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 Kuo151
Roger Meyer Temam124
Pekka Neittaanmäki108
Andrew Bernard Whinston108
Shlomo Noach (Stephen Ram) Sawilowsky105
Willi Jäger101
Alexander Vasil'evich Mikhalëv100
Ronold Wyeth Percival King100
Leonard Salomon Ornstein95
Erol Gelenbe95
Ludwig Prandtl89
Kurt Mehlhorn88
Yurii Alekseevich Mitropolsky88
Rudiger W. Dornbusch85
Selim Grigorievich Krein82
Andrei Nikolayevich Kolmogorov82
Olivier Jean Blanchard82
Bart De Moor82
David Garvin Moursund82
Richard J. Eden80
Bruce Ramon Vogeli80
Stefan Jähnichen79
Sergio Albeverio79
Arnold Zellner77
Egon Krause77

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Sharaf al-Dīn al-Ṭūsī165790
Kamāl al-Dīn Ibn Yūnus165789
Nasir al-Dīn al-Ṭūsī165788
Shams al‐Dīn al‐Bukhārī165787
Gregory Chioniadis1657861296
Manuel Bryennios165785
Theodore Metochites1657841315
Gregory Palamas165782
Nilos Kabasilas1657811363
Demetrios Kydones165780
Elissaeus Judaeus165757
Georgios Plethon Gemistos1657561380, 1393
Basilios Bessarion1657531436
Manuel Chrysoloras165726
Guarino da Verona1657251408
Vittorino da Feltre1657241416
Theodoros Gazes1657201433
Johannes Argyropoulos1657021444
Jan Standonck1656981490
Jan Standonck1656981474
Marsilio Ficino1656711462
Cristoforo Landino165671
Angelo Poliziano1656701477
Scipione Fortiguerra1656681493
Moses Perez165668

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
0193154
126488
29538
35517
43776
52960
62160
71769
81370
91209
10960
11797
12714
13600
14515
15412
16389
17368
18304
19234
20208
21195
22183
23157
24151
26114
28106
25104
2993
2790
3067
3457
3152
3352
3244
3538
3636
3932
3728
3828
4325
4024
4123
4221
4521
5218
4614
4814
5014
5313
4911
5611
4710
5110
449
559
609
548
588
576
615
655
685
695
825
594
644
724
774
623
633
673
733
702
752
762
792
802
882
952
1002
1082
711
741
851
891
1011
1051
1241
1511