Victor K.A.M. Gugenheim (1923-1995) ******************************************************************* The 1968 Chicago Circle conference was organized by Victor. I asked his friends and collaborators to contribute biographical and anecdotal material about him, with the following results, including a bibliography. Andrew Ranicki ******************************************************************* Full Name: Victor Kurt Alfred Morris Gugenheim Born: August 28, 1923, Berlin Education: Oxford B.A. 1948, M.A. 1950, D.Phil. 1952 (sometimes listed as 1951) under J.H.C. Whitehead Positions: Princeton University (Visitor as a Commonwealth Fellow), 1952-54 Birkbeck College, University of London (Assistant Lecturer),1954-56 Johns Hopkins University (Assistant Professor), 1956-64 Imperial College, University of London (Reader), 1964-66 University of Illinois at Chicago (Professor), 1966-91 Died: August 3, 1995, Chicago Victor established a strong topology tradition at UICC, which is now the University of Illinois at Chicago. Pete Bousfield ************************************************************************ Victor Gugenheim was born in Berlin on August 28, 1923. When he was six, his father taught him to sail which he enjoyed very much. In 1930, he was enrolled in a small private school run by a Fraulein Wunderlich where the older children were often given the assignment of adding numbers with seven or eight digits -- the younger ones were given the simpler assignment of adding the same numbers with the last four columns wiped out. This was his earliest memory of doing mathematics. Victor quickly learned to read and read quite a bit throughout his childhood including books concerning engineering and science, but especially anything to do with astronomy. He also mentioned once that he had read Erich K\"astner's, "Emil und die Detektive" and "Der 35. Mai" and that they had a great influence on him. He entered the "Franz\"osisches Gymnasium" in April of 1933. As the name would seem to imply, the first two years were devoted to learning French after which all instruction was in French (with the exception of mathematics and science which were taught in German). He recalled that when his mathematics instructor taught him about factoring integers into products of primes, it instantly occurred to him that there was a possibility that if instead of starting with two, then three, and then five and so on as he was being taught, if he chose a different order, a different answer might occur. Thus he recognized the necessity for uniqueness proofs early on. Starting in January of 1934, he went to school in Trogen, Switzerland. While there, he read "popular" books on science by Jeans, Eddington, and Karlson. Karlson's book "Du und die Natur" fascinated him and he mentioned that it had influenced him to want to become a theoretical physicist. He stayed in Trogen from 1933 to 1939 when it was decided that he would go to England. At Oxford, when deciding on his graduate studies, he mentioned that, at the time, it looked like what J.H.C. Whitehead was doing in topology looked far more exciting than what was going on in theoretical physics and J.H.C. Whitehead became his PhD adviser. When I was a graduate student at the University of Illinois at Chicago in the late 1970's, I was studying algebraic topology, but my PhD adviser was John Wood. Victor was ill around then and we did not have much chance to talk -- except for the time he administered my German language exam which I passed with a bit of coaching from him! It was later in the mid 1980's when I came back to UIC as a faculty member that Victor and I had fascinating conversations about his work on twisting cochains and related matters. We found much common ground which led to a series of papers on differential homological algebra. During this period, I remember reading "Alan Turing: The Enigma" by Andrew Hodges to find a passage about Turing visiting various Universities in England to get a better idea of what field he would like to enter. It mentioned that he had gone to Bristol to visit the topologist Guggenheim. I recognized, of course, that this name had two g's while Victor's last name had only one, but nonetheless, the next day, while chatting with him in the coffee room, I mentioned this passage and Victor said, "Ah yes, I remember when Alan came to see me"! He then mentioned that after dinner, they went for a walk and there was a full moon. Alan took out his handkerchief and doubled it up holding that up to the full moon to create a Moir\'e pattern. He said, "What does your topology tell us about this Gugenheim?" Victor then looked at me and said, in his typical humorous style, "Well, I don't need to tell you that he did not go into topology". Victor was diagnosed as having Parkinson's disease in the very late 1980's. In spite of this, he would meet me on Saturdays for coffee and bagels on Taylor Street just down the road from UIC and we would discuss mathematics, science, and many of the things I have mentioned above. We would then spend the afternoon at the office scratching out ideas on the blackboard until the disease became too advanced around 1992. Victor Gugenheim died in Chicago on August 3, 1995. Larry Lambe ************************************************************************ I have only a little to add to Larry's excellent account, but here are a few points. One comment is from Bill Cockcroft a long time ago, saying that Victor's interest in knot theory and low dimensional topology in his thesis was very much ahead of his time, and perhaps most in the VKAMG nature, but was unfashionable when he went to the USA. Hence his thoroughly professional take up of simplicial theory. Victor responded immediately when I sent him an offprint of my obscurely published note on what is now called Homological Perturbation Theory (HPT), and which overlapped with his 1972 paper. Ronnie Brown ************************************************************************ My favorite Victor anecdote dating from after the Nazis came to power but before he went to school in Switzerland: One day the local Gauleiter came to give a lecture on the Aryan race concluding by singling out the best example - blond, blue eyed... Victor Gugenheim Oh, and the one about his father writing to Herr Hitler with praise for all the good he was doing if only he would not bother the Jews. And how the Lutheran chaplain at the Swiss school confirmed him in spite of Victor's non-belief Victor once said: there are several answers to the question Is there a God? Yes No I don't know and Victor's own `I don't understand the question' Jim Stasheff *************************************************************************** I remember one exchange with Victor when we were collaborating, about American vs English, and specifically simplices vs simplexes, which he ended by telling me to get over my complices. Peter May *************************************************************************** While living in Hyde Park, a racially integrated neighborhood in Chicago, Victor was walking down the street and was suddenly surrounded by a group of quite young teenage boys who demanded his wallet. He was a little reluctant to give it to them, so he began to dialog with them. One of them - he seemed to be the leader - said you speak funny. Where are you from. Victor told him, and he immediately said "oh, we thought that you was one of those white guys" and they all took off. Brayton Gray *************************************************************************** I think Victor went to a school in Cheltenham after moving to England and then joined a research team in aeronautics (perhaps the Aircraft Research Establishment at Farnborough) where he claimed he wrote papers that as a German national he was forbidden to read. A scrutiny of the dates suggests that Victor may have entered Magdalen College and passed the First Public Exam in Mathematics in the year before two years of war service, doing research such as in aviation. His German origins may have stood in his way as a recruit to Bletchly Park, and paradoxically permitted him to speak more freely about what he did. Only now are some of the activities of the other gang (including work on codes) becoming known [officially]. In 1946 both he and his Magdalen College (Oxford) tutor D. G. Kendall FRS were released from war related duties. After getting a First Class degree in Honours Mathematics Victor started as an Advanced Student for his doctorate, with J.H.C.[Henry] Whitehead. At that time the titles of Henry's student's theses were all permutations of one set words involving Problems, Applications, Algebra and Topology; however the graduate students were expected to find their own thesis topics, perhaps provoked by the regular seminar Henry conducted with E.C. Thompson. However, Victor's thesis did not build on any work of Henry's, and its originality earned him a Research Fellowship at Magdalen, and the respect of Hugh Dowker. As our first postgraduate year stumbled to a close, Victor and I stared glumly from a bridge into dark swirling waters perfectly reflecting our grasp of algebraic topology. The fact that we had financing for another year kept us out of that water, and in fact during that year we each acquired promising seedlings to nurture (though sadly our interests began to diverge). (Nicholas) Avrion Mitchison FRS, a biologist of intellectually impressive ancestry, third of three brilliant sons of Baron Mitchison CBE, QC, and famous writer Naomi Mitchison CBE (which is the way Jos. Wedgwood and Darwin get in the act) was appointed along with Victor to a research Fellowship at Magdalen College in 1950 at that time the College appointed two such Prize Fellows each year. Avrion, like Victor, took the opportunity of a Commonwealth Fund Fellowship research in America in 1952. Michael Barratt *************************************************************************** I knew Victor briefly in Oxford during what must have been our first, or possibly second year there. I also remember visiting him at home, I think in Maida Vale, and meeting his rather pale and unforthcoming mother and his more lively older brother there. I can't at all recall what we talked about on our Oxford walks and occasional river trips. Certainly not mathematics! I do recall him as nice and interesting. I am very glad he had such a distinguished academic career both in Oxford and subsequently, and that his colleagues clearly regarded him with affection. Sula Wolff *************************************************************************** I knew Victor in Baltimore when he was at Hopkins where he always wore red ties, so much so that one Christmas his students presented him with a multicolored one. He had a cat with whom he shared one bowl of cereal in the mornings. He adored movies and went constantly, sometimes 2-3 in 1 day. Among his favorites were The Wages of Fear and Les Enfants du Paradis. He himself actually was the voice over of a cat in a short, and became even more realized as King Alonso in The Tempest in a local college production. In 1965 he returned to Berlin and attempted to find his family? home in the Eastern Sector. The house, mansion really, was no longer there only a few front steps remained. What was there, however, were stakes to which German Shepherds, dogs, were tethered. The property had become a canine training field. He said very little, and I, too young then to ponder about much less ask his thoughts, simply munched on my marzipan and hoped we could move on since it was bitter cold. The racial incident mentioned by Brayton Gray is a little inaccurate. It happened years earlier in Baltimore, but then perhaps Victor himself had forgotten where, which, however, is of least importance. He helped me with my German, and more so with my geometry, taught me how to drive, introduced me to the works of C. S. Lewis, the delights of junk food, and, I supply here with mixed appreciation, that one goes to the movies at their beginning not whenever and wherever in the plot. This last is problematic for me since before Victor I somehow had the skill not to be lost no matter what was happening on the screen. I add here since I note on your homepage some gesture to food, that he also introduced me to blood pudding, a pivotal event from which I established a healthy aversion to suspicious looking and sounding cuisine. His initials stand for Kurt, Alfred, Morris, and were given to him because his father worried that perhaps being a Jew, he might be compelled to change his name, and so could rely on these which were legitimate. When he visited me in Seattle for a few days, on an impulse I asked if he would give a talk on Greek mathematics to the Classics Department at the U. of WA. Even on short notice, many grad students and faculty attended, and much darkness lifted from our collective (mis) understanding. He truly loved teaching, and was genuinely interested in his students' work and success. Virginia Magboo ******************************************************************************** Bibliography V. K. A. M. Gugenheim, L. A. Lambe and J. D. Stasheff, Perturbation theory in differential homological algebra II. Illinois J. Math. 35 (1991), no.3, 357--373; MR1103672 (93e:55018) V. K. A. M. Gugenheim, L. A. Lambe and J. D. Stasheff, Algebraic aspects of Chen's twisting cochain. Illinois J. Math. 34 (1990), no.2, 485--502; MR1046572 (91c:55018) V. K. A. M. Gugenheim and L. A. Lambe, Perturbation theory in differential homological algebra I. Illinois J. Math. 33 (1989), no.4, 566--582; MR1007895 (91e:55023) V. K. A. M. Gugenheim and J. D. Stasheff, On perturbations and A_{\infty} structure. Bull. Soc. Math. Belg. S'er. A 38 (1986), 237--246 (1987); MR0885535 (88m:55023) V. K. A. M. Gugenheim, On a perturbation theorem for the homology of the loop-space, J. Pure Appl. Algebra 25 (1982), no.2, 197--205; MR0662761 (83j:55021) V. K. A. M. Gugenheim, On a modified Eilenberg-Moore theorem, in Geometric applications of homotopy theory (Proc. Conf., Evanston, Ill., 1977), II, 177--190, Lecture Notes in Math., 658, Springer, Berlin, 1978; MR0513574 (80k:55058) V. K. A. M. Gugenheim, On the multiplicative structure of the deRham cohomology of induced fibrations. Illinois J. Math. 22 (1978), no.4, 604--609; MR0501054 (58 #18515) V. K. A. M. Gugenheim, On Chen's iterated integrals. Illinois J. Math. 21 (1977), no.3, 703--715; MR0482748 (58 #2802) A. K. Bousfield and V. K. A. M. Gugenheim, On PL deRham theory and rational homotopy theory. Mem. Amer. Math. Soc. 8 (1976), no.179, {rm ix+94 pp.; MR0425956 (54 #13906) V. K. A. M. Gugenheim, On the multiplicative structure of the de Rham theory, J. Differential Geometry 11 (1976), no. 2, 309--314; MR0418083 (54 #6127) V. K. A. M. Gugenheim and J. P. May, On the theory and applications of differential torsion products, Mem. Amer. Math. Soc., 142, Amer. Math. Soc., Providence, R.I., 1974; MR0394720 (52 #15519) V. K. A. M. Gugenheim and H. J. Munkholm, On the extended functoriality of Tor and Cotor, J. Pure Appl. Algebra 4 (1974), 9--29; MR0347946 (50 #445) V. K. A. M. Gugenheim, On the chain-complex of a fibration, Illinois J. Math. 16 (1972), 398--414; MR0301736 (46 #891) V. K. A. M. Gugenheim and R. J. Milgram, On successive approximations in homological algebra, Trans. Amer. Math. Soc. 150 (1970), 157--182; MR0260838 (41 #5459) V. K. A. M. Gugenheim, Semisimplicial homotopy theory, in Studies in Modern Topology, 99--133, Math. Assoc. Amer. (distributed by Prentice-Hall, Englewood Cliffs, N.J.), 1968; MR0225322 (37 #916) V. K. A. M. Gugenheim, Cohomology theory in the category of Hopf algebras, in Colloque de Topologie (Brussels, 1964), 137--148, Librairie Universitaire, Louvain, 1966; MR0227251 (37 #2836) V. K. A. M. Gugenheim, On extensions of algebras, co-algebras and Hopf algebras. Amer. J. Math. 84 (1962), 349--382; MR0143788 (26 #1340) V. K. A. M. Gugenheim, On a theorem of E.H. Brown, Illinois J. Math. 4 (1960), 292--311; MR0112135 (22 #2990) M. G. Barratt, V. K. A. M. Gugenheim and J. C. Moore, On semisimplicial fibre-bundles, Amer. J. Math. 81 (1959), 639--657; MR0111028 (22 #1895) V. K. A. M. Gugenheim and J. C. Moore, Acyclic models and fibre spaces, Trans. Amer. Math. Soc. 85 (1957), 265--306; MR0086301 (19,160a) V. K. A. M. Gugenheim, On supercomplexes, Trans. Amer. Math. Soc. 85 (1957), 35--51; MR0086299 (19,159c) V. K. A. M. Gugenheim and D. C. Spencer, Chain homotopy and the deRham theory, Proc. Amer. Math. Soc. 7 (1956), 144--152; MR0087150 (19,310b) V. K. A. M. Gugenheim, Piecewise linear isotopy and embedding of elements and spheres. Proc. London Math. Soc. (3) 3 (1953), I. 29--53, II. 129--152; MR0058204 (15,336d) V. K. A. M. Gugenheim, Some theorems on piecewise linear embedding, Proc. Nat. Acad. Sci. U. S. A. 38 (1952), 333--337; MR0048817 (14,74a) ************************************************************************* last updated 15.5.2005