A Richer Picture of Mathematics : The Göttingen Tradition and Beyond

Historian David E. Rowe captures the rich tapestry of mathematical creativity in this collection of essays from the “Years Ago” column of The Mathematical Intelligencer. With topics ranging from ancient Greek mathematics to modern relativistic cosmology, this collection conveys the impetus and spirit of Rowe’s various and many-faceted contributions to the history of mathematics. Centered on the Göttingen mathematical tradition, these stories illuminate important facets of mathematical activity often overlooked in other accounts. Six sections place the essays in chronological and thematic order, beginning with new introductions that contextualize each section. The essays that follow recount episodes relating to the section’s overall theme. All of the essays in this collection, with the exception of two, appeared over the course of more than 30 years in __The Mathematical Intelligencer__. Based largely on archival and primary sources, these vignettes offer unusual insights into behind-the-scenes events. Taken together, they aim to show how Göttingen managed to attract an extraordinary array of talented individuals, several of whom contributed to the development of a new mathematical culture during the first decades of the twentieth century. Historian David E. Rowe Captures The Rich Tapestry Of Mathematical Creativity In This Collection Of Essays From The Years Ago Column Of The Mathematical Intelligencer. With Topics Ranging From Ancient Greek Mathematics To Modern Relativistic Cosmology, This Collection Conveys The Impetus And Spirit Of Rowe's Various And Many-faceted Contributions To The History Of Mathematics. Centered On The Göttingen Mathematical Tradition, These Stories Illuminate Important Facets Of Mathematical Activity Often Overlooked In Other Accounts. Six Sections Place The Essays In Chronological And Thematic Order, Beginning With New Introductions That Contextualize Each Section. The Essays That Follow Recount Episodes Relating To The Section's Overall Theme. All Of The Essays In This Collection, With The Exception Of Two, Appeared Over The Course Of More Than 30 Years In The Mathematical Intelligencer. Based Largely On Archival And Primary Sources, These Vignettes Offer Unusual Insights Into Behind-the-scenes Events. Taken Together, They Aim To Show How Göttingen Managed To Attract An Extraordinary Array Of Talented Individuals, Several Of Whom Contributed To The Development Of A New Mathematical Culture During The First Decades Of The Twentieth Century. Part I. Two Rival Centers : Göttingen Vs. Berlin -- On Gauss And Gaussian Legends : A Quiz -- Gauss, Dirichlet, And The Law Of Biquadratic Reciprocity -- Episodes In The Belin-göttingen Rivalry, 1870-1930 -- Deine Sonia : A Reading From A Burned Letter By Reinhard Bölling, Translated By D. E. Rowe -- Who Linked Hegel's Philosophy With The History Of Mathematics -- Part Ii. The Young Felix Klein -- Models As Research Tools : Plücker, Klein, And Kummer Surfaces -- Debating Grassman's Mathematics : Schlegel Vs. Klein -- Three Letters From Sophus Lie To Felix Klein On Mathematics In Paris -- Klein, Mittag-leffer, And The Klein-poincaré Correspondence Of 1881-1882 -- Part Iii. David Hilbert Steps Onstage -- Hilbert's Early Career -- Klein, Hurwitz, And The Jewish Question In German Academia -- On The Background To Hilbert's Paris Lecture Mathematical Problems -- Poincaré Week In Göttingen, 22-28 April 1909 -- Part Iv. Mathematics And The Relativity Revolution -- Hermann Minkowski's Cologne Lecture, Raum Und Zeit -- Max Von Laue's Role In The Relativity Revolution -- Euclidean Geometry And Physical Space -- The Mathematicians' Happy Hunting Ground : Einstein's General Theory Of Relativity -- Einstein's Gravitational Field Equations And The Bianchi Identities -- Puzzles And Paradoxes And Their (sometimes) Profounder Implications -- Debating Relativistic Cosmology, 1917-1924 -- Remembering An Era : Roger Penrose's Paper On Gravitational Collapse : The Role Of General Relativity -- Part V. Göttingen In The Era Of Hilbert And Courant -- Hermann Weyl, The Reluctant Revolutionary -- Transforming Tradition : Richard Courant In Göttingen -- Otto Neugebauer And The Göttingen Approach To History Of The Exact Sciences -- On The Myriad Mathematical Traditions Of Ancient Greece -- The Old Guard Under A New Order : K. O. Friedrichs Meets Felix Klein -- An Enchanted Era Remembered : Interview With Dirk Jan Struik -- Part Iv. People And Legacies -- Is (was) Mathematics An Art Or A Science? -- Coxeter On People And Polytopes -- Mathematics In Wartime : Private Reflections Of Clifford Truesdell -- Hilbert's Legacy : Projecting The Future And Assessing The Past At The 1946 Princeton Bicentennial Conference -- Personal Reflections On Dirk Jan Struik By Joseph W. Dauben. David E. Rowe. Includes Bibliographical References And Index. Front Matter ....Pages i-xix Front Matter ....Pages 1-1 Introduction to Part I (David E. Rowe)....Pages 3-18 On Gauss and Gaussian Legends: A Quiz (David E. Rowe)....Pages 19-28 Gauss, Dirichlet, and the Law of Biquadratic Reciprocity (David E. Rowe)....Pages 29-39 Episodes in the Berlin-Göttingen Rivalry, 1870–1930 (David E. Rowe)....Pages 41-49 Deine Sonia: A Reading from a Burned Letter by Reinhard Bölling, Translated by D. E. Rowe (David E. Rowe)....Pages 51-56 Who Linked Hegel’s Philosophy with the History of Mathematics? (David E. Rowe)....Pages 57-65 Front Matter ....Pages 67-67 Introduction to Part II (David E. Rowe)....Pages 69-79 Models as Research Tools: Plücker, Klein, and Kummer Surfaces (David E. Rowe)....Pages 81-94 Debating Grassmann’s Mathematics: Schlegel vs. Klein (David E. Rowe)....Pages 95-103 Three Letters from Sophus Lie to Felix Klein on Mathematics in Paris (David E. Rowe)....Pages 105-109 Klein, Mittag-Leffler, and the Klein-Poincaré Correspondence of 1881–1882 (David E. Rowe)....Pages 111-133 Front Matter ....Pages 135-135 Introduction to Part III (David E. Rowe)....Pages 137-149 Hilbert’s Early Career (David E. Rowe)....Pages 151-169 Klein, Hurwitz, and the “Jewish Question” in German Academia (David E. Rowe)....Pages 171-182 On the Background to Hilbert’s Paris Lecture “Mathematical Problems” (David E. Rowe)....Pages 183-194 Poincaré Week in Göttingen, 22–28 April 1909 (David E. Rowe)....Pages 195-202 Front Matter ....Pages 203-203 Introduction to Part IV (David E. Rowe)....Pages 205-218 Hermann Minkowski’s Cologne Lecture, “Raum und Zeit” (David E. Rowe)....Pages 219-232 Max von Laue’s Role in the Relativity Revolution (David E. Rowe)....Pages 233-241 Euclidean Geometry and Physical Space (David E. Rowe)....Pages 243-251 The Mathematicians’ Happy Hunting Ground: Einstein’s General Theory of Relativity (David E. Rowe)....Pages 253-261 Einstein’s Gravitational Field Equations and the Bianchi Identities (David E. Rowe)....Pages 263-271 Puzzles and Paradoxes and Their (Sometimes) Profounder Implications (David E. Rowe)....Pages 273-278 Debating Relativistic Cosmology, 1917–1924 (David E. Rowe)....Pages 279-299 Remembering an Era: Roger Penrose’s Paper on “Gravitational Collapse: The Role of General Relativity” (David E. Rowe)....Pages 301-311 Front Matter ....Pages 313-313 Introduction to Part V (David E. Rowe)....Pages 315-330 Hermann Weyl, The Reluctant Revolutionary (David E. Rowe)....Pages 331-341 Transforming Tradition: Richard Courant in Göttingen (David E. Rowe)....Pages 343-355 Otto Neugebauer and the Göttingen Approach to History of the Exact Sciences (David E. Rowe)....Pages 357-368 On the Myriad Mathematical Traditions of Ancient Greece (David E. Rowe)....Pages 369-374 The Old Guard Under a New Order: K. O. Friedrichs Meets Felix Klein (David E. Rowe)....Pages 375-377 An Enchanted Era Remembered: Interview with Dirk Jan Struik (David E. Rowe)....Pages 379-391 Front Matter ....Pages 393-393 Introduction to Part VI (David E. Rowe)....Pages 395-405 Is (Was) Mathematics an Art or a Science? (David E. Rowe)....Pages 407-411 Coxeter on People and Polytopes (David E. Rowe)....Pages 413-419 Mathematics in Wartime: Private Reflections of Clifford Truesdell (David E. Rowe)....Pages 421-433 Hilbert’s Legacy: Projecting the Future and Assessing the Past at the 1946 Princeton Bicentennial Conference (David E. Rowe)....Pages 435-443 Personal Reflections on Dirk Jan Struik By Joseph W. Dauben (David E. Rowe)....Pages 445-451 Back Matter ....Pages 453-461 Historian David E. Rowe captures the rich tapestry of mathematical creativity in this collection of essays from the "Years Ago"ŗ column of The Mathematical Intelligencer. With topics ranging from ancient Greek mathematics to modern relativistic cosmology, this collection conveys the impetus and spirit of Rowe's various and many-faceted contributions to the history of mathematics. Centered on the Göttingen mathematical tradition, these stories illuminate important facets of mathematical activity often overlooked in other accounts. Six sections place the essays in chronological and thematic order, beginning with new introductions that contextualize each section. The essays that follow recount episodes relating to the sections overall theme. All of the essays in this collection, with the exception of two, appeared over the course of more than 30 years in The Mathematical Intelligencer. Based largely on archival and primary sources, these vignettes offer unusual insights into behind-the-scenes events. Taken together, they aim to show how Göttingen managed to attract an extraordinary array of talented individuals, several of whom contributed to the development of a new mathematical culture during the first decades of the twentieth century Historian David E. Rowe captures the rich tapestry of mathematical creativity in this collection of essays from the "Years Ago" column of The Mathematical Intelligencer. With topics ranging from ancient Greek mathematics to modern relativistic cosmology, this collection conveys the impetus and spirit of Rowe's various and many-faceted contributions to the history of mathematics. Centered on the GoÌ#x88;ttingen mathematical tradition, these stories illuminate important facets of mathematical activity often overlooked in other accounts. Six sections place the essays in chronological and thematic order, beginning with new introductions that contextualize each section. The essays that follow recount episodes relating to the section's overall theme. All of the essays in this collection, with the exception of two, appeared over the course of more than 30 years in The Mathematical Intelligencer. Based largely on archival and primary sources, these vignettes offer unusual insights into behind-the-scenes events. Taken together, they aim to show how GoÌ#x88;ttingen managed to attract an extraordinary array of talented individuals, several of whom contributed to the development of a new mathematical culture during the first deca