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 Kuo161
Roger Meyer Temam125
Pekka Neittaanmäki121
Shlomo Noach (Stephen Ram) Sawilowsky110
Andrew Bernard Whinston108
Alexander Vasil'evich Mikhalëv101
Willi Jäger100
Ronold Wyeth Percival King100
Erol Gelenbe95
Leonard Salomon Ornstein95
Ludwig Prandtl90
Kurt Mehlhorn90
Yurii Alekseevich Mitropolsky88
Rudiger W. Dornbusch85
Bart De Moor83
Olivier Jean Blanchard82
David Garvin Moursund82
Andrei Nikolayevich Kolmogorov82
Selim Grigorievich Krein82
Stefan Jähnichen81
Dimitris John Bertsimas81
Richard J. Eden80
Bruce Ramon Vogeli80
Sergio Albeverio80
Arnold Zellner79

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Sharaf al-Dīn al-Ṭūsī189825
Kamāl al-Dīn Ibn Yūnus189824
Nasir al-Dīn al-Ṭūsī189823
Shams al‐Dīn al‐Bukhārī189822
Gregory Chioniadis1898211296
Manuel Bryennios189820
Theodore Metochites1898191315
Gregory Palamas189817
Nilos Kabasilas1898161363
Demetrios Kydones189815
Elissaeus Judaeus189792
Georgios Plethon Gemistos1897911380, 1393
Basilios Bessarion1897881436
Manuel Chrysoloras189761
Guarino da Verona1897601408
Vittorino da Feltre1897591416
Theodoros Gazes1897551433
Johannes Argyropoulos1897371444
Jan Standonck1897331474
Jan Standonck1897331490
Marsilio Ficino1897061462
Cristoforo Landino189706
Angelo Poliziano1897051477
Scipione Fortiguerra1897031493
Moses Perez189703

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
0205866
128471
210219
35849
44081
53119
62364
71872
81503
91249
101021
11870
12787
13648
14560
15467
16410
17376
18315
19257
20239
22208
21202
23169
24144
25138
26111
27106
28103
2998
3075
3158
3455
3253
3350
3542
3636
3734
3932
4329
3828
4227
4026
4122
5218
4417
4616
4916
4515
4813
4712
5012
5312
5412
5111
5611
5510
579
589
609
617
687
635
645
695
624
654
724
824
593
733
763
803
672
702
752
772
812
902
952
1002
711
741
781
791
831
851
881
1011
1081
1101
1211
1251
1611