Title

By Making Use of the Resources of the Web, May History of Mathematics Improve the Level of Math Teaching?

Abstract Course

History of science has always tried to defend its purpose, particularly during the Enlightenment when it was considered to be a militant cause in favour of progress and against obscurantism. Auguste Comte modified the aim of history of science to build a pedagogy for mankind, claiming that the necessarily simplified history of the Galileo case and the heliocentric system would be indispensable to prepare the ground for social changes. To be more specific, the development of the history of the mathematical sciences as a learned subject from the end of the 19th century at least has shown that the help to teaching situations was difficult indeed. Historical facts proved very difficult to disentangle, as if said in another way, it seemed necessary to explain errors as well. But mathematicians easily follow Descartes by generally considering that it is always a better thing to be an ignorant than to think something false.  As now mathematics at different levels of teaching has avoided the strong and dogmatic axiomatic presentation, that the name of Bourbaki seems to summarize, history of mathematics is thought by some people as another way, if not a better way, to teach mathematics. This is not my opinion, as this claim does not answer the main issue that is the distinction between doing mathematics and doing history of mathematics. A distinction, which is as well the old one between philosophy of mathematics and mathematics. There is no history in Euclid’s Elements or in Newton’s Principia, and so little in Von Neumann’s Mathematical Foundations of Quantum mechanics. But, and this is important, there has always been notices about history in the books written by Bourbaki all along the years. It was certainly a biased history, in the sense that it had been written in order to show how the right way – Bourbakist’s choice for sure - was established.

My aim then is to argue that the astonishing resources of the web, with the ability to cover so various sources and so many explanations, and errors as well, may just be a sort of experimental way to teach mathematics. I would like to do so on two examples only, to be able to conduct some critical discussion. I’ll choose Kepler’s third law and Descartes’ rule of signs.

References

• Dhombres J (2015) Les savoirs mathématiques et leurs pratiques culturelles. Paris, Hermann [forthcoming]

Contact

jean.dhombres@cnrs.fr