Evaluating the Quality of History of Mathematics Web Pages

The World Wide Web is fast becoming a standard research tool for use in class. It is especially useful in courses dealing with the history of mathematics, for you can quickly find information about a great number of individuals and topics. The questions, however, is: How reliable is the information on the WWW? Our purpose here is to instill a healthy skepticism in your mind about what you read on the web.

How do you evaluate what you read on the web? I suggest that you be very skeptical of everything you read there. The purposes of these exercises is to take a look at a few pages that contain errors and to recognize them. Hopefully this will help you develop the skills to recognize errors elsewhere. Let me be bold and make a

Big Claim: The ability to critically judge what you hear and read is a necessary skill in a democratic society.

Your responses to the following questions should be posted to our class email list. Please identify the message you are referring to by URL (Universal Resource Locator) and give the name of the author and date posted so that we can all easily look at the messages you are talking about. Be sure to explain what errors you think the web pages contain as well as your reasons for your views. The aim of this set of exercises is to spark discussion of some of the problems that you will encounter when using the internet to do historical research.

Exercise 1

Look at the web page on Leonhard Euler. Now this was written by a student in the fourth grade, so you would not expect great insight. What errors do you find?
  1. What language is "Swiss"? What languages did Euler read? Speak? How do we know?
  2. Did Euler lose his sight at "an early age"? What age was he?
  3. Where do you think Omar got the idea for Euler's fancy head-gear in his picture?
  4. Can you verify that Euler wrote "I die" on his slate just before he died?
  5. Can you verify that Euler was called the "Beethoven of Mathematics"?
  6. Look at other pages in The Moldy Oldies Collection and see if you can find other errors. Report them on our class email list. You may wish to compare these with the "Your Mathematician" biographies that were posted to our class list.
  7. Note the teacher's proviso: "A lot of what we found was hard to understand because it was written by adults for adults." If you were assigning a similar exercise for high school students, which mathematics of Euler do you think that they could understand, appreciate, and write about?
Nota bene:Omar deserves high praise for doing this internet assignment, and his fourth grade teacher, Kathy Heller, deserves even more for posing such an interesting assignment. I don't, by any means, want to belittle what they have done. I think the pages are really neat! They are being used here as a vehicle for us to learn from.

Exercise 2

Look at the page on William Fogg Osgood at the St. Andrew's web site. Is it really true that Felix Klein lectured at Harvard in 1885-87? Check out the Dictionary of Scientific Biography and see what it says on this issue.

Exercise 3

Did you know that the catenary had an asymptote? What do you think caused this error?

Exercise 4

There is an email list on the history of mathematics called math-history-list. The archive of this list is available. Take a look the postings for August 1997 and see what you can learn.
  1. Are there postings that you find particularly interesting and informative?
  2. Postings that are quite scholarly?
  3. Are there postings which are not well thought out?
  4. Are there postings that are "off-topic," i.e., that have nothing to do with the history of mathematics?
  5. Do you find instances of inappropriate behavior on the part of the poster?
  6. Are there postings by "cranks" or "nuts"?

Exercise 5

Mail groups can be notorious for the postings that appear. Flame wars erupt periodically and the participants frequently return to the same old issues. This is definitely true for sci.math which attracts many individuals with a casual interest in mathematics.

Let's consider just one theme of Archimedes Plutonium, Euclid's proof that there are infinitely many primes. Here are a few of his postings on the topic:

  1. Was Euclid's IP really reductio ad absurdum. I suspect not by Archimedes Plutonium
  2. V.War:Manin & Panchishkin fail to give a valid proof of Euclid Infinitude of Primes by Archimedes Plutonium.
  3. Euclid's Infinitude of Primes proof, Corrected; part 1 of 3.
After reading a few of these, many questions present themselves. Here are a few. I encourage you to ask others
  1. Is Archimedes Plutonium a real person? What can you find out about him? Remember one of the best ways to judge web pages is to know (or find out) something about the author and his reputation.
  2. Does Euclid provide an indirect proof of Proposition 1X.20 or a direct proof?
  3. Do modern textbooks state and prove the theorem the same way Euclid did?
  4. What do you think of this author after reading his postings?

Exercise 6

Now that I have pointed you to a few inaccurate web pages, it is time for you to do some browsing on your own and to find some pages that you think are wrong (don't take things off the mail groups; that's too easy). In each case you should give the URL, indicate the error, and state your reasons and source for concluding that you found an error. Hopefully we can generate a nice discussion about this.

After posting the above exercises, I told a few historians about them. They suggested the following:

Exercise 7

There are some new results from Euclid that we ought to take a look at. What do you think?

There is a meeting of the American Mathematical Society in Manhattan, Kansas, on March 27-28. One session is Saturday morning the other is Saturday afternoon. The sessions have been arranged by Prof. Andrew G. Bennett of Kansas State

At that meeting I will be speaking about quality on the internet. Here is the title of my presentation and the abstract:

Student Evaluation of the Quality of History of Mathematics Web Pages.

The World Wide Web is a valuable resource for students in history of mathematics courses. The various ways of using the internet and the web will be briefly described, with attention to the most serious problem that faces the instructor: How do you teach students to make judgments about the quality of the information that they find on the web? My attempt at a solution is to have students look at web sites which contain errors (Did Euler speak "Swiss," did Felix Klein really lecture at Harvard in 1885-87, and does the catenary really have an asymptote?) and to then use other sources to correct the errors. The key is to introduce a sense of skepticism about whatever they read. The exercises for the students are available at http://www.bgsu.edu/~vrickey/math311/web-quality.html

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If you have comments, send email to rickey@math.bgsu.edu
The URL of this page is http://www.bgsu.edu/~vrickey/math311/web-quality.html
Posted 2 February 1998. Revised 15 February 1998.