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Electronic Communication who would like to be part of this com- twice in his book, all known manu- Isolates Some Mathematicians munity but simply cannot afford the scripts before the advent of printing I turned recently to the pages of your hardware and software now required. differed from one another, often in Notices in order to seek information In the old days all that was required hundreds of places. A few changed concerning the forthcoming Interna- were a few rupees or pesos for letters are quite enough to destroy tional Congress of Mathematicians in stamps, a post office in the neigh- his “codes” and those of Rips. Berlin. I have previously attended two borhood, and a friendly and recep- In a similar vein, his “prediction” of tive Hardy at the other end. Are those the comet collision with Jupiter was such Congresses, but I now find that days definitely gone? made months after it had been an- because I have not kept up with the nounced by astronomers. Even then he technology, I may never be able to at- Bernardo Recamán Santos got the date in the Jewish calendar tend another. Indeed, as an indepen- Bogotá, Colombia wrong due to not knowing that the dent mathematician, I am not con- Jewish day ends at sunset. (However, nected to the Internet and still rely (Received September 29, 1997) the Hebrew translation of War and mostly on the post to keep in touch. Peace gives the right date.) But, alas, nowhere in the information Editor’s Note: Dr. Recamán’s letter Just as amazing is Drosnin’s claim provided by the Notices is there any refers to the September announce- that I “searched for many past assas- help for those of us not yet connected. ment in the Mathematics Calendar. sinations in many texts” until I “found I do not believe I am the sole back- The first announcement of ICM98, one random pattern.” Drosnin knows ward mathematician in the world yet which appeared in the November No- full well that he chose Moby Dick him- to go electronic, and I am very con- tices (page 1392), tells how to register self and that I found, not one, but cerned that the enormous amount of using paper mail. many assassinations. In fact, I can find emphasis that is being placed on ad- almost any I look for, including that vanced modes of communication, far Reply to Bible Code Author of Rabin. from making it easier for all to have Having recently had the doubtful plea- The bottom line is that the only access to information, is widening the sure of hearing Bible Code author thing Drosnin did that I have not re- gap between those who have and those Michael Drosnin telling a litany of lies peated in Moby Dick is to predict an who have not the means, financial and and half-truths to the media here in assassination before it happened. Even otherwise, to keep up with the tech- Australia, it is rather amusing to read that prediction can be best described nology and hence to keep in touch his accusation (Notices, November) as a guess, as the words Drosnin with the international mathematical that I am the one perpetrating a hoax. claims as “assassin that will assassi- community. I worry in particular for Take for example his claim to have nate” are from a verse about acci- young mathematicians in many parts the “original Hebrew text” of the Bible. dental homicide and can be read in a of the world—budding Ramanujans Contrary to the very explicit lie made variety of ways that include Rabin

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being the killer or the killer being uniform continuity; one variable and Benefits of Electronic Journals killed. one quantifier is thereby removed. Despite the many benefits of elec- On the matter of Ilya Rips, I am But it is not enough to rename and tronic publishing of mathematical re- sure that he sincerely believes in his δ; their significance must be illus- search journals, Steven Krantz’s edi- “codes”, but he has not presented clear trated. Here is a natural way of doing torial (in the September 1997 Notices) evidence that requires a miraculous this. chose to highlight and exaggerate explanation. Until he does so we are A function is a rule or algorithm some potential drawbacks without entitled to withhold belief in his that for each input of a real number discussing the actions that are widely claims. Everyone who alleges scien- x in the domain of the function pro- taken to address them. I wish to help tific proof of a miracle should expect duces a real number y as output. This inform Notices readers about those the same response. concept is more abstract than it actions, so that we can all participate Readers are invited to inspect a hu- sounds, because the input x is an in- to help direct this inevitable change to morous reply to Drosnin and a serious finite decimal; it would take an algo- our profession. reply to Rips at http://cs.anu. rithm an infinite amount of time to Most of the e-journals that cur- edu.au/~bdm/dilugim/torah.html. process it. To achieve finiteness, we rently exist (such as those published observe that at no time are we inter- by the AMS) hold to the same editor- Brendan McKay ial and ethical standards as main- Australian National University ested in the exact value of the output y; we only need to know it within a stream paper journals—a paper is sub- mitted to an editor and then (Received October 3, 1997) certain tolerance, dictated by the use to which it is put. The tolerance varies anonymously refereed by one or two from occasion to occasion; sometimes suitable peers. No big difference there Use Uniform Continuity to we need to know y with 2-digit accu- from paper journals. Why should there Teach Limits racy, sometimes with 6-digit accuracy, be? It is a system that has worked well for a long time. In the May issue of these Notices, but we never need infinitely many dig- However, an enormous difference pp. 559–563, David Mumford argues its. passionately that when teaching cal- Suppose now that our function has between paper and e-journals is the culus to “the millions”, the basic con- the following property: To compute time lag between acceptance of a cepts should be introduced in an in- the output y with 2-digit accuracy, paper and publication. Paper journals tuitive fashion in terms familiar to the we need to know the input x with, say, often have backlogs of two years or uninitiated. In this spirit Mumford ac- only 3-digit accuracy; to compute y more; no e-journal leaves a paper in final form waiting for more than a cepts the Harvard Calculus definition with 6-digit accuracy, we may need couple of months. Another big ad- of continuity of a function: “the closer to know x with, say, 9-digit accuracy. vantage of e-journals is that authors x gets to a, the closer f (x) gets to In general, in order to compute the and readers can subsequently append f (a).” In the September Notices, p. 893, output with k-digit accuracy, we need (edited and refereed) notes to the Saunders Mac Lane objects to this de- to know only a finite number, say n, paper so that future readers can fol- finition, because it seems to imply digits of x. This property of a func- low later developments in the sub- that f (x) approaches f (a) monotoni- tion is called uniform continuity. ject. cally and also because it fails to say Since a continuous function on a Krantz voices the popular fear that that f(x) gets arbitrarily close to f (a). closed interval is uniformly continu- “deans” will not “count” papers in ref- Therefore, he holds out for the (,δ) ous, our students encounter mostly definition of continuity, although he ereed, respected e-journals for pro- uniformly continuous functions. allows the substitution of Latin let- motion and tenure decisions. Why There are other reasons for prefer- ters for Greek ones. shouldn’t they? Why would a poorly ring uniform to pointwise continuity: In my opinion neither Mumford nor edited paper journal be worth more to it trains the mind to think of a func- Mac Lane nor Leonard Gillman in a a dean? On the contrary, most uni- tion, not as the conglomeration of its note in the September Notices, versity administrators are keen to en- values, but as a thing in itself. This is pp. 932–934, has come up with a de- courage electronic journals, since they finition that is congenial to “the mil- of great help even at the introductory appreciate the potential financial ben- lions”. As Gillman points out, the dif- calculus level—for instance, in grasp- efits. ficulty that students have with the ing the idea of the definite integral, in Krantz worries about the archiv- notion of continuity is the number of discussing uniformly converging se- ing of mathematical material; he be- quantifiers and their subtle placement quences of functions, and in many lieves that as new media for storing in the definition: “For any a and for other contexts. data emerge, the technical world will any > 0, there is a δ depending on not be willing to find a way to move a and such that when x differs from Peter D. Lax current data to the new media. Why a by less than δ, f (x) differs from f (a) Courant Institute, wouldn’t businesses and governments by less than .” New York University want to find a way to restore their old For this reason, but not for this rea- data? Does Krantz think they won’t son alone, I advocate the teaching of (Received October 7, 1997) share that technology? In fact, sev-

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eral nonprofit corporations and lead- given topic in the electronic Math- and here was the AMS shifting an- ing academic libraries are currently SciNet will not be easily persuaded to other burden onto them.) engaged in making old, important go back to browsing through endless Of course there still remains the (paper) science literature available on- issues of Math Reviews. Moreover, the question of exactly where the re- line, despite the difficulties of doing top researchers in certain areas of sponsibility for typing papers lies. A that. They believe that this is a more mathematics and physics (combina- number of my colleagues prefer to do accessible yet cheaper way to store torics and stellar modelling) now pub- it themselves, but I most certainly do important older work—check out lish much of their most important not. I regard manuscript typing as an http://www.jstor.org/ to find ex- work in electronic journals. absolutely essential service my de- cellently scanned copies of the An- The main commercial publishers partment provides for me. Some de- nals, the Journal and Transactions of are eagerly changing with the new partments, however, are cutting back the AMS, and Math. Comp., every ar- technology. The AMS has invested or entirely eliminating their manu- ticle from every issue up to five years many of its resources into electronic script-typing positions, thereby forc- ago. Moreover, most of the leading publishing (after a slow start) and is ing mathematicians to type their own presses are making all of their current now working through many of the papers. This is a continuation of the paper journals available in electronic trickier issues. Unfortunately, there trend of assuming burdens that are form; they recognize the benefits of are still a few loud voices in the math- not our responsibility and is to me an presenting academic work in this ematical community, such as Krantz, alarming development. I would like medium. who cannot look forward and seem to rally my colleagues against it. This all seems to suggest the exact unable to embrace or even acknowl- opposite of Krantz’s fearful predic- edge the benefits of electronic pub- Steven H. Weintraub tions! lishing. Rather than fearing what is to Louisiana State University Krantz makes the (correct) point come, we must shape these changes (Received October 15, 1997 that e-journals are not “free”. Indeed, to support mathematics so that the in- the hours of editing, refereeing, type- evitable transition to e-publication is setting, and the cost of buying com- Use of the Overhead Projector valuable to everyone interested in puters all add up, though this is the At professional meetings the over- mathematical research. case whether the journal is on paper head projector is probably one of the or electronic. For years mathematics most valuable aids for successful com- Andrew Granville professors have been donating their munication. For the most part, its use University of Georgia time by serving on editorial boards, yet is ineffective and an embarrassment nobody previously included this time to the lecturer, an observation that (Received October 10, 1997) in the costs of producing a journal; in- spans invited addresses to presenta- deed, most publishers have long ex- tion of 10-minute papers. It is ab- ploited such contributed services yet Departments Should Provide solutely thoughtless and a total dis- valued them at next to nothing. Manuscript Typing regard to the audience not to utilize Krantz fears that e-journals will be the overhead to the fullest. This is es- of lower visual “quality”. However, I I am in strong agreement with almost pecially true at international confer- didn’t find this when comparing the all of Steve Krantz’s editorial in the ences. Recently an outstanding indi- most recent issues of the Electronic September 1997 Notices. vidual from a distinguished American Research Announcements and the (on- There is one point, however, in university presented an invited hourly paper) Bulletin. Indeed, after learning which I believe he is mistaken. He address by reading from the overlays from some initial mistakes, e-journals writes: “We are slowly being co-opted before him while all but the very top look quite similar to paper journals, by electronic media: (i) our papers of the screen was blocked by his body. while allowing “search” and other ad- used to be typed for us, but now we In meeting rooms presenters read vantageous electronic features. do it ourselves.…” Actually, this trend from the screen with their backs Publishing is going to change in significantly predates electronic turned to the audience. The puzzling the next few years whether math- media, and the AMS shares part of aspect is that today the overhead pro- ematicians like it or not. We are best the blame for it. It began when the jector is considered to be an integral off being in the vanguard of the rev- AMS started encouraging authors to part of American classroom instruc- olution, helping to make these submit their papers in TEX, thereby tion. That experience should be trans- changes acceptable to our needs. We shifting typesetting, traditionally the ferable. will surely benefit from the enormous job of the publisher, to the author. Examine the presentation of a financial savings (universities will Other publishers soon followed. (I “short” paper. Most of the contents probably pay about a tenth as much found it ironic that this occurred can be condensed, organized, and pre- for e-journals as for paper journals), around the same time the David Re- pared from the article itself on a word and we can also benefit academically port appeared. That report remarked processor with font size at least 18 pt. from some of the added features. In- that mathematics departments will- The number of overlays required re- deed, anyone who has discovered how ingly took on themselves burdens lates to the length and the style of easy it is to research references on a they should have sought support for, presentation, under the assumption

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that time will be permitted to let the rows? These members of the audi- audience assimilate each overlay. This ence may be there because of either is particularly important for a de- the impairments noted above or an scriptive portion. For the presenter inarticulate speaker. to read an overlay is distracting to an There is one other helpful sugges- audience that is capable of doing and tion. If it is possible to have screens will attempt to do the same if given pivot from the bottom as they move sufficient time. Presenting need not forward and down from the top, one imply speaking. eliminates the “v-ing” of the image If there is a reason to either ex- whenever the screen is upright. pand on or to highlight a point, place So with forethought and prior plan- a pencil at the line in question on the ning a presentation accompanied by overlay or use a pointer. Face the au- an overhead projector can reflect a dience and speak clearly; some read professional maturity compatible with lips. Glance at the screen occasion- the occasion. ally to assure that the exposed part of the overlay and the lecture correlate. H. Bechtell Being nonchalant, folksy, or “cute” di- University of New Hampshire minishes the value of the investigation under discussion—it is an impedance (Received October 14, 1997) to those who are impaired by either hearing or lack of fluency in English, the accepted professional language. In order not to block the view, examine the room prior to speaking; the rooms About the Cover are usually open at an early hour. A The computer-generated image of the small room may require one to sit be- “Singly Periodic Genus One Helicoid” side the projector. The lecture is a was made by James T. Hoffman of MSRI. communication, and presumably the It is a picture of a complete minimal sur- topic and the contents are sufficiently face that is singly periodic (invariant important to engage the audience’s under a vertical translation), free of self- time and to either challenge its intel- intersections (embedded), and asymp- totic to the helicoid. The quotient of this lect or be of value as a body of knowl- surface by its translational symmetries edge. In brief, if one’s work is impor- is a surface of genus one. Like the heli- tant enough to be accepted for coid, it contains a vertical axis. Modulo presentation, this should be reflected vertical translations, it has two parallel in the delivery itself. horizontal lines crossing the axis. It was These same observations apply to discovered by Fusheng Wei (Virginia Tech), Hermann Karcher (U. Bonn), and an hourly presentation. Often in this David Hoffman (MSRI) (Bulletin of the case the overlay serves as an orga- AMS 29(1) (1994), 77–84). The proof of nized set of notes, each point of which its existence and embeddedness appears will elicit more elaboration directed to- in a soon-to-be-published article—named ward the audience by the speaker. after the surface—in the Comment. Math. Sometime prior to the delivery it is es- Helvet. This surface played an impor- tant role in their discovery of the “genus sential to walk through the audito- one helicoid”, a complete minimal sur- rium or banquet hall in order to un- face asymptotic to the helicoid, which is derstand how best to either position not periodic and has infinite total cur- oneself or to rearrange the stage set- vature. (See “The genus one helicoid and ting in order to avoid blocking the the minimal surfaces that led to its dis- screen. During the delivery have some- covery”, Global Analysis and Modern Mathematics, (K. Uhlenbeck, ed.), Pub- one sit within the first few rows to sig- lish or Perish Press, 1993, pp. 119–170.) nal adjustment of the overlay should For a survey of the theory of “Com- that be necessary. plete embedded minimal surfaces of fi- The local chairperson in charge of nite total curvature”, see the article with arrangements should keep all of the this title in the recently published Vol- above in mind as the projectors are ume 90 of the Springer Encyclopaedia of Mathematical Sciences, edited by Robert positioned in each room and audito- Osserman, pp. 5–95. rium. For example, is the lectern re- —David Hoffman ally needed, particularly if it blocks the view for those seated in the first few

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