Comments on: Tremellius and Naibod

By: Jonathan Vos Post

Jonathan Vos Post — Sat, 13 Sep 2008 19:07:10 +0000

There are other ways to interpret the teacher-student and mentor-mentee relationships.

http://www.magicdragon.com/JVPteachers.html

Although I am something of an autodidact, I have had some significant teachers. When I began to trace whom the teachers were of my teachers, and who were their teachers before them, quite a number of prominent names emerge. Albert Einstein, Ezra Pound, Bertrand Russell…

Going back to the 1600s in Mathematics, the coinventor of Calculus
(simultaneously with Newton) Gottfried Wilhelm Leibnitz. In Astronomy, I can trace back to about 1600, with Christiaan Huygens, who discovered the Rings of Saturn, and his mentor, Descartes. Further back, to the 1400s, come the revolutionary anatomists: Vesalius and Fallopius. Then, more than 24 generations before me, the Islamic medicine faculty at the University of Montpellier. Quite a journey in time and imagination!

Almost all the links shown are formal student-teacher connections in colleges, universities, or master classes/tutorials…

Below, I give a very partial diagramming of my heritage in these domains:
Music, Poetry, Science/Philosophy, Science/Physics, Computers and Mathematics, and Acting/Theatre. Coming soon: Fiction, Karate, Politics, Business….

By: Anonymous II

Anonymous II — Fri, 12 Sep 2008 19:06:51 +0000

John Armstrong: I think the change was gradual. I know for a fact that in early nineteenth century Holland the profs did only teaching; they did not do any research at all. Over the course of 19th century research labs become available
Actually, the University of Leiden opened a “theatrum physicum”
theatrum physicum as early as 1675, but that was only used for demonstrations; students weren’t allowed to touch the equipment! By the early 19th century the “theatrum physicum” had fallen in disrepair, and in 1861 a new physics lab was built. I guess that at first the new lab was mostly used for lab courses and demonstrations, but at least this provided an opportunity for original research.
In the Netherlands the sciences didn’t really take off until 1863, when a new type of highschool was introduced. Prior to that there was only the traditional highschool, which emphasized languages and eloquence; very little science classes, if any at all. The new type highschool however did away with Greek and Latin, and emphasized math and physics instead. From there on there is a remarkable growth in the sciences.

By: John Armstrong

John Armstrong — Fri, 12 Sep 2008 18:28:02 +0000

AnonII: interesting about when math/physics were elevated. But how did the style change?

You indicated that doctoral degrees used to be granted mostly on the basis of (advanced) regurgitation rather than creatively pushing the boundaries. Clearly it’s not like that now, at least not in math and physics.

By: Anonymous II

Anonymous II — Fri, 12 Sep 2008 16:31:17 +0000

John Armstrong: The development of advanced degrees in math and sciences was stimulated by the Industrtial Revolution. Engineering schools were opened, and there was a need for teachers with an advanced degree in math and physics. In the Netherlands math and physics were elevated to the same level as Theology, Law, and Medicine in 1877. So degrees earned after 1877 would be proper Ph.D.’s; but degrees earned before 1877 would be the equivalent of a Master’s degree.
In practice I suspect that improvement in academic standards was a gradual process as more job opportunities for scientists and engineers opened up.
That said, even before 1877 there was a teacher/pupil relationship, even though the degrees were only on master’s degree level.
AnonI: If you have concerns about specific entries in the Math Geneology I would encourage you to submit appropriate updates. But the entry in MGP can never replace a proper biography, which should have specific information on a person’s education. When available, MGP provides a link to the MacTutor biography; if not Wikipedia may have one.

By: Peter

Peter — Fri, 12 Sep 2008 08:36:24 +0000

Anonymous II writes: “Basically, the primary goal of higher education was to further discussion skills; furthering science was not part of it.”

Since the over-riding goal of higher education from the founding of European universities from 1200 AD to about 1800 was the training of priests and advocates/lawyers, a focus on discussion and verbal skills rather than on writing skills or research was entirely appropriate. It is easy to forget that the dominance which our modern, western culture gives to text is historically and geographically peculiar: most societies historically have, and most societies currently still do, privilege the spoken over the written word; only we do not.

By: Anonymous I

Anonymous I — Thu, 11 Sep 2008 16:26:39 +0000

That’s exactly what bothers me: once you go far enough back, most mathematicians just don’t have anyone who could fairly be described as an “advisor”, but the math genealogy site insists on assigning each of them one or two advisors, based on unexplained criteria that apparently vary from person to person. Even in more modern times, there are issues. For example, neither Hardy nor Littlewood ever received a Ph.D. (such degrees weren’t offered in Great Britain until after they were students). Littlewood’s advisor is listed as Barnes, which seems like a fair choice even if he wasn’t an official advisor, since Barnes was the person who introduced Littlewood to research (and suggested proving the Riemann hypothesis!). Hardy’s advisors are listed as Love and Whittaker, and I have no idea where these names came from. Maybe they are reasonable, but no explanation is given. Furthermore, Whittaker is listed as having received a Ph.D. from Cambridge in 1895, which is not only false but I believe impossible (in the sense that nobody ever received a Ph.D. from Cambridge in the 1800’s). According to Wikipedia, 1895 is the year Whittaker took the Tripos. In any case, entries like this don’t inspire confidence.

So what bothers me is that the site leads people to believe that there is a simple, unambiguous notion of an “advisor” and that this information has been reliably tabulated. For recent years I’m sure that’s true, but farther back in the past it just isn’t.

By: John Armstrong

John Armstrong — Thu, 11 Sep 2008 13:33:55 +0000

AnonII should be more proud of his words and sign them — he’s managed to say something nontrivial, and about something that’s not even quadrivial!

So, Anonymous II, I’m curious: when/how did the nature of an advanced degree evolve into what we know today?

By: Anonymous II

Anonymous II — Thu, 11 Sep 2008 13:17:12 +0000

Anonymous: Advanced degrees in mathematics (and the sciences in general) only exist since the mid-19th century. Before that there were only advanced degrees in Theology, Law, and Medicine. Math was part of the "liberal arts", taught at the undergraduate level. Also, the requirements for an advanced degree were entirely different from present day standards; it didn't involve original research at all. What was involved were exams, in which the candidate was examined on his knowledge of the classics. E.g. for a degree in medicine you were required to regurgitate what Galen, Hippocrates, and Celsus had written 1500 years earlier. Once you passed those exams you had to write and defend a dissertatio. Basically, a dissertatio was a response of the candidate to one or more theses. A thesis was what we would call an hypothesis, a single sentence expressing a point of view on a certain subject. Those theses were often written by the professors, but sometimes by other students. The candidate had to submit a response to those theses, expressing his opinion about it. It didn't involve any original research at all, all it did is discuss what other had written about the subject, and was typically no more than 10 or 20 pages. Then there would be a public discussion on the subject, in which everybody who felt like it could particitate: not only professors, but also other students, and other spectators. Basically, the primary goal of higher education was to further discussion skills; furthering science was not part of it.

By: Jonathan Vos Post

Jonathan Vos Post — Thu, 11 Sep 2008 06:03:51 +0000

There are non-human animals with Erdos numbers, including at least 1 horse and 2 dogs, but that’s a different social network than the Geneology project.

The Devil’s in the details. The Bible seems to indicate that, going all the way back, God was Satan’s mentor and advisor. Both of them were clearly Mathematicians. It suggests that Satan was subsequently demoted to an office on a lower floor, did considerable field research, and lacks the research publications under his own name. However, Satan has a large and growing number of research assistants accumulating on site, some of whom had considerable clout as professors, deans, provosts, university presidents, and a disproportionate number of Business School and Law School graduates. I tried to check this with an avowed expert on the public policy implications, but she was busy studying for her VP slot.

By: Anonymous

Anonymous — Thu, 11 Sep 2008 05:28:57 +0000

Am I the only one who is driven crazy by the extrema in the math genealogy site? As far as I can tell, all sufficiently old data on the site is pretty much gibberish, with mentors or teachers or even older colleagues being designated as “advisors” in a totally ad hoc and unprincipled way. I find this particularly irritating since most mathematicians are not terribly historically oriented: as a general rule, we feel happy to tell stories that, at best, represent the way things should have happened. My fear is that the math genealogy “advisors” will become part of popular math history, and that this will obscure what actually happened for those who care.

I wish they would at least distinguish clearly between proper advisors and other mentors. The notion of a “proper advisor” isn’t well defined, I guess, but it should roughly mean the following. The advisee wrote a dissertation on original research, for which he/she received a higher academic degree than the typical first university degree, and the university considered the advisor to be the advisee’s official supervisor during the research and writing process.