Always look forward to your emails – always interesting and thought-provoking!

One of your points sparked my thoughts on an issue which has intrigued me for decades – the “invention” of the calculus.

I initially perceived the calculus in the 50s as some obscure (arcane!) study only highly intelligent and highly skilled mathematicians could approach – thankfully WW Sawyer in Mathematician’s Delight later saved me in that respect (it was his 110th birthday recently by the way; a fact no-one seemed to be interested in.)

It was, of course, the fault of my schoolmasters, and, I hate to say, the textbooks available at the time (I used Durell and Robson’s Elementary Calculus to teach myself – ah! I’ve still got them, but I’d recommend them to only very keen students.)

Only years afterwards – after a career in Fleet Street and training as a teacher at the age of 40 in 1987 – was I able to say with confidence to students that calculus is “just the maths of change, get over it.”

Again as a youngster, I’d used National Certificate Mathematics by Mahon and Abbott (still the best for introductory maths; I’ve secretly used them in class for exercises), and during lockdown I’ve combed the web for them as completely revised by WE Fisher.

In vol 3, page 96, Fisher says: “A distinguished physicist [Lighthill on Shock Waves] recently referred in a public lecture to the ‘special language invented by Newton and Leibniz, called calculus.’ That language was not invented and subsequently applied to the solutions to Newton’s problems: it is the expression of the way in which these problems had been (italics) attacked and solved. The calculus is not just a discipline invented by professors of mathematics but a method of expression which takes the place of arithmetic when it is necessary to deal with quantities which are changing – whether with time, or position, or anything else.”

That sums it up for me.

(Also during lockdown I’ve been delving into medieval maths, logic and metaphysics – the Oxford Calculators in the 1300s and later the pre-Newton scientific clubs and societies here and in Italy and France were nibbling at the idea of change/flux. Perhaps, if it had not been for the Black Death and Wycliffe, Merton/Oxford would have been the axis for the advance in science and not Newton/Trinity/Cambridge!

How the concepts attached to “impetus” developed from the Greeks onwards I find fascinating.)

Thoroughly enjoyed your superstructure MOOC by the way.

Tony Patey (Bristol. Retired.) ]]>

An interesting analysis. I have just done the same calculation and my percentage of uncited publications is 34% compared to Peter’s 45%. Google Scholar picks up a lot of junk at the bottom of the list which has not been peer-reviewed and, or are short abstracts presented at conferences that no one would cite. Maybe the latter is more common in Peter’s field than mine?

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