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
Andrew Bernard Whinston107
Pekka Neittaanmäki106
Shlomo Noach (Stephen Ram) Sawilowsky104
Alexander Vasil'evich Mikhalëv100
Willi Jäger100
Ronold Wyeth Percival King100
Leonard Salomon Ornstein95
Ludwig Prandtl89
Yurii Alekseevich Mitropolsky88
Kurt Mehlhorn88
Erol Gelenbe87
Rudiger W. Dornbusch85
Selim Grigorievich Krein82
Andrei Nikolayevich Kolmogorov82
David Garvin Moursund82
Olivier Jean Blanchard82
Bart De Moor82
Richard J. Eden80
Bruce Ramon Vogeli80
Stefan Jähnichen79
Sergio Albeverio79
Egon Krause77
Arnold Zellner77

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Sharaf al-Dīn al-Ṭūsī162275
Kamāl al-Dīn Ibn Yūnus162274
Nasir al-Dīn al-Ṭūsī162273
Shams al‐Dīn al‐Bukhārī162272
Gregory Chioniadis1622711296
Manuel Bryennios162270
Theodore Metochites1622691315
Gregory Palamas162267
Nilos Kabasilas1622661363
Demetrios Kydones162265
Elissaeus Judaeus162242
Georgios Plethon Gemistos1622411380, 1393
Basilios Bessarion1622381436
Manuel Chrysoloras162211
Guarino da Verona1622101408
Vittorino da Feltre1622091416
Theodoros Gazes1622051433
Johannes Argyropoulos1621871444
Jan Standonck1621831490
Jan Standonck1621831474
Marsilio Ficino1621561462
Cristoforo Landino162156
Angelo Poliziano1621551477
Moses Perez162153
Scipione Fortiguerra1621531493

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
0189013
125817
29288
35434
43752
52877
62103
71733
81356
91193
10912
11780
12707
13580
14505
15401
16382
17365
18291
19235
20195
21193
22176
23153
24145
26115
25106
2992
2890
2788
3064
3461
3150
3248
3343
3535
3635
3829
3928
3726
4024
4124
4223
4323
4520
5015
4814
5214
4613
5113
5313
4911
4410
5510
479
569
608
577
587
546
595
615
655
825
624
644
674
704
774
633
683
693
723
1003
712
732
752
762
792
802
882
741
851
871
891
951
1041
1061
1071
1241
1511