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 Kuo140
Roger Meyer Temam119
Andrew Bernard Whinston104
Ronold Wyeth Percival King100
Pekka Neittaanmäki100
Alexander Vasil'evich Mikhalëv99
Willi Jäger98
Leonard Salomon Ornstein95
Shlomo Noach (Stephen Ram) Sawilowsky91
Yurii Alekseevich Mitropolsky88
Ludwig Prandtl87
Rudiger W. Dornbusch85
Kurt Mehlhorn84
David Garvin Moursund82
Bart De Moor82
Andrei Nikolayevich Kolmogorov82
Selim Grigorievich Krein81
Olivier Jean Blanchard80
Sergio Albeverio80
Richard J. Eden80
Stefan Jähnichen79
Bruce Ramon Vogeli79
Johan F. A. K. van Benthem77
Arnold Zellner77
Charles Ehresmann77

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Nasir al-Din al-Tusi140094
Shams ad-Din Al-Bukhari140093
Gregory Chioniadis140092
Manuel Bryennios140091
Theodore Metochites1400901315
Gregory Palamas140088
Nilos Kabasilas1400871363
Demetrios Kydones140086
Elissaeus Judaeus140063
Georgios Plethon Gemistos1400621380, 1393
Basilios Bessarion1400591436
Manuel Chrysoloras140035
Guarino da Verona1400341408
Vittorino da Feltre1400331416
Theodoros Gazes1400291433
Jan Standonck1400081490
Jan Standonck1400081474
Johannes Argyropoulos1400081444
Rudolf Agricola1399781478
Geert Gerardus Magnus Groote139978
Florens Florentius Radwyn Radewyns139978
Thomas von Kempen à Kempis139977
Cristoforo Landino139977
Marsilio Ficino1399771462
Alexander Hegius1399761474

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
0162672
121577
28053
34776
43289
52468
61818
71461
81197
9992
10798
11650
12600
13483
14428
15369
16326
17286
18239
19192
21169
22153
20152
23131
24109
25100
2688
2783
2883
2959
3450
3048
3241
3140
3340
3628
3527
4325
3824
4124
4223
3922
3721
4018
4517
5216
5013
5513
4412
4710
4810
5310
5610
499
468
547
577
617
516
606
636
754
593
673
713
773
803
823
582
622
652
662
682
692
732
792
1002
641
701
721
761
811
841
851
871
881
911
951
981
991
1041
1191
1401