The History of Mathematics: A Source-Based Approach, Volume 2

June Barrow-Green, The Open University, Milton Keynes, United Kingdom. Jeremy Gray, The Open University, Milton Keynes, United Kingdom. Robin Wilson, The Open University, Milton Keynes, United Kingdom.

Introduction The 17th and 18th centuries: Introduction: The 17th and 18th centuries The invention of the calculus Newton and Leibniz The development of the calculus Newtons' $\textit{Principia Mathematica}$ The spread of the calculus The 18th century 18th-century number theory and geometry Euler, Lagrange, and 18th-century calculus 18th-century applied mathematics 18th-century celestial mechanics The 19th century: Introduction: The 19th century The profession of mathematics Non-Euclidean geometry Projective geometry and the axiomatisation of mathematics The rigorisation of analysis The foundations of mathematics Algebra and number theory Group theory Applied mathematics Poincare and celestial mechanics Coda Exercises References Index

This volume picks up where the authors left off in their first volume (2019), from about 1650 to the start of the 20th century. The intent of these books is to ask: Who did the mathematics, and why? How was the work disseminated (or not)? How did it emerge from the culture of the time, and why is it still relevant today? The approach is to use extensive quotations from original sources as the best way to answer some of those questions. The book concludes uniquely with dozens of suggested essay exercises that are ""firmly historical, rather than primarily mathematical;"" some call for supporting or contesting claims about mathematical discoveries. The two volumes were designed for a year-long course, and they provide excellent material for a senior-level course to help students survey the mathematics that they have learned and put it into cultural and scientific context."" - Mathematics Magazine ""...this volume (and the series as a whole) is an outstanding addition to the body of history of mathematics texts now available to instructors and students, providing a wonderfully rich treasure trove of primary source material. While few may choose this book as a text for a one-semester survey course on the history of mathematics, it is certainly an excellent option for those who wish to focus solely on the modern era from a professional historical perspective."" - Calvin Jongsma, Dordt University