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 Kuo179
Egbert Havinga143
Pekka Neittaanmäki133
Roger Meyer Temam130
Ramalingam Chellappa127
Shlomo Noach (Stephen Ram) Sawilowsky111
Andrew Bernard Whinston109
Willi Jäger101
Alexander Vasil'evich Mikhalëv101
Ronold Wyeth Percival King100
Dimitris John Bertsimas98
Johan Pieter Wibaut97
Erol Gelenbe96
Leonard Salomon Ornstein95
Bart De Moor93
Kurt Mehlhorn93
Rutger Anthony van Santen90
Ludwig Prandtl90
Yurii Alekseevich Mitropolsky88
Rudiger W. Dornbusch85
Wolfgang Karl Härdle85
David Garvin Moursund82
Andrei Nikolayevich Kolmogorov82
Selim Grigorievich Krein82
Olivier Jean Blanchard82

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Abu Mansur al-Hasan ibn Nuh al-Qumri234718
Abu Abdallah Al-Husayn ibn Ibrahim al-Natili234718
Abu Sahl 'Isa ibn Yahya al-Masihi234718
Abu ʿAli al-Husayn (Avicenna) ibn Sina234717
Bahmanyār ibn al-Marzubān234716
Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm al-Khayyām al-Nīsābūrī2347151068
Saraf al-Dīn Muhammad al-Masʿūdī al-Marwazī234714
Sharaf al-Dīn al-Ṭūsī234712
Fakhr al-Dīn Muhammad al-Rēzī234712
Qutb al-Dīn Ibrāhīm al-Mīṣrī2347111222
Kamāl al-Dīn Ibn Yūnus234711
Athīr al-Dīn al-Mufaḍḍal al-Abharī2347101264
Nasir al-Dīn al-Ṭūsī234709
Shams al‐Dīn al‐Bukhārī234706
Gregory Chioniadis2347051296
Manuel Bryennios2347041300
Theodore Metochites2347031315
Gregory Palamas2347001316
Nilos Kabasilas2346991363
Demetrios Kydones234698
Elissaeus Judaeus234673
Georgios Plethon Gemistos2346721380, 1393
Basilios Bessarion2346691436
Giovanni Conversini2346601363
Manuel Chrysoloras234660

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
0244655
133380
212223
37002
44772
53650
62774
72239
81886
91540
101258
111047
12959
13810
14652
15597
16533
17458
18364
19328
20325
22249
21247
23242
24185
25181
26178
28132
27130
29103
30101
3178
3273
3670
3367
3565
3461
3745
3937
3835
4234
4331
4029
4129
4527
4626
4420
5219
4918
5116
5416
5315
4714
4814
5014
5514
5713
5612
6010
589
649
618
728
687
737
596
656
706
635
624
814
824
663
693
713
743
753
803
762
782
792
852
902
932
1012
671
771
881
951
961
971
981
1001
1091
1111
1271
1301
1331
1431
1791