In the early 1980s, the University of Erlangen emerged as the academic platform where an experienced student immersed themselves in the realm of mathematics. At this German university, obtaining a first degree was comparable to finishing a master’s program, encompassing the rigorous task of a dissertation. This mathematics qualification, typically referred to as a diploma, lasted eight to nine demanding semesters, with numerous students extending their studies even further. The foundational courses in mathematics, particularly analysis and algebra, were rigorous, consisting of double lectures lasting ninety minutes each, spread across four days a week. Each double lecture required the painstaking preparation of eight to ten A4 pages of notes, keeping students thoroughly occupied. Additional weekly exercise sheets accompanied these classes, providing practical problem-solving opportunities along with afternoon sessions dedicated to review and correction. By the third semester, the academic schedule broadened to include seminars, requiring students to prepare and present papers on intricate topics.
For this specific student, analysis emerged as a preferred subject, eclipsing algebra in interest. The compulsory choice of a subsidiary subject led to a focus on philosophy. This decision fortuitously aligned with the commencement of Christian Thiel’s role as a philosophy professor at Erlangen. This era signified a transformative fusion of mathematics with the exploration of the history and philosophy of science under the mentorship of Professor Thiel and other prominent educators. As the student’s interest shifted from strictly mathematical inquiries to their historical context, they transitioned after five semesters to pursue a master’s degree in philosophy, taking history and English as subsidiary subjects. This academic transition laid the groundwork for a career centered around writing and contemplating the history of mathematics.
The venture into the realm of analysis began much earlier. As a teenager with solid proficiency in O-level and A-level mathematics, this individual was one of those rare pupils who enjoyed solving mathematical challenges, particularly thriving in calculus, then referred to as analysis. A standout experience was achieving an unusual 102% on a derivatives exam, which featured 50 functions, where precision and speed were essential. Despite facing challenges with exams due to AD(H)S, a condition impacting focused performance during assessments, this instance showcased a standout achievement through careful comprehension.
A lifelong enthusiasm for history, partly nurtured by a historian father, led to a deep engagement with Eric Temple Bell’s “Men of Mathematics,” a book noted for its accessibility yet riddled with inaccuracies. Over time, it became clear that while Bell’s work motivated a pursuit of historical studies in mathematics, it also contained historical errors, as critiqued by historian Ivor Grattan-Guinness. This critique ignited a broader intellectual exploration into the history of mathematics, particularly exploring works like Stephen Körner’s “Philosophy of Mathematics” and Karl Popper’s “Conjectures and Refutations.”
The interest in the historical development of calculus grew significantly from the understanding that it was independently discovered by both Leibniz and Newton. Their infamous ‘calculus wars’ have been immortalized in the chronicles of mathematical history, with their narratives captured in numerous scholarly articles and biographies, including dedicated works such as A. Rupert Hall’s “Philosophers at War” and Jason Bardi’s “The Calculus Wars.”
As exploration continued, it became clear that the story of calculus’s invention by Newton and Leibniz was an oversimplified account. Rather, calculus represented the zenith of over two millennia of mathematical development, with countless contributors preceding Newton and Leibniz. During the 17th century, mathematicians like these two figures integrated the existing knowledge into coherent frameworks, addressing some complexities while leaving others for future mathematicians to resolve.
Looking back on this academic journey, the misrepresentation of calculus’s origins became evident. Now driven by a desire to clarify this intricate history, it is time for a comprehensive investigation of this mathematical evolution, honoring the foundational contributions of numerous mathematicians throughout history. Through a series of extensive posts, the narrative of calculus’s two-thousand-year progression will be unveiled, reexamining the accolades traditionally attributed to Leibniz and Newton.