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 Kuo169
Roger Meyer Temam130
Pekka Neittaanmäki126
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
Wolfgang Karl Härdle82
Stefan Jähnichen81
Sergio Albeverio81
Richard J. Eden80
Bruce Ramon Vogeli80

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Abu ʿAli al-Husayn (Avicenna) ibn Sina211772
Bahmanyār ibn al-Marzubān211771
Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm al-Khayyām al-Nīsābūrī2117701068
Saraf al-Dīn Muhammad al-Masʿūdī al-Marwazī211769
Sharaf al-Dīn al-Ṭūsī211767
Fakhr al-Dīn Muhammad al-Rēzī211767
Qutb al-Dīn Ibrāhīm al-Mīṣrī2117661222
Kamāl al-Dīn Ibn Yūnus211766
Athīr al-Dīn al-Mufaḍḍal al-Abharī2117651264
Nasir al-Dīn al-Ṭūsī211764
Shams al‐Dīn al‐Bukhārī211761
Gregory Chioniadis2117601296
Manuel Bryennios2117591300
Theodore Metochites2117581315
Gregory Palamas2117551316
Nilos Kabasilas2117541363
Demetrios Kydones211753
Elissaeus Judaeus211728
Georgios Plethon Gemistos2117271380, 1393
Basilios Bessarion2117241436
Giovanni Conversini211715
Manuel Chrysoloras211715
Guarino da Verona2117141408
Gasparino da Barzizza211714
Vittorino da Feltre2117131416

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
0224273
130750
211242
36367
44514
53338
62574
72128
81650
91419
101129
11951
12881
13721
14604
15537
16469
17406
18335
19302
20269
22237
21232
23188
24169
25166
26131
28119
27117
29100
3080
3169
3257
3457
3356
3651
3550
3736
3935
3830
4126
4226
4025
4325
4422
4521
4920
4619
5217
5116
5014
5313
5413
4812
4711
5611
5510
5710
6010
588
597
617
636
646
686
655
695
725
745
825
624
704
733
783
672
712
772
802
812
952
1002
751
761
791
851
861
881
901
911
931
1011
1081
1111
1261
1301
1691