List of second-generation mathematicians

This is a dynamic list and may never be able to satisfy particular standards for completeness. You can help by adding missing items with reliable sources.

Math ability is passed from parent to child ^[1] with the most famous example being the Bernoulli family.^[2] This second generation phenomenon also holds in physics ^[3] but in that field the Nobel prize gives a tool for tracking it, since it has been given out for more than 120 years, and there are on average more than two Nobel prizes in physics given each year.^[4] There is no comparable award in mathematics ^[5] but perusing (for example) the MacTutor ^[6] list of biographies enables the construction of a similar list of notable two-generation pairs of mathematicians.

The following is a list of parent-child pairs who both made contributions to mathematics signficiant enough to be noted in the citation for a prestigious prize, in an obituary in a major math journal, or in a similarly authoritative source. All are father-son except for Emmy Noether and Cathleen Morawetz. The list is in chronological order by birth date of the parent.

List

Parent	Notable for	Awards	Child	Notable for	Awards
Johann Bernoulli	L'Hôpital's rule catenary brachistochrone curve		Daniel Bernoulli	Bernoulli's principle Gamma function
Farkas Bolyai	Wallace–Bolyai–Gerwien theorem		Janos Bolyai	Non-Euclidean geometry
Elie Cartan	Structure of Lie groups exterior algebra moving frame		Henri Cartan	Cartan's theorems A and B Projective module	Émile Picard Medal Wolf Prize
Max Noether	Brill–Noether theory Noether's formula Noether inequality		Emmy Noether	Noether's theorem Noetherian Property
George David Birkhoff	Ergodic Theorem	Bocher Memorial Prize	Garrett Birkhoff	Universal algebra	George David Birkhoff Prize
J. L. Synge	Synge's theorem		Cathleen Morawetz	Work on equations of mixed type, with its striking consequences for the theory of flow around airfoils, work on local energy decay for waves in the complement of an obstacle, and results concerning the existence of transonic flow with shocks. [7]	Leroy P. Steele Prize
Emil Artin	Solved Hilbert's seventeenth problem partially solved Hilbert's ninth problem		Michael Artin	Artin approximation theorem Algebraic spaces	Leroy P. Steele Prize Wolf Prize
Petr Novikov	Word problem for groups		Sergei Novikov	Adams–Novikov spectral sequence Surgery theory	Fields Medal
Jacques-Louis Lions	With Giovanni Prodi independently proved the uniqueness of weak solutions in dimension two of the incompressible Navier-Stokes equations. With 0. A. Ladyzhenskaya, ]. Serrin, and others, contributed to the beginning of the modern theory of mathematical fluid dynamics. Work with Emico Magenes on nonhomogeneous boundary value problems, which led eventually to the publication of a three-volume book in 1968. [8]	John von Neumann Prize Japan Prize	Pierre-Louis Lions	Breakthrough 1983 paper with M.G. Crandall, which introduced "viscosity solutions" for Hamilton-Jacobi equations. Extraordinary 1989 paper with R. J. DiPerna, the first mathematical work to show rigorously the existence of solutions to Boltzmann's equation for the density of colliding hard spheres, with general initial data. [9]	Fields Medal
Joram Lindenstrauss	Characterization (joint with L. Tzafriri) of the Hilbert space as the unique Banach space all of whose closed subspaces are complemented (solution of a 1930 Banach and Mazur's problem). [10]	Israel Prize Stefan Banach Medal	Elon Lindenstrauss	major advance on Littlewood conjecture	Fields Medal

See also

• List of second-generation physicists