Occasionally I am asked how I became interested in the history of mathematics. Since this has some impact on my views about history of mathematics textbooks, let me relate the story. As a freshman at Notre Dame, I took a one-hour course in number theory and set theory for math majors that was taught by R. Catesby Taliaferro. One day, after he had presented a proof that the set of points on the line was equinumerous with the set of points in the plane, a student pointed out a flaw in the proof. Dr. Taliaferro was stunned. This is Cantor's proof he said. That left a lasting impact on me: he cared enough about our education to go back to the original sources and to present them in class. Two years later, when I began taking logic courses from Boleslaw Sobocinski (1906-1980), who eventually became my thesis advisor, I learned that there was a tradition in Poland of telling the history of problems. Thus history in the classroom was part of my education, and, without consciously realizing it at the time, I appreciated its value.
In the fall of 1968 when I was a new PhD and faculty member, Carl Boyer's brand new History of Mathematics was one of the selections for the Library of Science book club. I bought a copy and used it for bedtime reading. Then, without much thinking about it, I started to relate bits of history in all of my classes. Apparently, I did more of this than I realized, and with some success, for in the fall of 1970 several of my students approached me and asked if I would teach a course in the history of mathematics. Being young and naive, I agreed. [My advice to you should you be asked to do likewise is to refuse -- it is too much work.]
Realizing that I really did not know much about the history of mathematics, I started a systematic reading program. I obtained a copy of Eves and read it too, along with much else. But it was a hopeless task. There was no way that in a couple of months that I could obtain a systematic enough knowledge of the history of mathematics to present a reasonable course. I still have some of my class notes from that course, and it is embarrassing how poorly I was prepared and how little I knew. Thus from my own experience, I can offer my best piece of
Advice: Start reading now!When choosing a textbook that first time, I was fully aware that Boyer was a better textbook. It is rich with detail and written in an excellent style. But I was concerned that it would be too hard for my students to read. So I chose Eves. I briefly considered Struik's Concise History of Mathematics, but realized that while it is an excellent history which does a wonderful job with setting the social scene, it demanded that the reader know far more mathematics than my students would.
Let me indicate why I chose Eves as a textbook: I considered my students. Almost all of them were prospective secondary school teachers. Thus I believed (and still do) that they needed to know about the history of the subjects that they would teach: algebra, geometry, trigonometry, and perhaps calculus. Once this was realized, I knew that a survey of the history of mathematics up to about 1700 was what was needed. I did discuss some topics after then, but not much.
The high point of the Eves text (and this is mentioned in a review by Phillip Jones of the first edition) is its problems. But I have never been very successful in using them. On occasion, I have had the students do a problem from each chapter of their choosing. Most of them chose the most mundane problems. My idea was that they would read all of the problems, for there is much of interest in them, and then pick one that really interested them.
A weak point ─ although others may consider it a strong point ─ of the book is that Eves is fascinated by geometry and so the book has a heavy emphasis on geometry. This is not necessarily bad, for my students definitely had a weak background in geometry, and so this helped them. Later I came to realize that the book had other faults. It is based primarily on secondary sources and these are not always the best or most up to date. The historical sense of the book is not as strong as it could be.
But Eves turned out to be a very satisfactory textbook. I definitely made the right choice for a first time teacher of the course who was not too experienced. I still feel that I made the right choice back then, and recommend that any first time teacher of the course seriously consider the text of Eves.
In 1983-84 I was on sabbatical at the University of Vermont where I was asked to teach their history of mathematics course. I took this as an opportunity to use the Boyer book. While I had read all of it several times, I don't know that I had ever read it straight through, so I was anxious to do this. Another reason for my choice was that I expected the Vermont students to be better than the Bowling Green students.
Boyer turned out to be a good choice. The students liked the book and there were certainly no complaints about its readability. Perhaps this was because I was a visitor, but when I returned to Bowling Green, I used the book here and again readability turned out to be no difficulty. It really is an excellent book. When you look at it there is not much symbolism so you may thing there is not much mathematics in it, but actually it is really packed with information.
I was scheduled to teach history of mathematics in the spring of 1995 and had decided that I would do the course in a different way. It was not so much that I was dissatisfied with a survey course using the Boyer/Merzbach text, but that I just felt it was time to do something different. I have long realized that if the students are to encounter an interesting course the teacher has to be excited and interested. I considered using Bill Dunham's Journey Through Genius, and had decided to use it as a text for a topics course in the history of mathematics, but then the National Science Foundation funded an Institute in the History of Mathematics and Its Use in Teaching. Since Victor Katz was the co-Project Director for this Institute and since he has just published his survey text A History of Mathematics, I knew that I should use it as it would be a frequent item of conversation at the Institute.
I decided that I would use the Katz book in a naive way. Some of the Institute participants would not have had too much experience in teaching the history of mathematics and many would be inclined to use the book of Katz. So I decided to use it the way a neophyte might. I plowed straight through, not omitting any sections, and hoping that I would get up to at least the seventeenth-century. Well I did that, but it was tough going. The text was difficult for my students.
But do not misunderstand me. The Katz text is super! It is by far the best of the books available for a survey course. The material is based on a thorough knowledge of the best of the research literature in the history of mathematics and a broad knowledge of primary sources. But such erudition makes for a difficult book, no matter how well written it is. [Victor is a good friend, but, I hope, I make this assessment of his text independent of that.]
Without doubt I will use the Katz book again in the future. Indeed I look forward to it. But I will use it differently. I will pick and choose from the wealth of material that is there. Some sections I will omit entirely (some of those dealing with Apollonius come to mind) and I will find a way to move more quickly through the text so that more can be discussed about modern mathematics.
I am scheduled to teach history of mathematics in the spring of 1997 and I have decided to do a course where the reading of original sources plays an essential role. The reason for this is that so many of the Institute participants chose to base their courses on the use of original sources. I wanted to know for myself how such a course would go. Before the Institute I was aware of the absolute importance of teachers reading some original sources, for I knew from personal experience that it provided a depth of knowledge of the history that is not attainable in any other way. But always before, I was concerned that it would prove to be too difficult for my students. Were it a second course, or a course for graduate students, that would be entirely different; of course, I would use original sources.
There were two books that I considered:
The only one of these four books that I have not used as a textbook is that of Burton, although I have a well read copy of each edition. It is not so much that I have rejected it, but that I have always had a text that I have been satisfied with. I do know people who have used the Burton book with great success. I think it quite a suitable for an instructor that does not have a lot of background. I believe my students could read it. However, I will admit the reviews of the book that I know of have not been particularly positive.
There is no doubt that my teaching has benefited from using all of these books. From the first time I taught a history of mathematics course in 1971, I have had several of these books, and many more, constantly on my desk. It is imperative that the conscientious teacher draw on a wide selection of the many works available, be they textbooks, research papers and monographs, or original sources. Our students deserve no less of us.
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Posted 2 December 1996. Last revision July 2005.