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
Alexander Vasil'evich Mikhalëv101
Willi Jäger101
Ronold Wyeth Percival King100
Dimitris John Bertsimas98
Johan Pieter Wibaut97
Erol Gelenbe96
Leonard Salomon Ornstein95
Bart De Moor93
Kurt Mehlhorn93
Ludwig Prandtl90
Rutger Anthony van Santen90
Yurii Alekseevich Mitropolsky88
Wolfgang Karl Härdle85
Rudiger W. Dornbusch85
Andrei Nikolayevich Kolmogorov82
David Garvin Moursund82
Olivier Jean Blanchard82
Selim Grigorievich Krein82

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Abu Sahl 'Isa ibn Yahya al-Masihi234822
Abu Mansur al-Hasan ibn Nuh al-Qumri234822
Abu Abdallah Al-Husayn ibn Ibrahim al-Natili234822
Abu ʿAli al-Husayn (Avicenna) ibn Sina234821
Bahmanyār ibn al-Marzubān234820
Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm al-Khayyām al-Nīsābūrī2348191068
Saraf al-Dīn Muhammad al-Masʿūdī al-Marwazī234818
Fakhr al-Dīn Muhammad al-Rēzī234816
Sharaf al-Dīn al-Ṭūsī234816
Qutb al-Dīn Ibrāhīm al-Mīṣrī2348151222
Kamāl al-Dīn Ibn Yūnus234815
Athīr al-Dīn al-Mufaḍḍal al-Abharī2348141264
Nasir al-Dīn al-Ṭūsī234813
Shams al‐Dīn al‐Bukhārī234810
Gregory Chioniadis2348091296
Manuel Bryennios2348081300
Theodore Metochites2348071315
Gregory Palamas2348041316
Nilos Kabasilas2348031363
Demetrios Kydones234802
Elissaeus Judaeus234777
Georgios Plethon Gemistos2347761380, 1393
Basilios Bessarion2347731436
Manuel Chrysoloras234764
Giovanni Conversini2347641363

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
0244761
133389
212230
37010
44774
53647
62774
72239
81890
91542
101257
111048
12960
13810
14649
15601
16531
17459
18366
20328
19325
22250
21248
23241
24185
25181
26178
28133
27129
29104
30101
3178
3273
3670
3367
3566
3460
3745
3937
3835
4234
4331
4029
4129
4527
4626
4420
4919
5219
5116
5416
5315
4714
5014
4813
5513
5612
5712
5810
6010
649
618
728
687
737
596
656
706
635
624
814
824
663
693
713
743
753
793
803
762
782
852
902
932
1012
671
771
881
951
961
971
981
1001
1091
1111
1271
1301
1331
1431
1791