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 Kuo147
Roger Meyer Temam124
Andrew Bernard Whinston107
Pekka Neittaanmäki106
Ronold Wyeth Percival King100
Willi Jäger100
Alexander Vasil'evich Mikhalëv100
Shlomo Noach (Stephen Ram) Sawilowsky99
Leonard Salomon Ornstein95
Ludwig Prandtl88
Yurii Alekseevich Mitropolsky88
Kurt Mehlhorn86
Rudiger W. Dornbusch85
Selim Grigorievich Krein82
Andrei Nikolayevich Kolmogorov82
Bart De Moor82
David Garvin Moursund82
Erol Gelenbe82
Olivier Jean Blanchard80
Richard J. Eden80
Stefan Jähnichen79
Bruce Ramon Vogeli79
Sergio Albeverio79
Arnold Zellner77
Egon Krause77

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Sharaf al-Dīn al-Ṭūsī156660
Kamal al Din Ibn Yunus156659
Nasir al-Din al-Tusi156658
Shams ad-Din Al-Bukhari156657
Gregory Chioniadis1566561296
Manuel Bryennios156655
Theodore Metochites1566541315
Gregory Palamas156652
Nilos Kabasilas1566511363
Demetrios Kydones156650
Elissaeus Judaeus156627
Georgios Plethon Gemistos1566261380, 1393
Basilios Bessarion1566231436
Manuel Chrysoloras156596
Guarino da Verona1565951408
Vittorino da Feltre1565941416
Theodoros Gazes1565901433
Johannes Argyropoulos1565721444
Jan Standonck1565681490
Jan Standonck1565681474
Marsilio Ficino1565411462
Cristoforo Landino156541
Angelo Poliziano1565401477
Scipione Fortiguerra1565381493
Moses Perez156538

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
0181930
124550
28994
35234
43646
52787
62055
71655
81297
91134
10882
11759
12663
13545
14468
15398
16366
17354
18273
19214
20200
21180
22175
23145
24145
26104
25100
2899
2981
2778
3061
3451
3349
3147
3239
3537
3633
3727
3927
4226
4125
3822
4022
4520
4319
5015
4914
4713
5213
4412
5312
5512
4611
5110
489
609
568
597
546
575
615
635
705
825
584
654
674
774
623
643
793
1003
682
722
732
742
752
802
882
661
691
711
761
851
861
951
991
1061
1071
1241
1471