The Richness of the History of Mathematics: A Tribute to Jeremy Gray

這本書是對數學歷史學家Jeremy Gray的致敬，提供了數學歷史及其與哲學和其他學科密不可分的連結的概述。對於研究數學歷史的許多不同方法已經被發展出來。了解這種多樣性對於學習這些領域至關重要，但很少有書籍涉及到這些領域的豐富性以及對於這些研究領域的「什麼、為什麼和如何」的具體建議。編者和作者通過具體例子來回答數學歷史是什麼的基本問題。對於「如何」的問題，從數學家和歷史學家的不同觀點出發，討論了基本的方法論問題。本書包含了領先學者的論文，提供了多種關於數學、其在文化和發展中的角色以及與其他科學的聯繫的觀點，使其成為歷史和哲學數學領域的學生和學者的重要資源。

Karine Chemla is a French historian of mathematics and sinologist who works as a director of research at the Centre national de la recherche scientifique (CNRS), Research group SPHERE. She is also a senior fellow at the New York University Institute for the Study of the Ancient World. She was elected a Member of the American Philosophical Society in 2019 and received the Otto Neugebauer Prize from the European Mathematical Society in 2020.

José Ferreirós is a historian and philosopher of Mathematics, a Professor of Logic and Philosophy of Science at the University of Seville (Spain) and member of the Institute of Mathematics at Seville (IMUS). He is the author of Mathematical Knowledge and the Interplay of Practices (Princeton UP, 2016), and editor of The Architecture of Modern Mathematics (with J. Gray, Oxford UP, 2006). Ferreirós has served as president of the Association for the Philosophy of Mathematical Practice, and has also done research onthe physical sciences and the philosophy of experimental science.

Lizhen Ji is a mathematician interested in the history of mathematics. In the past few years, he has started to develop active interest in the history of mathematicshas. In mathematics, he has studied several topics in analysis, geometry, topology and group theory. In particular, he has studied symmetric spaces, locally symmetric spaces, arithmetic groups and related discrete groups from various points of view. SL(n, Z) is one of the most basic examples of arithmetic groups, and it acts on the symmetric space of positive definite matrices of determinant 1. The quotient of the symmetric space by SL(n, Z) is a locally symmetric space, which occurs naturally in many subjects from differential geometry, topology, geometry group theory to number theory. Though these spaces and groups have been studied extensively by many people over a long period of time, there are still many open problems. In the history of mathematics, he has been interested in the works of Poincaré and Galois.

Scholz studied mathematics at the University of Bonn and the University of Warwick from 1968 to 1975 with Diplom from the University of Bonn in 1975. In 1979, he completed his doctorate (Promotion) at the University of Bonn with thesis Entwicklung des Mannigfaltigkeitsbegriffs von Riemann bis Poincaré (Development of the concept of manifold from Riemann to Poincaré) under the supervision of Egbert Brieskorn and Henk J. M. Bos. In 1986, Scholtz habilitated at the University of Wuppertal. There he became in 1989 an associate professor of the history of mathematics and retired in 2012. He also works at the University of Wuppertal's Interdisziplinären Zentrum für Wissenschafts- und Technikforschung (IZWT, Interdisciplinary Center for Science and Technology Research), which he co-founded in 2004. In 1993, he was a visiting professor at the Institut für Wissenschaftsgeschichte (Institute for the History of Science) at the University of Göttingen.

Chang Wang, a professor of the history of mathematics in the Institute for Advanced Studies in History of Science, Northwest University, Xi'an, China. He has been studying the history of mathematics, especially the history of topology and Poincaré. He graduated from the Mathematical Department of Northwest University in 2012, and became a lecturer in the same year. In 2016, he became an associate professor of the history of mathematics in the Institute for Advanced Studies in History of Science, and was promoted to professorship in the year 2021. He was a council member of the Chinese Mathematical History Society. He has organized several international conferences in China. He serves as an expert reviewer for the Studies in the History of Natural Sciences and The Chinese Journal for The History of Science and Technology..

Karine Chemla是一位法國數學歷史學家和漢學家，目前擔任法國國家科學研究中心（CNRS）研究組SPHERE的研究主任。她還是紐約大學古代世界研究所的高級研究員。她於2019年當選為美國哲學學會會員，並於2020年獲得歐洲數學學會的Otto Neugebauer獎。

José Ferreirós是一位數學歷史學家和哲學家，現任西班牙塞維利亞大學（University of Seville）的邏輯和科學哲學教授，並且是塞維利亞數學研究所（IMUS）的成員。他是《數學知識與實踐的相互作用》（普林斯頓大學出版社，2016年）的作者，並與J. Gray合編了《現代數學的架構》（牛津大學出版社，2006年）。Ferreirós曾擔任過數學實踐哲學協會的主席，並且還研究過物理科學和實驗科學的哲學。

Lizhen Ji是一位對數學歷史感興趣的數學家。在過去幾年中，他開始對數學歷史產生了濃厚的興趣。在數學方面，他研究了分析、幾何、拓撲和群論等多個主題。特別是，他從不同的角度研究了對稱空間、局部對稱空間、算術群和相關的離散群。SL(n, Z)是算術群的最基本的例子之一，它作用於行列式為1的正定矩陣的對稱空間上。對稱空間除以SL(n, Z)得到局部對稱空間，在微分幾何、拓撲學、幾何群論和數論等許多學科中自然出現。儘管這些空間和群體已經被許多人廣泛研究了很長一段時間，但仍然存在許多未解決的問題。在數學歷史上，他對庞加莱和伽羅瓦的作品很感興趣。

Scholz在1968年至1975年間在波恩大學和華威大學學習數學，並於1975年在波恩大學獲得學士學位。1979年，他在波恩大學完成了他的博士學位，論文題目為《從黎曼到庞加莱的流形概念發展》（Development of the concept of manifold from Riemann to Poincaré），指導教授為Egbert Brieskorn和Henk J. M. Bos。1986年，Scholtz在韋珀塔爾大學完成了博士後資格（Habilitation）。他在那裡成為1989年的數學歷史副教授，並於2012年退休。他還在韋珀塔爾大學的跨學科科學與技術研究中心（IZWT）工作，該中心於2004年由他共同創立。1993年，他曾在哥廷根大學的科學史研究所擔任訪問教授。

Chang Wang是中國西北大學科學史高等研究所的數學歷史學教授。他一直致力於研究數學歷史，尤其是拓撲學和庞加莱的歷史。他於2012年畢業於西北大學數學系，並於同年成為講師。2016年，他成為西北大學科學史高等研究所的數學歷史學副教授，並於2021年晉升為教授。他曾擔任中國數學史學會的理事會成員，並在中國組織了幾次國際會議。他還擔任《自然科學史研究》和《中國科學技術史研究》的專家審稿人。