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

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Sharaf al-Dīn al-Ṭūsī156056
Kamal al Din Ibn Yunus156055
Nasir al-Din al-Tusi156054
Shams ad-Din Al-Bukhari156053
Gregory Chioniadis1560521296
Manuel Bryennios156051
Theodore Metochites1560501315
Gregory Palamas156048
Nilos Kabasilas1560471363
Demetrios Kydones156046
Elissaeus Judaeus156023
Georgios Plethon Gemistos1560221380, 1393
Basilios Bessarion1560191436
Manuel Chrysoloras155992
Guarino da Verona1559911408
Vittorino da Feltre1559901416
Theodoros Gazes1559861433
Johannes Argyropoulos1559681444
Jan Standonck1559641490
Jan Standonck1559641474
Marsilio Ficino1559371462
Cristoforo Landino155937
Angelo Poliziano1559361477
Scipione Fortiguerra1559341493
Moses Perez155934

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
0181138
124419
28963
35212
43636
52793
62045
71645
81292
91134
10869
11757
12654
13542
14473
15388
16370
17349
18269
19215
20197
21177
22173
23147
24142
25104
26100
2896
2984
2782
3059
3452
3348
3146
3239
3537
3632
3927
3726
4226
4124
3823
4023
4520
4319
5015
4914
5214
4713
5512
4411
4611
5311
5110
489
609
568
546
596
575
585
615
705
825
624
634
654
674
774
643
793
1003
682
722
732
742
752
802
882
661
691
711
761
851
861
951
991
1051
1061
1241
1471