Inspired by Prof. Petr Beckmann’s classic 1970 book “A History of Pi”, Eli Maor in 1994 wrote “e: The Story of a Number”. ISBN 0-691-03390-0. Maor’s view is that the teaching of mathematics suffers from a lack of context. Including the historical background and the characters whose struggles led to advances would, he thinks, make mathematics more interesting and accessible to students and the general population. He certainly makes that case in this book which spans the ages from Babylonians in 1700 BC to modern times, digging into the mysterious number 2.7182818284… which keeps on cropping up in everything from interest rates to nuclear explosions. Math will always be math, causing fear & loathing in the kind of non-numerate person who ends up devising national budgets in Western democracies, but putting a human face on it may make it more intriguing.
One of the many fascinating elements in this book is the story from the 1600s of Sir Isaac Newton (upon whose head the apple fell) and Baron Gottfried Wilhelm von Leibniz. Back in high school math class, most of us were told that these two gentlemen independently invented calculus; there was some debate at the time about who should get the credit, but nowadays no-one really cares. Then it was on to memorizing formulae.
As Maor tells the story, it is much more interesting. Newton came from an ordinary rural English family which had been crossed by misfortune. He was an archetypal nerd student at Cambridge U. in England when, in 1665, Europe suffered a genuine plague – truly deadly, unlike today’s CovidScam. The young Newton withdrew to his family’s rural home and, working in isolation over a period of 2 years, developed the central ideas of calculus – the mathematics of change. Newton seems to have been a rather reclusive untrusting type, reluctant to publish his work. When not breaking new ground in mathematics or physics, Newton spent a lot of energy on astrology.
In contrast, Baron von Liebniz was the gifted son of a German philosophy professor. He had wide interests in philosophy, law, languages, and literature as well as mathematics. A highly sociable man, Liebniz spent much of his life as a diplomat. In the 1670s, he fully developed both differential and integral calculus – including the notation and rules which are still used today. (Newton’s more awkward notation is now of historical interest only). Liebniz openly shared his work with Newton, but Newton refused to reciprocate.
Liebniz published his development of calculus in 1684, sharing it with the world. Newton did not publish his own work until 1704, but did so with an implication that Liebniz had seen this almost 30 years previously before publishing his 1684 book. The resulting controversy over who invented calculus dragged on for decades, outliving both men.
Curiously, the touchy & unsociable Newton became a national hero in England. When he died in 1727, he was given a State funeral and buried in Westminster Abbey. In contrast, by the time Liebniz, the man of the world who gave us the form of calculus we still use today, died about 10 years earlier, he had almost been forgotten in his native land; only his secretary attended his funeral. Life is unfair!
OK, knowing all that does not make mathematics any easier – but it may tweak the occasional person’s interest in the topic.