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 Kuo134
Roger Meyer Temam119
Ronold Wyeth Percival King100
Andrew Bernard Whinston98
Alexander Vasil'evich Mikhalëv98
Willi Jäger96
Pekka Neittaanmäki95
Leonard Salomon Ornstein95
Shlomo Noach (Stephen Ram) Sawilowsky88
Yurii Alekseevich Mitropolsky88
Ludwig Prandtl87
Kurt Mehlhorn83
Andrei Nikolayevich Kolmogorov82
David Garvin Moursund82
Selim Grigorievich Krein81
Bart De Moor81
Richard J. Eden80
Arnold Zellner78
Stefan Jähnichen78
Bruce Ramon Vogeli78
Charles Ehresmann78
Johan F. A. K. van Benthem77
Egon Krause76
David Hilbert75
Wilhelm Magnus74

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Shams ad-Din Al-Bukhari132793
Gregory Chioniadis132792
Manuel Bryennios132791
Theodore Metochites1327901315
Gregory Palamas132788
Nilos Kabasilas1327871363
Demetrios Kydones132786
Elissaeus Judaeus132763
Georgios Plethon Gemistos1327621380, 1393
Basilios Bessarion1327591436
Manuel Chrysoloras132735
Guarino da Verona1327341408
Vittorino da Feltre1327331416
Theodoros Gazes1327291433
Johannes Argyropoulos1327081444
Jan Standonck1327081490
Jan Standonck1327081474
Florens Florentius Radwyn Radewyns132678
Rudolf Agricola1326781478
Geert Gerardus Magnus Groote132678
Thomas von Kempen à Kempis132677
Marsilio Ficino1326771462
Cristoforo Landino132677
Angelo Poliziano1326761477
Alexander Hegius1326761474

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
0154039
120138
27654
34488
43111
52315
61682
71402
81166
9935
10751
11614
12553
13450
14404
15341
16312
17263
18210
19181
21171
20150
22145
23131
25109
2496
2680
2880
2767
2956
3445
3042
3141
3341
3238
3527
3624
4124
4224
3821
3921
4320
4019
3716
4516
5313
5012
5512
5211
499
569
488
608
447
467
477
517
636
575
595
615
544
784
673
652
682
702
712
732
742
812
822
882
952
982
581
621
641
661
721
751
761
771
801
831
871
961
1001
1191
1341