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 Kuo165
Roger Meyer Temam128
Pekka Neittaanmäki126
Shlomo Noach (Stephen Ram) Sawilowsky111
Andrew Bernard Whinston108
Alexander Vasil'evich Mikhalëv101
Willi Jäger100
Ronold Wyeth Percival King100
Erol Gelenbe95
Leonard Salomon Ornstein95
Kurt Mehlhorn93
Ludwig Prandtl90
Dimitris John Bertsimas88
Yurii Alekseevich Mitropolsky88
Bart De Moor86
Rudiger W. Dornbusch85
David Garvin Moursund82
Olivier Jean Blanchard82
Selim Grigorievich Krein82
Andrei Nikolayevich Kolmogorov82
Stefan Jähnichen81
Bruce Ramon Vogeli80
Richard J. Eden80
Sergio Albeverio80
Wolfgang Karl Härdle79

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Saraf al-Dīn Muhammad al-Masʿūdī203632
Sharaf al-Dīn al-Ṭūsī203630
Fakhr al-Dīn Muhammad al-Rēzī203630
Kamāl al-Dīn Ibn Yūnus203629
Qutb al-Dīn Ibrāhīm al-Mīṣrī2036291222
Athīr al-Dīn al-Mufaḍḍal al-Abharī2036281264
Nasir al-Dīn al-Ṭūsī203627
Shams al‐Dīn al‐Bukhārī203624
Gregory Chioniadis2036231296
Manuel Bryennios203622
Theodore Metochites2036211315
Gregory Palamas203618
Nilos Kabasilas2036171363
Demetrios Kydones203616
Elissaeus Judaeus203593
Georgios Plethon Gemistos2035921380, 1393
Basilios Bessarion2035891436
Manuel Chrysoloras203562
Guarino da Verona2035611408
Vittorino da Feltre2035601416
Theodoros Gazes2035561433
Johannes Argyropoulos2035381444
Jan Standonck2035341490
Jan Standonck2035341474
Marsilio Ficino2035071462

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
0218070
129913
210844
36169
44382
53274
62495
72042
81595
91340
101111
11936
12827
13688
14588
15510
16452
17402
18320
19290
20266
22226
21219
23185
24162
25149
28123
26117
27111
2996
3075
3167
3257
3353
3452
3550
3645
3733
3830
3930
4229
4027
4325
4124
4420
4918
4517
4617
4716
5115
5215
4814
5514
5312
5011
5411
5711
609
568
588
647
697
596
616
636
685
624
654
724
824
673
703
733
743
773
803
782
792
882
952
1002
661
711
751
761
811
851
861
901
931
1011
1081
1111
1261
1281
1651