Blog of Andrés Aravena

03 November 2019

The Department of Mathematics of North Dakota State University handles the Mathematics Genealogy Project. This is a database listing most mathematicians and their advisors. It is a genealogy since usually these can be seen as family relationships. Your Ph.D. advisor is your parent, their advisor is your grandparent, and so on, to all your ancestors. If you have advised someone, they become your children, and their students are your descendants.

You can see in my page that I have two advisors: my “father” Alejandro Maass from Chile, and my “mother” Anne Siegel, from France. Then you can click them and see who are their advisors. And their advisors, and their advisors.

For the modern times, each person has to register his/herself. For the older generation, they use historic data, as good as available. Some people have more than one advisor, which in old times was not always formal. In other words, it includes the cases of master–disciple relationships. In some cases the date of diploma is included.

With some simple command-line tools, I downloaded my academic family tree. Looking at the tree, I find many interesting names and connections.

• One of my great-great-parents is Jacques Neveu (1955), who wrote the book of probabilities that I used as a student of mathematical engineering. His grandparent is René Fréchet, creator of a particular kind of derivative
• My two advisors have a common ancestor: Jacques Hadamard (1892), which is famous for several works including a particular “inequality”.
• One grandparent of Hadamard is Charles Hermite, which is recognized in the Hermitian matrices
• On the other branch of Hadamard’s ancestors we find Michel Chasles (1814) who worked in projective geometry. His advisor was Simeon Poisson (1800) with his probability distribution.
• Poisson had two advisors: Lagrange and Laplace. Pierre-Simon de Laplace (1769) did many things, and is remembered by the Laplacian operator in partial differential equations.
• Joseph Louis Lagrange (1754) is also famous for several things, including the method for optimization under constraints called Lagrange multiplier. He had two advisors. The most famous is Leonard Euler (1726).
• Euler is one of the really great mathematicians of all time. His advisor was Johann Bernoulli (1694), whose advisor was his brother Jacob Bernoulli (1684). The grand-parent of Jacob was Gottfried Wilhelm Leibniz, co-inventor of calculus.
• Leibniz had several advisors, including the astronomer Christiaan Huygens (1655), whose grand-parent was another famous astronomer: Marin Mersenne
• Following other ancestors of Leibniz we find, six generations earlier, another important astronomer: Nicolaus Copernicus.
• The drawing does not show the “uncles”. There are at least two notables. Johannes Argyropoulos (1444) was advisor of Leonardo da Vinci (1471), and Angelo Poliziano (1477) was advisor of Michelangelo Buonarroti (1492).
• At this level there are many ancestors on each generation, so it is harder to follow the connections. Some recognizable names are Desiderius Erasmus de Rotterdam (1506) and his grand-parent Rudolf Agricola (1478). They are philosophers, writing mostly in Latin.
• Before them, around the year 1300, there are several Greek names, corresponding to philosophers and astronomers from the Byzantine empire, such as Gregory Chioniadis (1296) and Theodore Metochites (1315). Essentially, I came back home.
• The Byzantines got their knowledge from Persian. The oldest ancestors in my tree are four Persian scholars. One of them is Nasir al-Dīn al-Ṭūsī, born near 1200, who wrote the first book of trigonometry as an independent subject, and independent of astronomy. In other words, he invented trigonometry as an independent branch of mathematics. In particular, the law of sines is called al-Ṭūsī’s Law.
• My oldest known academic ancestor is Sharaf al-Dīn al-Muẓaffar ibn Muḥammad ibn al-Muẓaffar al-Ṭūsī, born c. 1135 and died c. 1213 in Persia.

We do not know who were the advisors of many people on the tree. We can only imagine that there should be a connection with Indian and Babylonian, and other Persian mathematicians.

This is the family where I’m proud to belong. Do you recognize any other famous name?