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 Kuo144
Roger Meyer Temam119
Pekka Neittaanmäki105
Andrew Bernard Whinston105
Ronold Wyeth Percival King100
Alexander Vasil'evich Mikhalëv99
Willi Jäger98
Leonard Salomon Ornstein95
Shlomo Noach (Stephen Ram) Sawilowsky92
Yurii Alekseevich Mitropolsky88
Ludwig Prandtl87
Kurt Mehlhorn86
Rudiger W. Dornbusch85
Bart De Moor82
David Garvin Moursund82
Andrei Nikolayevich Kolmogorov82
Selim Grigorievich Krein81
Richard J. Eden80
Olivier Jean Blanchard80
Sergio Albeverio79
Stefan Jähnichen79
Bruce Ramon Vogeli79
Arnold Zellner77
Egon Krause77
Charles Ehresmann77

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Kamal al Din Ibn Yunus145721
Nasir al-Din al-Tusi145720
Shams ad-Din Al-Bukhari145719
Gregory Chioniadis145718
Manuel Bryennios145717
Theodore Metochites1457161315
Gregory Palamas145714
Nilos Kabasilas1457131363
Demetrios Kydones145712
Elissaeus Judaeus145689
Georgios Plethon Gemistos1456881380, 1393
Basilios Bessarion1456851436
Manuel Chrysoloras145661
Guarino da Verona1456601408
Vittorino da Feltre1456591416
Theodoros Gazes1456551433
Jan Standonck1456341474
Jan Standonck1456341490
Johannes Argyropoulos1456341444
Florens Florentius Radwyn Radewyns145604
Geert Gerardus Magnus Groote145604
Rudolf Agricola1456041478
Thomas von Kempen à Kempis145603
Cristoforo Landino145603
Marsilio Ficino1456031462

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
0169782
122885
28467
34969
43459
52590
61905
71548
81226
91045
10825
11692
12617
13503
14451
15377
16339
17296
18266
19195
21178
20167
22164
23130
24117
25108
2692
2886
2784
2968
3455
3051
3142
3342
3237
3629
3826
3525
3925
4223
3722
4022
4121
4520
4319
5216
4414
4614
5513
5012
4811
4911
4710
5610
538
517
617
576
606
636
545
585
594
654
774
673
683
733
793
823
622
692
712
722
752
762
802
1052
641
661
701
811
851
861
871
881
921
951
981
991
1001
1191
1441