Graph structure

In July 2016, Cosmin Ionita and Pat Quillen of MathWorks used MATLAB to analyze the Math Genealogy Project graph. At the time, the genealogy graph contained 200,037 vertices. There were 7639 (3.8%) isolated vertices and 1962 components of size two (advisor-advisee pairs where we have no information about the advisor). The largest component of the genealogy graph contained 180,094 vertices, accounting for 90% of all vertices in the graph. The main component has 7323 root vertices (individuals with no advisor) and 137,155 leaves (mathematicians with no students), accounting for 76.2% of the vertices in this component. The next largest component sizes were 81, 50, 47, 34, 34, 33, 31, 31, and 30.

For historical comparisonn, we also have data from June 2010, when Professor David Joyner of the United States Naval Academy asked for data from our database to analyze it as a graph. At the time, the genealogy graph had 142,688 vertices. Of these, 7,190 were isolated vertices (5% of the total). The largest component had 121,424 vertices (85% of the total number). The next largest component had 128 vertices. The next largest component sizes were 79, 61, 45, and 42. The most frequent size of a nontrivial component was 2; there were 1937 components of size 2. The component with 121,424 vertices had 4,639 root verticies, i.e., mathematicians for whom the advisor is currently unknown.

Top 25 Advisors

NameStudents
C.-C. Jay Kuo161
Roger Meyer Temam128
Pekka Neittaanmäki121
Shlomo Noach (Stephen Ram) Sawilowsky110
Andrew Bernard Whinston108
Alexander Vasil'evich Mikhalëv101
Willi Jäger100
Ronold Wyeth Percival King100
Erol Gelenbe95
Leonard Salomon Ornstein95
Kurt Mehlhorn91
Ludwig Prandtl90
Yurii Alekseevich Mitropolsky88
Dimitris John Bertsimas86
Rudiger W. Dornbusch85
Bart De Moor84
Olivier Jean Blanchard82
Selim Grigorievich Krein82
Andrei Nikolayevich Kolmogorov82
David Garvin Moursund82
Stefan Jähnichen81
Richard J. Eden80
Bruce Ramon Vogeli80
Sergio Albeverio80
Arnold Zellner79

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Sharaf al-Dīn al-Ṭūsī191684
Kamāl al-Dīn Ibn Yūnus191683
Nasir al-Dīn al-Ṭūsī191682
Shams al‐Dīn al‐Bukhārī191681
Gregory Chioniadis1916801296
Manuel Bryennios191679
Theodore Metochites1916781315
Gregory Palamas191676
Nilos Kabasilas1916751363
Demetrios Kydones191674
Elissaeus Judaeus191651
Georgios Plethon Gemistos1916501380, 1393
Basilios Bessarion1916471436
Manuel Chrysoloras191620
Guarino da Verona1916191408
Vittorino da Feltre1916181416
Theodoros Gazes1916141433
Johannes Argyropoulos1915961444
Jan Standonck1915921474
Jan Standonck1915921490
Marsilio Ficino1915651462
Cristoforo Landino191565
Angelo Poliziano1915641477
Scipione Fortiguerra1915621493
Moses Perez191562

Nonplanarity

The Mathematics Genealogy Project graph is nonplanar. Thanks to Professor Ezra Brown of Virginia Tech for assisting in finding the subdivision of K3,3 depicted below. The green vertices form one color class and the yellow ones form the other. Interestingly, Gauß is the only vertex that needs to be connected by paths with more than one edge.

K_{3,3} in the Genealogy graph

Frequency Counts

The table below indicates the values of number of students for mathematicians in our database along with the number of mathematicians having that many students.

Number of StudentsFrequency
0207781
128721
210293
35919
44134
53122
62390
71918
81512
91266
101030
11873
12800
13664
14556
15468
16415
17387
18308
19259
20246
22215
21203
23174
24146
25141
26115
27107
28105
29100
3075
3160
3452
3251
3350
3545
3636
3735
4330
3829
3929
4226
4025
4124
4418
5218
4917
4616
4514
4713
4813
5012
5112
5311
5511
5711
5410
5610
6010
698
617
586
595
625
635
645
654
684
724
824
733
763
803
672
702
752
772
952
1002
711
741
781
791
811
841
851
861
881
901
911
1011
1081
1101
1211
1281
1611