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 Kuo137
Roger Meyer Temam119
Andrew Bernard Whinston104
Ronold Wyeth Percival King100
Pekka Neittaanmäki99
Alexander Vasil'evich Mikhalëv99
Willi Jäger98
Leonard Salomon Ornstein95
Shlomo Noach (Stephen Ram) Sawilowsky90
Yurii Alekseevich Mitropolsky88
Ludwig Prandtl87
Kurt Mehlhorn84
David Garvin Moursund82
Andrei Nikolayevich Kolmogorov82
Selim Grigorievich Krein81
Bart De Moor81
Richard J. Eden80
Bruce Ramon Vogeli79
Stefan Jähnichen78
Charles Ehresmann78
Johan F. A. K. van Benthem77
Egon Krause76
Arnold Zellner76
David Hilbert75
Wilhelm Magnus75

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Shams ad-Din Al-Bukhari136337
Gregory Chioniadis136336
Manuel Bryennios136335
Theodore Metochites1363341315
Gregory Palamas136332
Nilos Kabasilas1363311363
Demetrios Kydones136330
Elissaeus Judaeus136307
Georgios Plethon Gemistos1363061380, 1393
Basilios Bessarion1363031436
Manuel Chrysoloras136279
Guarino da Verona1362781408
Vittorino da Feltre1362771416
Theodoros Gazes1362731433
Johannes Argyropoulos1362521444
Jan Standonck1362521490
Jan Standonck1362521474
Rudolf Agricola1362221478
Florens Florentius Radwyn Radewyns136222
Geert Gerardus Magnus Groote136222
Marsilio Ficino1362211462
Cristoforo Landino136221
Thomas von Kempen à Kempis136221
Angelo Poliziano1362201477
Alexander Hegius1362201474

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
0158763
120874
27861
34679
43192
52395
61753
71440
81176
9956
10775
11639
12583
13475
14410
15357
16312
17283
18224
19184
21167
22156
20153
23128
24109
25102
2686
2881
2775
2955
3448
3046
3242
3341
3140
3530
3626
4125
3924
3822
4222
4321
4017
4517
5216
3714
4912
4411
5511
5010
5610
469
479
489
539
609
548
617
516
636
575
593
683
733
753
662
672
702
712
762
782
812
822
992
581
621
641
651
721
741
771
791
801
841
871
881
901
951
981
1001
1041
1191
1371