Who Gave You the Epsilon?

After earning his Ph.D. in 1977, Marlow Anderson taught at Indiana-Purdue University in Fort Wayne before coming to Colorado. His graduate work at the University of Kansas was in algebra, specifically lattice ordered groups, and he maintained his interest and research momentum when he joined the department at Colorado College in 1982. Anderson has always had wide ranging interests in mathematics. Logic was an early fascination, geometry was one of the courses he enjoyed designing and teaching, and the history of mathematics became a strong interest. Victor J. Katz, born in Philadelphia, received his Ph.D. in mathematics from Brandeis University in 1968 and was for many years Professor of Mathematics at the University of the District of Columbia. He has long been interested in the history of mathematics and, in particular, in its use in teaching. His well-regarded textbook, A History of Mathematics: An Introduction, is now in its third edition. Its first edition received the Watson Davis Prize of the History of Science Society, a prize awarded annually by the Society for a book in any field of the history of science suitable for undergraduates. Robin Wilson is Professor of Pure Mathematics at the Open University (UK), a Fellow in Mathematics at Keble College, Oxford University, and Emeritus Gresham Professor of Geometry, London (the oldest mathematical Chair in England). He has written and edited about thirty books, mainly on graph theory and the history of mathematics. His research interests focus mainly on British mathematics, especially in the 19th and early 20th centuries, and on the history of graph theory and combinatorics.

• Introduction; 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.

As 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 Reviews