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
Alexander Vasil'evich Mikhalëv100
Ronold Wyeth Percival King100
Shlomo Noach (Stephen Ram) Sawilowsky100
Willi Jäger100
Leonard Salomon Ornstein95
Ludwig Prandtl88
Yurii Alekseevich Mitropolsky88
Kurt Mehlhorn86
Rudiger W. Dornbusch85
Bart De Moor82
Selim Grigorievich Krein82
Andrei Nikolayevich Kolmogorov82
David Garvin Moursund82
Erol Gelenbe82
Olivier Jean Blanchard81
Richard J. Eden80
Bruce Ramon Vogeli80
Sergio Albeverio79
Stefan Jähnichen79
Arnold Zellner77
Egon Krause77

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Sharaf al-Dīn al-Ṭūsī157261
Kamal al Din Ibn Yunus157260
Nasir al-Din al-Tusi157259
Shams ad-Din Al-Bukhari157258
Gregory Chioniadis1572571296
Manuel Bryennios157256
Theodore Metochites1572551315
Gregory Palamas157253
Nilos Kabasilas1572521363
Demetrios Kydones157251
Elissaeus Judaeus157228
Georgios Plethon Gemistos1572271380, 1393
Basilios Bessarion1572241436
Manuel Chrysoloras157197
Guarino da Verona1571961408
Vittorino da Feltre1571951416
Theodoros Gazes1571911433
Johannes Argyropoulos1571731444
Jan Standonck1571691474
Jan Standonck1571691490
Marsilio Ficino1571421462
Cristoforo Landino157142
Angelo Poliziano1571411477
Moses Perez157139
Scipione Fortiguerra1571391493

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
0183122
124773
29075
35265
43657
52799
62056
71670
81312
91142
10891
11761
12674
13559
14473
15399
16364
17360
18275
19220
20200
21178
22174
23147
24142
26109
25102
2897
2981
2779
3062
3456
3151
3348
3237
3534
3634
3727
3927
4227
4024
4124
3822
4520
4318
5016
4914
5213
5513
4412
5312
4611
4711
4810
5110
568
608
597
616
545
575
705
825
584
634
654
674
774
1004
623
643
683
722
732
742
752
792
802
882
661
691
711
761
811
851
861
951
1061
1071
1241
1471