In the early 1980s, I began an academic venture as a mature student pursuing mathematics at the University of Erlangen in Germany. At that time, a typical degree at a German university concluded with a diploma, comparable to a master’s degree in mathematics, usually lasting eight to nine semesters. Numerous students surpassed this duration, reflecting the demanding nature of the program.
The first four semesters established the foundation for our mathematical training, comprising double lectures in analysis and algebra four times a week. Each lecture, lasting ninety minutes, required significant dedication, often resulting in eight to ten A4 pages of notes per session. Weekly exercise sheets paired with afternoon review sessions offered an avenue for a deep understanding. Upon completing these early semesters, students participated in seminars on specific topics, where we presented papers, a process I found more stimulating in analysis than in algebra.
A compulsory subsidiary subject led me to philosophy, strengthening my studies under the mentorship of Professor Christian Thiel and others in the history and philosophy of science. My fascination with the history of mathematics ultimately guided me towards a master’s degree in philosophy with history and English as subsidiary subjects, paving the way for my current task of writing this blog post.
Mathematics had been a consistent companion since my teenage years during my O-level and A-level studies, where I thrived, especially in analysis, then commonly known as calculus. One notable examination on derivatives yielded an impressive score of 102%, due to a correction by my teacher who recognized my accurate answer.
My interest in history led me to the exploration of the history of mathematics, aided by my father’s gift of Eric Temple Bell’s “Men of Mathematics.” This book, despite its historical inaccuracies, deeply inspired me. Eventually, my collection grew to encompass works on the history of science, and I delved into the philosophy of mathematics and science through influential thinkers such as Stephen Korner and Karl Popper.
Referring back to Bell, his captivating narrative introduced me to the co-founders of calculus, Leibniz and Newton. Known as the “calculus wars,” their notorious debate over priority and plagiarism is a fundamental topic in mathematical historiography. While I possess two significant texts on this matter, “Philosophers at War” by A. Rupert Hall, and “The Calculus Wars” by Jason Bardi, my expanding comprehension over time unveiled a more intricate evolution of calculus.
The progression of calculus unfolded over two millennia, culminating in the seventeenth century. Leibniz and Newton amalgamated established mathematical concepts into a unified framework, resolving some elements while leaving others for later thinkers to elaborate over the next two centuries. This understanding prompted a personal reassessment of the tradition that accords them excessive credit for the discipline’s creation.
I have publicly articulated my stance on this misrepresentation of calculus’ origins and present a historical overview as a guest blogger. Currently, I am embarking on a comprehensive investigation into the evolution of calculus, highlighting the contributions over two thousand years, thereby revising the standard narrative surrounding Leibniz and Newton.