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 Kuo150
Roger Meyer Temam124
Andrew Bernard Whinston107
Pekka Neittaanmäki106
Shlomo Noach (Stephen Ram) Sawilowsky102
Ronold Wyeth Percival King100
Alexander Vasil'evich Mikhalëv100
Willi Jäger100
Leonard Salomon Ornstein95
Ludwig Prandtl89
Yurii Alekseevich Mitropolsky88
Erol Gelenbe86
Kurt Mehlhorn86
Rudiger W. Dornbusch85
Bart De Moor82
Selim Grigorievich Krein82
Andrei Nikolayevich Kolmogorov82
David Garvin Moursund82
Olivier Jean Blanchard81
Richard J. Eden80
Bruce Ramon Vogeli80
Sergio Albeverio79
Stefan Jähnichen79
Egon Krause77
Johan F. A. K. van Benthem77

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Sharaf al-Dīn al-Ṭūsī159703
Kamal al Din Ibn Yunus159702
Nasir al-Din al-Tusi159701
Shams ad-Din Al-Bukhari159700
Gregory Chioniadis1596991296
Manuel Bryennios159698
Theodore Metochites1596971315
Gregory Palamas159695
Nilos Kabasilas1596941363
Demetrios Kydones159693
Elissaeus Judaeus159670
Georgios Plethon Gemistos1596691380, 1393
Basilios Bessarion1596661436
Manuel Chrysoloras159639
Guarino da Verona1596381408
Vittorino da Feltre1596371416
Theodoros Gazes1596331433
Johannes Argyropoulos1596151444
Jan Standonck1596111490
Jan Standonck1596111474
Marsilio Ficino1595841462
Cristoforo Landino159584
Angelo Poliziano1595831477
Scipione Fortiguerra1595811493
Moses Perez159581

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
0185388
125140
29175
35339
43698
52813
62080
71688
81321
91154
10897
11792
12677
13577
14479
15396
17369
16364
18280
19227
20192
21189
22180
23149
24141
26111
25108
28102
2982
2777
3057
3457
3152
3346
3243
3635
3534
3727
3926
4126
4225
3824
4024
4321
4517
5015
4814
4913
5213
5313
5513
4412
4612
5111
4710
568
597
607
617
545
575
585
705
634
654
674
774
824
623
643
683
723
1003
732
742
752
792
802
862
691
711
761
811
851
881
891
951
1021
1061
1071
1241
1501