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
Pekka Neittaanmäki106
Andrew Bernard Whinston105
Willi Jäger100
Alexander Vasil'evich Mikhalëv100
Ronold Wyeth Percival King100
Shlomo Noach (Stephen Ram) Sawilowsky99
Leonard Salomon Ornstein95
Ludwig Prandtl88
Yurii Alekseevich Mitropolsky88
Kurt Mehlhorn86
Rudiger W. Dornbusch85
David Garvin Moursund82
Bart De Moor82
Selim Grigorievich Krein82
Andrei Nikolayevich Kolmogorov82
Erol Gelenbe82
Richard J. Eden80
Olivier Jean Blanchard80
Stefan Jähnichen79
Bruce Ramon Vogeli79
Sergio Albeverio79
Egon Krause77
Johan F. A. K. van Benthem77

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Sharaf al-Dīn al-Ṭūsī155294
Kamal al Din Ibn Yunus155293
Nasir al-Din al-Tusi155292
Shams ad-Din Al-Bukhari155291
Gregory Chioniadis1552901296
Manuel Bryennios155289
Theodore Metochites1552881315
Gregory Palamas155286
Nilos Kabasilas1552851363
Demetrios Kydones155284
Elissaeus Judaeus155261
Georgios Plethon Gemistos1552601380, 1393
Basilios Bessarion1552571436
Manuel Chrysoloras155230
Guarino da Verona1552291408
Vittorino da Feltre1552281416
Theodoros Gazes1552241433
Johannes Argyropoulos1552061444
Jan Standonck1552021490
Jan Standonck1552021474
Marsilio Ficino1551751462
Cristoforo Landino155175
Angelo Poliziano1551741477
Scipione Fortiguerra1551721493
Moses Perez155172

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
0180245
124290
28894
35199
43636
52782
62021
71631
81289
91132
10864
11756
12644
13537
14475
15386
16372
17343
18271
19210
20201
21172
22171
23154
24130
25103
26102
2896
2785
2984
3058
3454
3344
3143
3241
3535
3633
3927
3726
4225
4124
3823
4023
4320
4520
5015
4714
5214
4912
5512
4611
5311
4410
4810
5110
6010
568
546
586
575
595
825
614
624
634
654
674
774
643
703
793
1003
662
682
692
722
732
742
752
802
882
711
761
851
861
951
991
1051
1061
1241
1471