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 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
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 Sina211676
Bahmanyār ibn al-Marzubān211675
Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm al-Khayyām al-Nīsābūrī2116741068
Saraf al-Dīn Muhammad al-Masʿūdī al-Marwazī211673
Sharaf al-Dīn al-Ṭūsī211671
Fakhr al-Dīn Muhammad al-Rēzī211671
Kamāl al-Dīn Ibn Yūnus211670
Qutb al-Dīn Ibrāhīm al-Mīṣrī2116701222
Athīr al-Dīn al-Mufaḍḍal al-Abharī2116691264
Nasir al-Dīn al-Ṭūsī211668
Shams al‐Dīn al‐Bukhārī211665
Gregory Chioniadis2116641296
Manuel Bryennios2116631300
Theodore Metochites2116621315
Gregory Palamas2116591316
Nilos Kabasilas2116581363
Demetrios Kydones211657
Elissaeus Judaeus211632
Georgios Plethon Gemistos2116311380, 1393
Basilios Bessarion2116281436
Giovanni Conversini211619
Manuel Chrysoloras211619
Gasparino da Barzizza211618
Guarino da Verona2116181408
Vittorino da Feltre2116171416

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
0224198
130742
211227
36368
44512
53337
62577
72122
81650
91418
101129
11952
12878
13723
14604
15534
16469
17410
18331
19303
20270
22236
21232
23187
24169
25166
26130
28119
27117
29102
3078
3169
3257
3457
3356
3651
3550
3736
3935
3830
4126
4226
4025
4325
4423
4520
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
1251
1301
1691