Today is the 342^{nd} birthday of Johann (Jean, John) Bernoulli (new style)* the younger of the famous Swiss Bernoulli brothers, who were not, for those that don’t know their history of maths, a country and western duo or a circus juggling act but were two of the most important European mathematicians at the end of the 17^{th} and beginning of the 18^{th} centuries. Johann and his older brother Jakob (Jacques, James) collaborated with Gottfried Leibniz on the creation of that bane of nearly all American college students the Calculus. ** Both brothers also made other considerable contributions to the development of modern mathematics. Johann is also famous for his role as a teacher, his most famous private pupil Guillaume François Antoine, Marquis de l’Hospital wrote the first ever calculus textbook, which was actually the notes that he had made from his lesson with Bernoulli. All of my mathematical readers can of course quote the de l’Hospital rule for the determination of limits of indeterminate forms! However it was his most famous student when he was professor for mathematics in Basel who made the greatest contribution to the development of 18^{th} century mathematics, Leonard Euler. Euler together with Johann his professor and several second and third generation Bernoullis created, along side a group of French mathematicians, the foundations of modern mathematical physics out of a melange of the work of Newton, Leibniz and Descartes.

The mention of second and third generation Bernoullis illustrates another aspect for which this family is famous their role in the nature versus nurture debate. Those on the side of nature quote the Bernoullis along side the Bachs and Gregorys as examples of families where a high level of specific intelligence, in the case of the Bernoullis mathematical, was inherited through several generations. There are eight Bernoullis and three Gregorys (James, David and Duncan) in the MacTutor History of Mathematics Archive. As can be seen the Bernoulli family tree is very impressive and even Hermann Hesse, who is one of my favourite authors, married a Bernoulli, Maria, in his first marriage. The family habit of re-using first names through the generations leads to a great deal of confusion amongst people trying to understand the history of 18^{th} century mathematics and physics.

Anybody who wishes to claim even a nodding acquaintance with the history of mathematics should know the basics of Johann Bernoulli’s achievements; he’s one of the big guys!

*His birthday was on 27th July if one uses the old style Julian calendar!

**I have deliberately ignored the fraught topic of Newton contra Leibniz and the calculus in this post as it is a topic on which I intend to post at some point in the future

Confession: Today is also the birthday of my big sister and I was so occupied with typing this post that I forgot to ring her. I rang her just a minute ago but she wasn’t at home so I sang happy birthday to her answering machine instead!

I hope your singing voice is better than mine :o)

I wonder if mathematical ability runs in families or if it is growing up in the households of mathematicians that causes the children to not be afraid of mathematics.

Nature or nuture? Though perhaps that is best left to the great white ape.

You have found exactly the right criticism of the use of such families as proof of nature, they are of course just as good evidence of nurture 😉

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So, happy birthday to your big sister from France (Then you can pretend you were so occupied finding people all around the world to wish her a happy brithday)

What a pity that my reply to such an interesting note on the Bernoullis is just about the non-Bernoulli fact. I promise I’ll do my best in the future.