Euler genealogy

	Denied the void →	Parmenides (510-450BC)
		\|
		Aristotle (384-322BC)	Denied the void ← =190
		\|
	Piston and cylinder Vacuum pump Vacuum bulb Magdeburg hemispheres Vacuum engine	Otto Guericke (1602-1686)
		\|	← (Non-mathematical mentorship)
	Gunpowder engine → =175	Christiaan Huygens (1629-1695)
		\|
	Differential equations → =182-205	Gottfried Leibniz (1646-1716)
		\|
	"Bernoulli brothers" (differential equations)	Jacob Bernoulli (1654–1705)
		\|
	"Bernoulli brothers" (differential equations)	Johann Bernoulli (1667–1748)
		\|
	Reciprocity relation → =180-200	Leonhard Euler (1707-1783)	=185 →	Jean d’Alembert (1717-1783)
		\|		\|
	Lagrangian → =185	Joseph Lagrange (1736-1813)	Nebular hypothesis → =190	Pierre Laplace (1749-1827)
		\|		\|
	●-————	——— ● ———	——— ● ———	————-●
	\|	\|	\|	\|
(Analytical Theory of Heat) →	Joseph Fourier (1768-1830)	\| \| \| \| \| \| \|	Simeon Poisson (1781-1840)	\| \| \| \| \| \| \|
	Hamiltonian → =170	William Hamilton (1805-1865)	————————	\| \| \| ————-●
		\|
	Thermodynamics → =190-205	Rudolf Clausius (1822-1888)
		\|
●-————	——— ● ———	——— ● ———	————--————	————-●
\|	\|	\|		\|
Ludwig Boltzmann (1844-1906)	\| \| \| \| \| \| \| \|	Willard Gibbs (1839-1903)	Chemical thermodynamics ← Quantum mechanics →	Max Planck (1858-1947)
↑ Statistical mechanics =182 (Elements) ↓	\|	\|
↑ Statistical mechanics =182 (Elements) ↓	\| \| \| \| \| \| \| \|	Gilbert Lewis (1875-1946)	Chemical thermodynamics ←
Euclid (c.340-280BC) \|	\| \| \| \| \| \| \| \| \|	\| \| \| \| \| \| \| \| \|
●-————	————-●	\|
	\|	\|
E = mc² Relativity → =160-225	Albert Einstein (1879-1955)	\| \| \| \| \| \| \|
		\|
Rossini debate Political thermodynamics Chemical thermodynamics →		Frederick Rossini (1899-1990)		Stanley Sandler (1940-)
		\|		\|
		● ————	————--————	————-●
		\|
Human thermodynamics Human chemical thermodynamics Human chemistry Human physics →		Libb Thims (c.1975-)

In mathematics, Euler genealogy shows the advisor/student relationship, generally PhD advisor / graduate student relation, for the historical mentor-student lineage of Swiss mathematician Leonhard Euler and his descendants. The main points of the Euler genealogy are mapped adjacent.

Second to the Euler genealogy is the Johann Pfaff (advisor) Carl Gauss (student) genealogy.

Current director of the Mathematics Genealogy project and Mitchel T. Keller explains, in the following video, how over over one-third of all modern 150,000 known (mapped) mathematicians can trace their genealogy back to ether Euler or Gauss.

Discussion
To note, the mathematical linage from Gottfried Leibniz-Christiaan Huygens on back is not necessarily one of a PhD student / PhD advisor connection, nor is the Leibniz-Jacob Bernoulli connection exactly a PhD student / PhD advisor connection; although Mitchel Keller, Mathematics Genealogy Project head, lists the three (Christiaan Huygens → Gottfried Leibniz → Jacob Bernoulli) as such. [2]

The so-called “Bernoulli brothers” (Jacob Bernoulli → Johann Bernoulli) (see: Bernoulli family) certainly were among the first to promote Leibniz’s version of calculus, and the older Bernoulli (Jacob) seems to have been the advisor to the younger Bernoulli (Johann), but the connection between Huygens and Leibniz needs to be studied a bit more, as regards to mathematical influences.

In addition, the Otto Guericke → Christian Huygens linkage is not necessarily one of mathematical knowledge genealogy, but rather one of influence, especially in regards to Huygens prolonged effort, in coordinated synergy with Robert Boyle, Denis Papin, and Robert Hooke, to make a working gunpowder engine, and in general study the properties of the vacuum.

Furthermore, it remains to be tracked down how some of the other great mathematical thinkers, such as, in particular, Euclid, fit into the picture as well, being that both James Maxwell and Albert Einstein were greatly influenced by Euclid's Elements.

Quotes | On

The following are related quotes:

“Descartes took up almost without change what this anonymous mathematician of the thirteenth century had written; and henceforth, from Descartes to Wallis, from Wallis to Bernoulli, and from the former to Lagrange, then to Gibbs, the principle of virtual displacements continued to be extended.”
— Pierre Duhem (1913), “Research on the History of Physical Theories”, in: Essays in the History and Philosophy of Science (pg. 242)

See also
● Thomson genealogy
● Gauss genealogy

References
1. Leonhard Euler – Mathematics Genealogy Project.
2. Keller, Mitchel T. (2011). “Interview: on Mathematics Genealogy Project”, London School of Economics website, Feb. 23.

Further reading
● Struik, D.J. (1969). A Source Book in Mathematics, 1200-1800 (Euler, 69+ pgs). Harvard University Press.

External links
● Gauss and Euler genealogy (pdf) – 3.bp.blogspot.com.