Letters to the Editor, Volume 42, Number 3

letters.qxp 3/17/99 10:10 AM Page 325 Letters to the Editor Comments on Kahane- Krickeberg-Lorch Letter As a reciprocity member of both the American Mathematical Society and the Deutsche Mathematiker-Vere- inigung, I am very disturbed to see an about attack made in the letters to the No- this. As for the tices (vol. 41, number 6) on the DMV. “historically ac- The first question to be asked is how German curate perspective”, the AMS is involved: the letter should mathemati- Bieberbach’s activities surely have been directed to the DMV. cians but with the DMV are fully The authors say that an “historically which brought no described in the DMV cen- accurate perspective” on the past is personal advantage to him. Let it tenary publication Ein being “withheld”. Do they claim to only be said: Bieberbach later rec- Jahrhundert Mathematik, have a superior perspective to those ognized and deeply regretted these er- and his activities as de- who are genuinely trying to under- rors, as is confirmed by well-war- partment head in Berlin are stand what happened under Hitler? ranted assertions.” This is a perfectly described in highly critical terms. No The attacks which they proceed to fair statement, in accordance with the mathematician admires what Bieber- make on their mathematical colleagues usual perception of an obituary notice. bach did in these matters, but to do not suggest that they have. It is surely at least plausible that doubt “current willingness to face the Their first complaint concerns the Bieberbach did regret his activities: it past” in his case is absurd. obituary notice published about would be amazing if he had not re- Then comes Strubecker. Appar- Bieberbach in the Jahresbericht, writ- gretted making such a fool of himself. ently the offence of his obituary ten by the late H. Grunsky. This notice But no, this is not enough for our writ- writer, H. Leichtweiss, is to say that says the following: “This is not the ers, who want evidence of it. But he enjoyed the war years in Stras- place to look closely into these events, Grunsky’s article says “as is confirmed bourg. The obituary notice says that which susceptibly harmed mathemat- by well-warranted assertions”. There one of these enjoyments was his mar- ics in Germany and many individual is no reason to question his integrity riage, but this is not mentioned in MARCH 1995 NOTICES OF THE AMS 325 letters.qxp 3/17/99 10:10 AM Page 326 Letters to the Editor the letter. Was it a crime, then, to do accusation an example of the anti- matics and descriptive mathematics creative mathematics in Strasbourg German xenophobia which is so com- equal attention from the middle during the Nazi occupation? And our mon in the daily press (in England at school on. The (two-semester) course righteous letter writers are incensed least!) but which has up to now not that I teach to prospective elementary because Leichtweiss speaks of the “oc- reared its ugly head in the mathe- and middle school teachers prepares cupation” of Strasbourg by the Allied matical literature. I sincerely hope them to do deductive mathematics. forces. But that is what they did! To de- that the AMS is not going to change On the final exam (among other mand the use of a word with emotive this. things), I give definitions that they significance instead of “occupation” have not yet seen and new theorems is pure political correctness and has Norman Blackburn that depend on the definitions. The nothing to do with historical under- The University better students are able to provide standing. Manchester, England original proofs for the new theorems. The next attack is on the writers of Some of these better students started a review of Teichmüller’s life and work. (Received October 11, 1994) out with math anxiety. Here our defenders of the truth have The students in my present course a little difficulty, since everybody are much more excited than were the knows that Teichmüller was a genius. Balancing Deductive and students in a traditional section of the They fall back on the old method for Descriptive Mathematics course I first taught. In sections of the getting around this: “Yes, but his re- in the Schools present course, almost half the class sults were anticipated by someone I am writing this to research mathe- rated the course as excellent. In the else.” The writers of the review are maticians to interest as many as I can traditional course, almost none rated then taken to task for not saying this, in a course for prospective elementary it excellent. The course leads up to in particular for “hardly mentioning” and middle school teachers. A recur- certain student investigations. In the Grötzsch. I am in no position to judge ring theme in the letters and forum first investigation, students conjec- the importance of Grötzsch’s work to sections of the Notices is that very ture general set relationships from Teichmüller, but the letter writers ap- few people (educators, politicians, exploring diagrams. The students, on parently think themselves better funding sources) have any idea of their own, discover DeMorgan’s laws, judges of this than the distinguished what mathematics is or what mathe- the distributivity between set inter- mathematicians who wrote the article maticians do. This theme is a symp- sections and union, and some inter- on Teichmüller. Of course, Grötzsch’s tom of a problem I address in my esting relationships that have been work is also discussed in detail in Ein course. For the purpose of explaining new to me. By the time they get to the Jahrhundert Mathematik, the proper the course, I break mathematics into investigation sections, they are able place for it. Again there is no question two aspects (1) discovery/deduction to provide original proofs of their of unwillingness to face the past here; and (2) description computation. Dis- conjectures. A second investigation no one defends Teichmüller. But there covery/deductive mathematics asks has them extend certain order and is mention in the letter of the fact that the questions, What is true about this ring-theoretic properties of the inte- Grötzsch was an “anti-Nazi dismissed thing studied? and How do we know gers to the rational numbers by mak- on that account”; the inclusion of this it’s true? Descriptive mathematics, ing new definitions that are appro- information can only be interpreted as on the other hand, asks us to describe priately analogous to the definitions a suggestion that the authors of the Te- some physical or business situation for the integers. ichmüller article ignored Grötzsch for mathematically and to compute as- Students are taught to write proofs that reason. Such a slur is unaccept- sociated values. To most people who first in terms of a formal system with able. The fact is that the authors of the are otherwise well educated the tech- many inference rules. The rules model letter are unable to come to terms with niques associated with solving equa- what mathematicians do naturally. the fact that it was possible for some- tions, finding antiderivatives, dividing The explicit use of the rules gives one to be both a great mathematician whole numbers, and so on are math- way to implicit use, in somewhat ab- and a fanatical Nazi. ematics. breviated proofs, which look like tra- So the letter ends with an attack The reason for people’s misun- ditional mathematical proofs at a be- on the DMV itself. This is because a derstanding of mathematics is clear. ginning level. It is the explicit rules, “discussion article”—whatever that Their entire experience in twelve years however, which make possible the may be—was rejected by the Jahres- of school and most college courses description of a heuristic system for bericht with no invitation to reply. But will have been with descriptive math- discovering one’s own proof steps. you, sir, rejected a letter of mine about ematics. There are now high school The entire program of learning proof eleven years ago, with no explanation. geometry texts that boast that not is linguistically guided and has noth- Is this not what journals do with math- one proof is to be found in the text. ing to do with students’ quantitative ematical articles all the time? It is im- The solution that I propose to this abilities or familiarity with descriptive possible not to see in such a trivial problem is to give deductive mathe- mathematics. 326 NOTICES OF THE AMS VOLUME 42, NUMBER 3 letters.qxp 3/17/99 10:10 AM Page 327 Letters to the Editor Instructors that teach the same I turned my attention toward ele- making high school geometry increas- course here at the University of Maine, mentary teachers because of dis- ingly descriptive. The result of all this and to whom I have described my sys- couragement with math majors. We is that people don’t know what math- tem, are universally put off by the for- are getting fewer of them, and the ematics is. We get mathematics majors mality of the system at its initial ones we do get seem to have the that are discouraged and disappointed stages. I have been told that the trend wrong idea of mathematics. Our be- when they find out. these days is toward increased infor- ginning majors have seen nothing but In the 1960s the “new math” was mality. Students, however, are of ex- descriptive mathematics in their pre- introduced as a curriculum change. It actly the opposite opinion. When we vious education.

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