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-Ṭūsī155228
Kamal al Din Ibn Yunus155227
Nasir al-Din al-Tusi155226
Shams ad-Din Al-Bukhari155225
Gregory Chioniadis1552241296
Manuel Bryennios155223
Theodore Metochites1552221315
Gregory Palamas155220
Nilos Kabasilas1552191363
Demetrios Kydones155218
Elissaeus Judaeus155195
Georgios Plethon Gemistos1551941380, 1393
Basilios Bessarion1551911436
Manuel Chrysoloras155164
Guarino da Verona1551631408
Vittorino da Feltre1551621416
Theodoros Gazes1551581433
Johannes Argyropoulos1551401444
Jan Standonck1551361474
Jan Standonck1551361490
Marsilio Ficino1551091462
Cristoforo Landino155109
Angelo Poliziano1551081477
Scipione Fortiguerra1551061493
Moses Perez155106

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
0180146
124275
28895
35196
43635
52780
62016
71634
81288
91131
10866
11752
12643
13538
14475
15387
16371
17342
18272
19209
20201
21172
22170
23155
24129
25103
26103
2897
2785
2983
3058
3453
3344
3143
3241
3535
3633
3727
3927
4225
4124
4023
3822
4320
4520
5015
5215
4714
4912
5512
4611
4410
4810
5110
5310
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