Society, 1888 – 1938; Reprint of the 1938 original. American Mathematical Society semicentennial publications. Vol. II, Three Centuries of Science in America, Arno Press, New York, 1980. Reprint of the 1938 original. |

[4] | G. D. Birkhoff, Fifty Years of American Mathematics in [33, pp. 270-315]. · JFM 64.0003.04 |

[5] | J. Boyer, Drafting Salvation, The University of Chicago Magazine 88 (December 1995), accessible at http://magazine.uchicago.edu/archives. |

[6] | Felix E. Browder, The Stone Age of mathematics on the Midway, A century of mathematics in America, Part II, Hist. Math., vol. 2, Amer. Math. Soc., Providence, RI, 1989, pp. 191 – 193. · Zbl 0682.01012 |

[7] | Cronica: Asamblea de la Unión Matemática Argentina, Revista de la Unión Matemática Argentina 9 (1943), 144. |

[8] | R. Divine, Second Chance: The Triumph of Internationalism in America during World War II (New York: Atheneum, 1967). |

[9] | L. Fermi, Illustrious Immigrants: The Intellectual Migration from Europe, 1930/41, 2nd ed. (Chicago: University of Chicago, 1971). |

[10] | T. Glick, Science and Society in Twentieth-Century Latin America, in The Cambridge History of Latin America, ed. Leslie Bethell, vol. 6, pt. 1 (Cambridge: Cambridge University Press, 1994), pp. 463-535. |

[11] | A. Howson, Seventy-Five Years of the International Commission on Mathematical Instruction, Educational Studies in Mathematics 15 (1984), 75-93. |

[12] | A. Iriye and P.-Y. Saunier, The Palgrave Dictionary of Transnational History (London: Palgrave Macmillan Ltd., 2009). |

[13] | T. Judt, Postwar: A History of Europe since 1945 (New York: Penguin Books, 2005). |

[14] | D. Kevles, The Physicists: The History of a Scientific Community in Modern America (Cambridge, MA: Harvard University Press, 1987). |

[15] | Olli Lehto, Mathematics without borders, Springer-Verlag, New York, 1998. A history of the International Mathematical Union. · Zbl 0889.01021 |

[16] | George W. Mackey, Marshall H. Stone: mathematician, statesman, advisor, and friend, Operator algebras, quantization, and noncommutative geometry, Contemp. Math., vol. 365, Amer. Math. Soc., Providence, RI, 2004, pp. 15 – 25. · Zbl 1059.01539 · doi:10.1090/conm/365/06697 · doi.org |

[17] | A. Mason, Harlan Fiske Stone: Pillar of the Law (New York: The Viking Press, 1956). |

[18] | W. McNeill, Hutchins’ University: A Memoir of the University of Chicago, 1929-1950 (Chicago: University of Chicago Press, 1991). |

[19] | Report of the War Preparedness Committee of the American Mathematical Society and Mathematical Association of America at the Hanover meeting, Bull. Amer. Math. Soc. 46 (1940), no. 9, 711 – 714. · doi:10.1090/S0002-9904-1940-07267-2 · doi.org |

[20] | E. Ortiz, George D. Birkhoff, Harvard University, Roosevelt’s Policy, and the Inter-American Mathematical Network, History of Mathematics Research Report HM-11-1999, Imperial College, London. |

[21] | E. Ortiz, La polıtica interamericana de Roosevelt: George D. Birkhoff y la inclusión de América Latina en las redes matemáticas internacionales: Primera Parte, Saber y Tiempo: Revista de História de la Ciencia 15 (2003), 53-111. |

[22] | E. Ortiz, La polıtica interamericana de Roosevelt: George D. Birkhoff y la inclusión de América Latina en las redes matemáticas internacionales: Segunda Parte, Saber y Tiempo: Revista de História de la Ciencia 16 (2003), 21-70. |

[23] | K. Parshall, Historical Contours of the American Mathematical Research Community, in A History of School Mathematics, ed. George M. A. Stanic and Jeremy Kilpatrick, 2 vols. (Reston, VA: National Council of Teachers of Mathematics, 2003), 1: 113-157. |

[24] | K. Parshall, The Internationalization of Mathematics in a World of Nations: 1800-1960 in The Oxford Handbook of the History of Mathematics, ed. Eleanor Robson and Jackie Stedall (Oxford: Oxford University Press, 2009), 85-104. |

[25] | Karen Hunger Parshall, A mathematical ”good neighbor”: Marshall Stone in Latin America (1943), Rev. Bras. Hist. Mat. Special Issue 1 (2007), 19 – 31. · Zbl 1206.01058 |

[26] | Karen Hunger Parshall, Perspectives on American mathematics, Bull. Amer. Math. Soc. (N.S.) 37 (2000), no. 4, 381 – 405. · Zbl 0979.01015 |

[27] | Karen Hunger Parshall and Adrian C. Rice, The evolution of an international mathematical research community, 1800 – 1945: an overview and an agenda, Mathematics unbound: the evolution of an international mathematical research community, 1800 – 1945 (Charlottesville, VA, 1999) Hist. Math., vol. 23, Amer. Math. Soc., Providence, RI, 2002, pp. 1 – 15. · Zbl 1239.01005 · doi:10.1006/hmat.1996.0001 · doi.org |

[28] | Karen Hunger Parshall and David E. Rowe, The emergence of the American mathematical research community, 1876 – 1900: J. J. Sylvester, Felix Klein, and E. H. Moore, History of Mathematics, vol. 8, American Mathematical Society, Providence, RI; London Mathematical Society, London, 1994. · Zbl 0802.01005 |

[29] | J. Rey Pastor, Profesor Marshall H. Stone, Revista de la Unión Matemática Argentina 9 (1943), 138-140. |

[30] | Proceedings of the International Congress of Mathematicians: Cambridge, Massachusetts, U. S. A. 1950, Lawrence M. Graves, Einar Hille, Paul A. Smith, and Oscar Zariski, eds., 2 vols. (Providence, RI: American Mathematical Society, 1952). |

[31] | Report of the War Preparedness Committee of the American Mathematical Society and Mathematical Association of America at the Hanover meeting, Bull. Amer. Math. Soc. 46 (1940), no. 9, 711 – 714. · doi:10.1090/S0002-9904-1940-07267-2 · doi.org |

[32] | F. Roosevelt, Roosevelt’s Foreign Policy 1933-1941: Franklin D. Roosevelt’s Unedited Speeches and Messages (New York: Wilfred Funk, Inc., 1942). |

[33] | Semicentennial Addresses of the American Mathematical Society (New York: American Mathematical Society, 1938; reprint ed., New York: Arno Press, 1980). |

[34] | Reinhard Siegmund-Schultze, Rockefeller and the internationalization of mathematics between the two world wars, Science Networks. Historical Studies, vol. 25, Birkhäuser Verlag, Basel, 2001. Documents and studies for the social history of mathematics in the 20th century. · Zbl 0981.01013 |

[35] | R. Spector, ed., Listening to the Enemy: Key Documents on the Role of Communications Intelligence in the War with Japan (Wilmington, DE: Scholarly Resources, Inc., 1988). |

[36] | M. H. Stone, The generalized Weierstrass approximation theorem, Math. Mag. 21 (1948), 167 – 184, 237 – 254. · doi:10.2307/3029750 · doi.org |

[37] | M. Stone, International Relations in Mathematics, in Men and Institutions in American Mathematics, ed. J. Dalton Tarwater, John T. White, and John D. Miller, Graduate Studies, Texas Tech University, no. 13 (October 1976), pp. 31-39. |

[38] | M. Stone, Science and Statecraft, Science 105 (1947), 507-510. |

[39] | Marshall Harvey Stone, Linear transformations in Hilbert space, American Mathematical Society Colloquium Publications, vol. 15, American Mathematical Society, Providence, RI, 1990. Reprint of the 1932 original. · Zbl 0933.47001 |

[40] | Marshall H. Stone, Reminiscences of mathematics at Chicago, A century of mathematics in America, Part II, Hist. Math., vol. 2, Amer. Math. Soc., Providence, RI, 1989, pp. 183 – 190. · Zbl 0682.01014 |

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