"Lecture" for Week 1
Welcome to Math. 629, History of Mathematics, an Internet course.
Please read the official syllabus handout.
There will be no tests, but there will
be weekly homework assignments and some longer papers. A history course
is not a typical math course; I am confident that we will all find it
strange but enjoyable. There will be more about course procedures
at the end of this message. This week you should familiarize yourself
with this web site, the eCampus system (a tall order -- after a year,
I don't understand most of it), and the TAMU Library site.
(See the links back on the class home page.)
I intend to start every week with a message like this one. A big advantage
of the distance learning setup is that I am not obligated to fill up 150
minutes with talk if I don't have that much to say. Conversely, if I run
on a bit long some week, you won't be late to your next class.
Let me start by declaring some of my prejudices.
- Graduate students -- "distant" ones especially -- should be
largely self-directed. You will sometimes need to interpret and adapt
instructions to your personal situation. A large amount of the assignments
will be labeled "optional" or stated in an open-ended way. No one student
could possibly do all the things suggested. On the other hand, I
don't think that a student who always does just the bare minimum required
should expect a grade of A.
- A Web-based course should include
significant electronic communication among the students, thereby both
taking advantage of the technology and compensating for the lack of
personal contact in a classroom. The precise modalities of this
communication will be made clearer later, as I discover what is feasible.
(I wrote that in 2003, when we used an online system called WebCT.
When I taught the course again in 2006, that had been replaced by
something called Vista,
so I still needed to discover what is feasible. Now that has been
replaced by eCampus, so there is still no need to update the sentence.
Don't hesitate to make suggestions.)
It follows from the previous point (about optional and imprecise
assignments) that not all students will be doing the same things, and I
encourage you to make your productions available for the rest of the class
- Books versus the Web: The WWW has some obvious
advantages: Almost by definition, it is available to every
distance-learning student, whereas not everyone has easy access to equally
good libraries. Search engines make finding information (when it exists)
very easy. Documents can be kept up to date (although this is not always
done) when new information becomes available or mistakes are discovered.
On the other hand, the information available on the Web is still only a
small part of what is available in print. Documents online are hard to
reference properly and even tend to disappear without warning. And since
almost anybody can publish on the Web, without filtering by editors, etc.,
there is a problem of quality control. The reliability quotient is lower
than for archival printed material. Of course, you can't believe
everything you read in a book, either. One should be particularly
skeptical, and diligent to separate fact from opinion, while reading about
such an emotionally and politically charged subject as the early
scientific discoveries of non-Western cultures, the topic of our first
week of readings.
One of the most productive uses of the Web is getting
references to books and journal articles that one can then find in a
library if they are not, themselves, available online.
- The history
of mathematics is more important than the history of mathematicians.
Biography can be interesting and sometimes instructive, but the
development of ideas is central. Writings on the history of mathematics
often tend to lapse into an obsession with "genius" that can be
discouraging to students.
- Recent (e.g., 19th century) mathematics
history is important and interesting, but hard to cover in a historical
survey course because of the higher technical sophistication required to
Stillwell's book is more ambitious than Allen in this regard;
since I haven't completely read it myself yet, I'm eager to see how it
- One of the most important things about mathematics
and its history is the constant interplay between applications and
math-for-its-own-sake, or (something just slightly different) between the
abstract and the concrete. A new mathematical concept almost always arises
because it is needed to solve a particular problem. (The problem could be
one in pure math or one in a practical or scientific application.) Later
(with luck) the concept proves to be useful in a variety of a
far removed from the point of origin. For the first two weeks we
studying applied mathematics, because that is all there was. Later the
focus will shift, but we should always keep the technical developments
framed in the broader scope of ideas and human life.
Very early mathematics
(You might want to read Allen's first and second chapter first.)
What happened before Egypt? It is hard to know precisely about
peoples whose written records were primitive or nonexistent.
Perhaps the closest we can come is to look at isolated tribes that are
still alive today. Here are three recent anthropological research papers,
whose conclusions seem to point in opposite directions:
(You should have no trouble accessing Science -- or any other
journal I cite -- through the TAMU Evans Library portal. However, I do
sometimes have trouble creating direct Web links to the articles.)
- P. Gordon, "Numerical Cognition Without Words: Evidence from
Science 306 (15 October 2004) 496-499.
- P. Pica, C. Lemer, V. Izard, and S. Dehaene,
"Exact and Approximate Arithmetic in an Amazonian Indigene Group,"
Science 306 (15 October 2004) 499-503.
- S. Dehaene, V. Izard, P. Pica, and E. Spelke,
"Core Knowledge of Geometry in an Amazonian Indigene Group,"
Science 311 (20 January 2006) 381-384.
At a less isolated level (and much farther north), we have
"Culturally Negotiated Schooling: Toward a Yup'ik Mathematics,"
Journal of American Indian Education
33 (May 1994) Number 3 .
Clearly we could surf the Web forever, and I don't
expect you to read everything I found interesting. But here are some
optional threads you might like to pursue (maybe springboards to
- I found the Inuit article above while searching for information on
the Maya. Maya math is very
popular in precollege education right now, so there is a lot on the Web.
Type "Maya mathematics" into Google,
browse and enjoy.
(Don't feel obliged to read all 772,000 hits; even the relevant ones
quickly become repetitive.)
If you're in too much of a hurry to play the Web game, here are two good sites
I noted down (in 2003):
St. Andrews. (The second one has a link to a reference
list (things on actual paper!).)
The development of "culturally appropriate" pedagogy
for minority populations is highly controversial.
Although there is a huge difference between an isolated village in Alaska
and a high school in Harlem,
the Inuit article reminded me of this interesting debate:
- Diane Ravitch, "Multiculturalism," American Scholar
59 (Summer 1990) 337-354;
- Molefi Kete Asante and D. Ravitch, "Multiculturalism: An
Exchange," American Scholar
60 (Spring 1991) 267-276.
- Here's another site that was brought to my
Step-by-Step from the Land of the Incas. Great music and pictures.
More about practical matters
Professor Allen's on-line material gives better coverage of early history,
while the book of Stillwell is better on recent centuries.
So, the readings will gradually migrate from the one to the other.
Compared to other books, Stillwell has two unusual features, one of which
is just a practical complication for us while the other is more substantive.
- Most books, including Allen's and the one by Katz used in 2006,
are chronologically organized until they reach fairly modern times,
whereas Stillwell starts organizing by field or topic earlier. So, the
readings won't always be in synch.
I'm advising you to start reading Stillwell's chapters on Greece as soon as
you get the book, so that the Greek weeks (3 and 4) won't be overloaded.
- As the title of the book suggests and the preface says,
Stillwell's intention is "to
give a unified view of undergraduate mathematics by approaching the
subject through its history.... Mathematics is the main goal and history
only the means of approaching it."
This, I hope, somewhat alleviates the temptation to elevate biography
or dull facts over mathematical ideas.
It also follows, however, that the treatment of history is rather
selective (many topics and events are left out) and
I didn't like Katz as a textbook for this course, but if you want
to get a book on mathematical history for future reference,
Katz is an excellent one.
Here are some others.
If you haven't done so already, explore our class page at
There are 2 facilities installed so far:
- Gradebook (empty so far).
- Discussion forums. So far I have created 3, one for the short bios
and ones for discussion of the material of the first 2 weeks. Let's try
to keep them organized; that is, please exercise some judgment about
whether to post a message as a new one or a reply to a related old one.
- Please don't use the e-mail feature inside
eCampus to send me mail. Use my regular e-mail address.
How to submit written assignments
Timing and placement
- Contributions for general consumption (such as your little
autobiography) should be posted in the eCampus
Discussions right away.
- Weekly homework
and major papers (book review, etc.) should be sent to
privately. (Starting with Week 2, the weekly homework should also go to the
grader. Homework is due by
Monday noon of the week following the week concerned.)
Do not post them in eCampus before the due date.
On or after the due date they may be posted; should they be?
Probably other students are not interested in your routine
homework papers, but the book reviews will be of general
Communicating mathematical symbolism electronically is a
scandalous headache. Different students will have different
software and expertise available, so I do not aspire to impose
- Paper mail and Fax should be avoided unless necessary.
Occasionally you may need to send a hand-written diagram or (less
likely in this course) a long hand-written calculation.
- E-mail attachments will probably be the most common
mode, whether you are mailing things to me or installing them in eCampus
(Here is some
information on how to do that.
It refers to Wikis, but I think they work the same as Discussions.)
Various formats are possible.
I am very much a TEX partisan, but I understand that
many students will need to use something like Microsoft Word.
- I've been advised that a good method is to use Word or some
other word processor with an equation editor, and to export the
file in .rtf format (more portable than .doc or whatever the
processor's proprietary format is).
- If you can produce a .pdf file, that is probably the most
widely readable, apart from HTML.
- You can make an HTML file. The mathematical typesetting
available within HTML is primitive but often adequate (note the
subscript on "TeX" above). There are editors that make the
process easier (but I am largely ignorant of them).
- Sometimes (especially in informal e-mail) it is enough to
write plain ASCII text with the mathematics in
- For various reasons, it may sometimes be better to install
your paper on a personal Web page and e-mail the URL to me (and,
when appropriate, the class).