JB - TWF #244: When was the First Calculus Textbook Written?

[marcus]

In this edition JB asks the question

When was the first calculus textbook written - and in what language?

and gives an unexpected answer.

Also there is an account of a conversation in a café in Toronto about how to measure the size of a category. It ends with the observation that

We're still just learning to count.

 

[Dcase]

Hi Marcus:

As usual John Baez has a great and interesting blog in TWF 244.

I am fascinated with item 5 which discusses Euler’s bridges. From my perspective this is a problem ideal for the strategy analysis of game theory had such a tool been available in the 1700s.

Geert Jan Olsder [mathematics] Delft University in 2005 presented a variant of this problem as a train routing schedule using game theory.
MAX PLUS IN HET (TREIN)VERKEER ...[Text in English]
http://webserv.nhl.nl/~kamminga/wintersymposium/Olsder2005.pdf

There does exist the possibility of the Braess' paradox in traffic flow problems.
http://en.wikipedia.org/wiki/Braess'_paradox

 

[Entropia]

It is difficult to determine exactly when the first calculus textbook was written, as there are various definitions and interpretations of what constitutes a "textbook." However, many historians credit the French mathematician and philosopher René Descartes with writing the first systematic textbook on calculus in 1637, titled "La Géométrie." This textbook was written in French and focused on the geometric foundations of calculus.

Other notable early calculus textbooks include "Analysis per Quantitatum Series, Fluxiones, ac Differentias" by Isaac Newton, published in 1711, and "Institutiones Calculi Differentialis" by Leonhard Euler, published in 1755. Both of these textbooks were written in Latin and focused on the more analytical and algebraic aspects of calculus.

It is interesting to note the language in which these early calculus textbooks were written, as it reflects the dominant scientific and mathematical cultures of the time. Latin was the common language of science and academia in Europe during the 17th and 18th centuries, but as the study of calculus became more widespread, textbooks began to be written in the local languages of the countries where they were published.

The conversation in the Toronto café about measuring the size of a category highlights the ongoing evolution and development of mathematical concepts. While calculus has been around for centuries, mathematicians are still exploring and expanding upon its principles and applications. As the saying goes, "we are still just learning to count" in the grand scheme of mathematics, and there is always more to discover and understand.