## PREFACEMany who were growing up in America during the period from 1928 to 1942 will recall the extreme pleasure they experienced when they tuned in their radios to the NBC "Music Appreciation Hour." During those fourteen years an estimated five million school children and a large unknown number of just plain devotees listened each week to the beautifully modulated and hypnotic voice of Walter Damrosch, eminent musicologist and master popularizer of good music. Week after week the listeners auricularly drank in the "great moments in music," and, ever after, their lives were enriched by knowing something of the noble accomplishments of the world's famous composers. Some years later, while serving in the Mathematics Department of Oregon State College, it occurred to me that what Walter Damrosch so magnificently did for music could perhaps also be done for mathematics. Why not, I thought, develop a set of lectures devoted to the enthralling GREAT MOMENTS IN MATHEMATICS? I reacted to the idea with enthusiasm. I would aim the lectures, I decided, at a more specific audience than that chosen by Walter Damrosch - I had in mind, of course, a college and college-community audience. My major hope was to reach, without any great mathematical demands, anyone interested in learning something about the outstanding achievements in mathematics over the ages. The whole thing was to be an intellectual adventure, with no truly prohibiting or frightening prerequisites. And yet at the same time I also wanted to give something that would challenge a good mathematics student and perhaps be of use to teachers of mathematics. The somewhat conflicting aims of the lecture series were finally met as follows. A lecture sequence of some sixty chronologically ordered GREAT MOMENTS IN MATHEMATICS was designed, along with ample problem material, sometimes in the form of "junior" research, bearing on the subject matter of the lectures. The lectures, each fifty minutes long, and enough of them to carry through two semesters, were to be offered at two meetings each week, and the associated problem material was to be discussed at a third weekly meeting. The two-meeting sequence was to constitute an appreciation course, open to auditors and to seekers of a total of four elective college credits; for the first semester (which is covered in the present volume) an acquaintance with high school mathematics was the only prerequisite. The three-meeting sequence was to constitute a mathematics course, open to qualified students and teachers seeking a total of six college credits in mathematics; somewhat stiffer mathematical demands-say, mathematics through beginning calculus-were made of those registering for the extended sequence. Upon being invited by the Publication Committee for the Doiciani Mathematical Expositions to write up the GREAT MOMENTS IN MATHEMATICS lecture series, I decided, because of space problems, to attempt a curtailed version. Only forty of the lectures were selected, the first twenty from the period before 1650, and the remaining twenty from the period after 1650. Herewith are the first twenty. Each selected lecture has been mercilessly pared down, inasmuch as a transcript of a complete fifty-minute lecture would run into far too many pages. Thus, almost all of the humor and anecdotal material so fitting in an oral presentation, as well as many of the cultural ramifications and side trails, and, of course, all the visual props in the form of models, displays, maps, portraits, and overhead-projector material, are omitted. Consider, for example, LECTURIE 9 of the curtailed series, devoted to Archimedes and his method of equilibrium. Recently, at an oral presentation of this lecture, I had at the lecture desk a reproduction of an ancient Greek sand tray, a specimen of a palimpsest, an attractively boxed loculus Archimedius, a small demonstration model of an Archimedean screw, a large calibrated circular cylinder with a heavy removable inscribed sphere, working models of the three classes of levers for comparing their mechanical advantages, and a compound pulley attached to a heavy weight, which was almost effortlessly moved every now and then during the lecture. I showed, on an overhead projector, transparencies of the three questionable medallion portraits of Archimedes, a picture of the interesting mosaic portraying Archimedes' last moments now residing in the Municipal Art Institute at Frankfurt am Main, a portrait of Heiberg, a picture of a sculptured bust of Marcellus, and a map of ancient Syracuse. To lighten the oral presentation I introduced bits of humor-bits which might appear somewhat ridiculous if reproduced here in print. But, as I learned years ago at Harvard from my mentor Julian Lowell Coolidge, a touch of clownery can have a place in an oral presentation. The mathematical demonstration in the lecture, which appears so terse and stark in the written version, was carefully, slowly, and meticulously performed at a blackboard, so that the audience could almost see the elements of volume being slid to their appropriate positions along the balance bar. And, along with all the shortcuts and omissions, the lyrical and poetical flights of an oral presentation are also missing in the written version. What has been said Of LECTURE 9 can also be said-sometimes, it is true, not so fully-of each of the other lectures of the series. So, here, with sincere apologies, are cruelly condensed versions of some of the lectures on the GREAT MOMENTS IN MATHEMATICS. It could be that the only proper way to preserve the lectures would be on videotape, or, better, on educational TV, delivered by a gifted lecturer and with all the props and marvels possible with such a presentation. A few closing words are perhaps in order. The selection of the GREAT MOMENTS is, of course, my own, and could well differ from a selection made by someone else. Some of the GREAT MOMENTS can be precisely pinpointed in the time strip-others only vaguely. It must also be remembered that a HOWARD EVES
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