Description
Book SynopsisThis book picks up the history of mathematics from where Sherlock Holmes in Babylon left it. The 40 articles of Who Gave You the Epsilon? continue the story of the development of mathematics into the nineteenth and twentieth centuries. It is ideal for those interested in the history of mathematics.
Trade ReviewAs a collection of interesting articles on the history of 19th- and 20th-century mathematics, the present volume is hard to beat. The 41 papers, covering many diverse areas, not just calculus, are mostly accessible to undergraduate mathematics majors, yet their professors will also likely enjoy them and learn quite a bit as well. Highly Recommended."" - C. Bauer,
Choice""The present volume is a sequel to
Sherlock Holmes in Babylon and other tales of mathematical history, MAA Spectrum, Math Assoc. America, Washington, DC, 2004. The earlier book treated the period before 1800, while this book describes developments in the 19th and 20th centuries. It is an anthology of over 40 papers previously published in journals of the Mathematical Association of America, the majority in the
American Mathematical Monthly, about a third in
Mathematics Magazine and two in the
College Mathematics Journal. Except for seven Monthly papers from the years 1900 (2), 1913, 1920, 1934, 1937, and 1951, all the papers appeared between 1972 and 2000 inclusive. Many of the authors are respected historians of mathematics. Each of the four chapters is bracketed by a Foreword that gets forth the themes and an Afterward that provides a guide for further reading. There is a good mixture of material that focuses on mathematical developments and that treats the personalities and sociology of the mathematical community. For some topics, the treatment is quite detailed. In such a collection as this, the choice of topics is of necessity unbalanced; the papers are sorted into three chapters under the broad themes of analysis, geometry and axiomatics, and algebra and number theory. The final chapter includes three papers that survey the state of mathematics at the beginning, the midpoint and the end of the 20th century. This collection can be read with profit and enjoyment by both professional mathematicians and undergraduate students specializing in mathematics."" - E.J. Barbeau,
Mathematical ReviewsTable of ContentsIntroduction; Part I. Analysis: 1. Who gave you the epsilon? Cauchy and the origins of rigorous calculus Judith V. Grabiner; 2. Evolution of the function concept: a brief survey Israel Kleiner; 3. S. Kovalevsky: a mathematical lesson Karen D. Rappaport; 4. Highlights in the history of spectral theory L. A. Steen; 5. Alan Turing and the central limit theorem S. L. Zabell; 6. Why did George Green write his essay of 1828 on electricity and magnetism? I. Grattan-Guinness; 7. Connectivity and smoke-rings: Green's second identity in its first fifty years Thomas Archibald; 8. The history of Stokes' theorem Victor J. Katz; 9. The mathematical collaboration of M. L. Cartwright and J. E. Littlewood Shawnee L. McMurran and James J. Tattersall; 10. Dr David Harold Blackwell, African American pioneer Nkechi Agwu, Luella Smith and Aissatou Barry; Part II. Geometry, Topology and Foundations: 11. Gauss and the non-Euclidean geometry George Bruce Halsted; 12. History of the parallel postulate Florence P. Lewis; 13. The rise and fall of projective geometry J. L. Coolidge; 14. Notes on the history of geometrical ideas Dan Pedoe; 15. A note on the history of the Cantor set and Cantor function Julian F. Fleron; 16. Evolution of the topological concept of 'connected' R. L. Wilder; 17. A brief, subjective history of homology and homotopy theory in this century Peter Hilton; 18. The origins of modern axiomatics: Pasch to Peano H. C. Kennedy; 19. C. S. Peirce's philosophy of infinite sets Joseph W. Dauben; 20. On the development of logics between the two world wars I. Grattan-Guinness; 21. Dedekind's theorem: √2 × √3 = √6 David Fowler; Part III. Algebra and Number Theory: 22. Hamilton's discovery of quaternions B. L. van der Waerden: 23. Hamilton, Rodrigues, and the quaternion scandal Simon L. Altmann; 24. Building an international reputation: the case of J. J. Sylvester (1814–1897) Karen Hunger Parshall and Eugene Seneta; 25. The foundation period in the history of group theory Josephine E. Burns; 26. The evolution of group theory: a brief survey Israel Kleiner; 27. The search for finite simple groups Joseph A. Gallian; 28. Genius and biographers: the fictionalization of Evariste Galois Tony Rothman; 29. Hermann Grassmann and the creation of linear algebra Desmond Fearnley-Sander; 30. The roots of commutative algebra in algebraic number theory Israel Kleiner; 31. Eisenstein's misunderstood geometric proof of the quadratic reciprocity theorem Reinhard C. Laubenbacher and David J. Pengelley; 32. Waring's problem Charles Small; 33. A history of the prime number theorem L. J. Goldstein; 34. A hundred years of prime numbers Paul T. Bateman and Harold G. Diamond; 35. The Indian mathematician Ramanujan G. H. Hardy; 36. Emmy Noether Clark H. Kimberling; 37. 'A marvellous proof' Fernando Q. Gouvˆea; Part IV. Surveys: 38. The international congress of mathematicians George Bruce Halsted; 39. A popular account of some new fields of thought in mathematics G. A. Miller; 40. A half-century of mathematics Hermann Weyl; 41. Mathematics at the turn of the millennium Philip A. Griffiths; Index.
