Saunders Mac Lane was an extraordinary mathematician, a dedicated teacher, and a good citizen who cared deeply about the values of science and education. In his autobiography, he gives us a glimpse of his "life and times," mixing the highly personal with professional observations. His recollections bring to life a century of extraordinary accomplishments and tragedies that inspire and educate. Saunders Mac Lane's life covers nearly a century of mathematical developments. During the earlier part of the twentieth century, he participated in the exciting happenings in Göttingen---the Mecca of mathematics. He studied under David Hilbert, Hermann Weyl, and Paul Bernays and witnessed the collapse of a great tradition under the political pressure of a brutal dictatorship. Later, he contributed to the more abstract and general mathematical viewpoints developed in the twentieth century. Perhaps the most outstanding accomplishment during his long and extraordinary career was the development of the concept of categories, together with Samuel Eilenberg, and the creation of a theory that has broad applications in different areas of mathematics, in particular topology and foundations. He was also a keen observer and active participant in the social and political events. As a member and vice president of the National Academy of Science and an advisor to the Administration, he exerted considerable influence on science and education policies in the post-war period. Mac Lane's autobiography takes the reader on a journey through the most important milestones of the mathematical world in the twentieth century.
Table of Contents
Part One: Early Years 1. Heresy 2. High School 3. Undergraduate at Yale 4. Universal Knowledge and New Knowledge 5. The University of Chicago, 1930 6. Germany 1931-33 Part Two: First Teaching 7. Yale and Harvard 8. Cornell and Chicago 9. Surveying Modern Algebra 10. Algebraic Functions 11. First Graduate Students Part Three: Collaborative Research 12. Crossed Product Algebras and Group Extension 13. Eilenberg Enters 14. Naturality Part Four: The War Years 15. Much More Applied Math 16. Cynthia Enters 17. War Research: Roll, Pitch, and Yaw Part Five: Eilenberg and Mac Lane 18. Cautiously Publishing Category Theory 19. The Cohomology of Groups 20. Eilenberg-Mac Lane Spaces Part Six: Harvard Years 21. Professor at Harvard 22. University Presidents 23. Jib and Mainsail 24. Dorothy 25. Have Guggenheim, Will Travel Part Seven: Chicago in the Fifties 26. Return to Chicago 27. The Stone Age at Chicago 28. The Stone Age Comes to an End 29. Hutchins and the University 30. The College Mathematics Staff 31. Univeral Algebra and Think Tanks Part Eight: Mathematical Developments 32. Mathematical Organizations 33. Bourbaki-the Legend 34. The New Math 35. Categories Expand 36. The Grand Tour of Europe, 1954 37. Paris and Cartan. 1955-56 Part Nine: National Academy of Science 38. Membership in the National Academy of Sciences 39. The National Research Council 40. The Academy Proceedings Part Ten: The Sixties and Beyond 41. Homological Algebra 42. Categories 43. Geometrical Mechanics 44. Outdoors on the Indiana Dunes 45. Categories at Work Part Eleven: National Science Policy 46. As President of the AMS 47. Academy Reports 48. George Kistiakowski 49. Report Review 50. The National Science Board 51. Science Policy Part Twelve: Travels 52. Visits to China 53. Anniversary at the Dunes, 1983 54. Dorothy’s Delights Part Thirteen: Advising 55. Chicago Graduate Students 56. Friends and Mentors 57. Rating Research 58. The NAS Research Roundtable Part Fourteen: Later Developments 59. The Philosophy of Mathematics 60. Second Marriage 61. International Category Conferences Part Fifteen: Contemplating 62. Mathematics Departments 63. Collaborative Research 64. Career Choice