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 Whinston107
Shlomo Noach (Stephen Ram) Sawilowsky105
Willi Jäger101
Alexander Vasil'evich Mikhalëv100
Ronold Wyeth Percival King100
Erol Gelenbe95
Leonard Salomon Ornstein95
Ludwig Prandtl89
Kurt Mehlhorn88
Yurii Alekseevich Mitropolsky88
Rudiger W. Dornbusch85
Selim Grigorievich Krein82
Andrei Nikolayevich Kolmogorov82
David Garvin Moursund82
Bart De Moor82
Olivier Jean Blanchard82
Richard J. Eden80
Bruce Ramon Vogeli80
Stefan Jähnichen79
Sergio Albeverio79
Johan F. A. K. van Benthem77
Egon Krause77

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Sharaf al-Dīn al-Ṭūsī164733
Kamāl al-Dīn Ibn Yūnus164732
Nasir al-Dīn al-Ṭūsī164731
Shams al‐Dīn al‐Bukhārī164730
Gregory Chioniadis1647291296
Manuel Bryennios164728
Theodore Metochites1647271315
Gregory Palamas164725
Nilos Kabasilas1647241363
Demetrios Kydones164723
Elissaeus Judaeus164700
Georgios Plethon Gemistos1646991380, 1393
Basilios Bessarion1646961436
Manuel Chrysoloras164669
Guarino da Verona1646681408
Vittorino da Feltre1646671416
Theodoros Gazes1646631433
Johannes Argyropoulos1646451444
Jan Standonck1646411474
Jan Standonck1646411490
Marsilio Ficino1646141462
Cristoforo Landino164614
Angelo Poliziano1646131477
Moses Perez164611
Scipione Fortiguerra1646111493

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
0191698
126258
29444
35508
43775
52926
62137
71753
81367
91196
10953
11789
12704
13602
14507
15409
16379
17369
18304
19235
20203
21196
22183
23152
24147
26112
25108
28103
2994
2789
3067
3458
3150
3348
3246
3538
3637
3931
3729
3825
4325
4124
4023
4521
4220
5217
4814
5014
4613
5112
5312
4411
4711
5510
5610
499
609
548
588
576
615
645
685
695
825
594
624
654
774
673
723
733
632
702
712
752
762
792
802
882
952
1002
741
851
891
1011
1051
1071
1081
1241
1511