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
Andrei Nikolayevich Kolmogorov82
Bart De Moor81
Selim Grigorievich Krein81
Richard J. Eden80
Olivier Jean Blanchard79
Stefan Jähnichen79
Bruce Ramon Vogeli79
Charles Ehresmann78
Johan F. A. K. van Benthem77
Arnold Zellner77
Egon Krause76

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Shams ad-Din Al-Bukhari138152
Gregory Chioniadis138151
Manuel Bryennios138150
Theodore Metochites1381491315
Gregory Palamas138147
Nilos Kabasilas1381461363
Demetrios Kydones138145
Elissaeus Judaeus138122
Georgios Plethon Gemistos1381211380, 1393
Basilios Bessarion1381181436
Manuel Chrysoloras138094
Guarino da Verona1380931408
Vittorino da Feltre1380921416
Theodoros Gazes1380881433
Johannes Argyropoulos1380671444
Jan Standonck1380671474
Jan Standonck1380671490
Rudolf Agricola1380371478
Florens Florentius Radwyn Radewyns138037
Geert Gerardus Magnus Groote138037
Cristoforo Landino138036
Marsilio Ficino1380361462
Thomas von Kempen à Kempis138036
Angelo Poliziano1380351477
Alexander Hegius1380351474

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
0160835
121241
27981
34725
43260
52423
61795
71456
81187
9968
10776
11646
12590
13486
14420
15361
16325
17280
18230
19186
21174
20149
22147
23134
24112
25101
2689
2882
2776
2957
3449
3045
3144
3241
3341
3530
3825
4125
4224
3623
4322
3720
3920
4017
4517
5215
5513
4912
4411
5311
4610
5610
479
489
509
609
548
517
576
616
636
593
753
793
622
662
672
692
702
712
732
772
812
822
1002
581
641
651
681
721
741
761
781
801
841
851
871
881
911
951
981
991
1041
1191
1401