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 Kuo167
Roger Meyer Temam129
Pekka Neittaanmäki125
Shlomo Noach (Stephen Ram) Sawilowsky111
Andrew Bernard Whinston108
Alexander Vasil'evich Mikhalëv101
Ronold Wyeth Percival King100
Willi Jäger100
Erol Gelenbe95
Leonard Salomon Ornstein95
Kurt Mehlhorn93
Dimitris John Bertsimas91
Ludwig Prandtl90
Yurii Alekseevich Mitropolsky88
Bart De Moor86
Rudiger W. Dornbusch85
Andrei Nikolayevich Kolmogorov82
Selim Grigorievich Krein82
Olivier Jean Blanchard82
David Garvin Moursund82
Stefan Jähnichen81
Wolfgang Karl Härdle81
Sergio Albeverio81
Richard J. Eden80
Bruce Ramon Vogeli80

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm al-Khayyām al-Nīsābūrī206304
Saraf al-Dīn Muhammad al-Masʿūdī al-Marwazī206303
Sharaf al-Dīn al-Ṭūsī206301
Fakhr al-Dīn Muhammad al-Rēzī206301
Kamāl al-Dīn Ibn Yūnus206300
Qutb al-Dīn Ibrāhīm al-Mīṣrī2063001222
Athīr al-Dīn al-Mufaḍḍal al-Abharī2062991264
Nasir al-Dīn al-Ṭūsī206298
Shams al‐Dīn al‐Bukhārī206295
Gregory Chioniadis2062941296
Manuel Bryennios206293
Theodore Metochites2062921315
Gregory Palamas206289
Nilos Kabasilas2062881363
Demetrios Kydones206287
Elissaeus Judaeus206264
Georgios Plethon Gemistos2062631380, 1393
Basilios Bessarion2062601436
Manuel Chrysoloras206233
Guarino da Verona2062321408
Vittorino da Feltre2062311416
Theodoros Gazes2062271433
Jan Standonck2062051490
Jan Standonck2062051474
Florens Florentius Radwyn Radewyns206172

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
0220121
130201
210965
36225
44407
53289
62538
72070
81611
91367
101115
11942
12842
13710
14589
15511
16461
17408
18316
19295
20270
22231
21228
23188
24164
25158
26126
28117
27109
29100
3077
3166
3259
3354
3453
3547
3647
3734
3934
3829
4027
4227
4326
4124
4420
4919
4518
4618
5117
4715
4814
5214
5413
5312
5512
5010
5610
589
609
578
598
637
616
686
696
645
655
624
724
744
824
673
703
773
813
712
732
782
802
952
1002
751
761
791
851
861
881
901
911
931
1011
1081
1111
1251
1291
1671