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
Shlomo Noach (Stephen Ram) Sawilowsky100
Ronold Wyeth Percival King100
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
Richard J. Eden80
Bruce Ramon Vogeli80
Olivier Jean Blanchard80
Sergio Albeverio79
Stefan Jähnichen79
Arnold Zellner77
Egon Krause77

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Sharaf al-Dīn al-Ṭūsī156983
Kamal al Din Ibn Yunus156982
Nasir al-Din al-Tusi156981
Shams ad-Din Al-Bukhari156980
Gregory Chioniadis1569791296
Manuel Bryennios156978
Theodore Metochites1569771315
Gregory Palamas156975
Nilos Kabasilas1569741363
Demetrios Kydones156973
Elissaeus Judaeus156950
Georgios Plethon Gemistos1569491380, 1393
Basilios Bessarion1569461436
Manuel Chrysoloras156919
Guarino da Verona1569181408
Vittorino da Feltre1569171416
Theodoros Gazes1569131433
Johannes Argyropoulos1568951444
Jan Standonck1568911490
Jan Standonck1568911474
Marsilio Ficino1568641462
Cristoforo Landino156864
Angelo Poliziano1568631477
Scipione Fortiguerra1568611493
Moses Perez156861

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
0182791
124721
29040
35252
43651
52787
62057
71668
81309
91144
10891
11759
12665
13561
14473
15397
16365
17359
18275
19219
20199
21178
22176
23147
24140
26108
25104
2896
2983
2777
3061
3455
3150
3347
3237
3535
3634
3728
3927
4227
4125
3822
4022
4520
4318
5016
4914
5213
5513
4412
4712
5312
4611
5110
489
568
608
597
616
545
575
655
675
705
825
584
634
774
1004
623
643
803
682
722
732
742
752
792
882
691
711
761
851
861
951
1061
1071
1241
1471