My Path by Wolfgang Gaschütz
Below is a translation by Stefanie Eminger of the speech of thanks which Wolfgang Gaschütz gave when emeritus status as professor for mathematics was conferred on him at the University of Kiel on 25 November 1988 in the Great Auditorium of the Mathematical Seminar at Kiel. The original German text was published as W Gaschütz, Mein Weg, Proc. F. Scorina Gomel State Univ. No. 3 (16) (2000), 7-10.
Chancellor, Dean, dear esteemed guests, colleagues and fellow students!
After having heard the kind portrayal of my temperament just now, you should all be able to spot how unaccustomed I am to situations like today, where I am condemned - albeit lovingly - to passiveness.
And if I am cheekily pressing forward yet again, I am not doing this because I want to elude any more age-related demonstrations of fondness beyond the ones I have already gratefully received. Instead, I want to explain, rather apologetically, how the celebration that you have been asked to attend came about and, in doing so, express many a thank-you.
In order to introduce to you the first mathematician who had a definitive influence on my life I have to go back to the year 1746: Friedrich, who was not yet the Great at that point, but who had escaped from the two Silesian wars victoriously and more experienced, now looked for less risky ways of gaining land. Hence he turned to the Oderbruch, an area of 10x40 km, 60 km east of Berlin. It was not useable due to a geophysical defect, as the optimal flow of the Oder was diverted there because of a height prominence. This forced the river to gush into the unprotected swamp during floods. His dyke surveyor, Simon von Harlem, advised the King to cut off this obstacle so as to enable the Oder to run off faster and thus create new farmland.
Despite his desistance from mathematics, Friedrich appreciated mathematics enough to use its advice before undertaking this costly enterprise: Leonhard Euler, perhaps not the mathematician most profound in ideas, but for me the mathematician most rich in ideas of our millennium, and who had been appointed as director of the Berlin Academy by Friedrich, was asked to give a final judgement of the plan.
After having visited and surveyed the barren land, Euler eventually gave his approval, and with it he gave me the chance to begin my life in the crown land Karlshof, which had been established on this terrain.
Thus, mathematics initially served me only indirectly, by facilitating a wonderful and untroubled childhood in this swath of land by the river. But soon it conceded me the favour of a more direct encounter: In 1931, when we made an effort to find common divisors in order to cancel fractions by trying, in the second year of secondary school in Wriezen - I wistfully remember this little old town in the East, which was declared a fortress by a maniac spree killer even at the end of the last war, and was thereby almost wiped out. The excessive thoroughness of this procedure bored me, and coaxed me into declaring that one merely had to try up to the difference of the numerator from the denominator.
The mathematics teacher, Mr Kempin, who had tolerated our efforts without this constraint, turned to the blackboard, perhaps a little embarrassed. There he probably wrote down this line, which confirmed my remark, but which I did not yet understand:
a = ud, b = vd ⇒ a-b = (u-v)dThe memory of my discovery of this beneficial little theorem from number theory then remained such a distinct one probably because it was a first mathematical experience for me, and because the praise I received for it afterwards encouraged me to perform well in mathematics from then on. Out of everything that I have accomplished so far this is proof to myself that I am a mathematician more than anything else.
At the age of 17 I left my parents' house after having finished school - at the age of 24 I found myself, a released officer in a family of three, with hardly any belongings, staying with helpful friends between Schleswig and Husum. We had to start life over again. Anyhow, I was in the quarter of my school class that was allowed to escape from the war.
And if I had pursued mathematics primarily for disport, it now really began to become fate for me: In 1945, the nearby University of Kiel was one of the first to open its gates, and one could hand in one's application in the - asylum in Schleswig. Not because the English deemed it necessary to mentally cleanse us from the NS-ideology there, of course, - after everything that we had been through; no, because Creutzfeld, the great psychiatrist, had been installed there as rector by the occupying forces and transferred there with his hospital due to the bombs.
As little deeply symbolic this matriculation venue was for a well-regulated further development of the mind, as fortunate a place of study the University of Kiel proved to be for me after all: It offered an ample and stimulating selection of lectures; and freedom of mathematical interests was encouraged at the slightest hint of formal patronizing.
We owe the fact that this form of studying, which suited our age very well, could stand the test of time to the - in light of the indescribable distress - sacrificial commitment of two characters, who, in addition, complemented one another splendidly: Mr Weise, who we will hopefully see among us like today for many years to come, and Friedrich Bachmann, who was suddenly torn away from us six years ago. Whilst Mr Weise catered for the liberal aspects of our studies - for example, he took responsibility for the venture of letting me obtain my doctorate for a thesis in group theory; Mr Bachmann catered for mental discipline, which protected us from scholarly adventures. The effects of the success of this kind of study were that we could obtain our doctorates after eight semesters, and that there are about 30 professors lecturing at universities today, whose scientific careers began under the guidance of those two.
If the fortuities of the consequences of the war benefited me with Kiel as my place of studies, then chance played an even bigger part when it came to decide on my main research area, as I like to recall time and time again.
In 1946, all of us students lived in the berths of the Orla, a ship ready to be handed over to the English. We lived on barter in all areas of life. Among my meek belongings was a rather special mathematics book. It had been published in 1942, and after the disastrous winter in the East the wartime economy must have deemed it beneficial to winning the war and therefore worthy of publication, despite the shortage in demand, due to its title: 'The Geometry of Fabrics'. In any case, to me it seemed dispensable as a basis for studying mathematics. - One of my roommates offered me a book for it, whose title admittedly meant less to me, but which would hardly hold less interest for me than mine. The exchange was made.
The book that I had acquired then became a revelation to me: Andreas Speiser's 'Group Theory'. With this book I got to know a tool, which the good Lord - whom mathematicians, good heavens, not just perceive as a social worker as narrow-mindedly as is often preached nowadays - which he gave to us as a benchmark for the harmony and order of our knowledge: the notion of groups.
The effects that this simple exchange of books had on the development of the mathematical seminar in Kiel can arguably still be perceived today. This is an example that shows how minor variations of the initial conditions can influence the solutions of an equation considerably.
The proximity of Hamburg meant that studying at the University of Kiel did not have to take place in the remoteness caused by its geographical location. For us, Hamburg was the gateway to the world then, also in terms of mathematics. Artin, Hasse and Witt lectured there, mathematicians who played a crucial part in shaping our science in this century. I gratefully recall the Hamburg hospitalities and the reciprocal visits of the mathematicians in these years. I am thrilled that the then young colleagues from this group, now scattered across Germany, are here today: Jehne, Leptin and Roquette. I am sure that the talk, with which Roquette is so kind as to honour this event, will illustrate how valuable the connection to Hamburg was to us then.
I would also like to express my thanks for longer hospitalities at other institutions: at our mathematical Tusculum in the Black Forest, where I spent three-fourths of a year in total; to Michigan, Padua, Florence, London, Warwick, Chicago, and Canberra. I am delighted to be able to thank Mr Zacher from Padua in person. He probably had the longest journey out of all of us.
In fact, I would like to thank everybody who embarked on the, always long, journey to Kiel to attend our colloquium.
I was offered two serious opportunities to leave Kiel. - I could reject the chair at Karlsruhe on the grounds that, following ancient family tradition, Karl was one of my given names and that Karlshof - often written with 'ff' by its owners - was my place of birth. Being in my early forties, to me Karlsruhe clearly had to forebode all too early scientific twilight years. - In short, I stayed in Kiel, with the same offer and keeping the abundant range of research projects.
The decision was much more difficult when I was appointed to Mainz, where my colleague Bertram Huppert was one of the main figures. I had been communicating with him on scientific matters for a long time, through the medium of Helmut Wielandt, our great mentor in group theory; and we were united by a fate: Huppert's book - no, not book, but thesaurus on finite groups. - The genesis of this plan of creating the book had committed me to participate in the editing process and to contribute my humble advice. - Dear Mr Huppert, I hope that you will approve this paraphrase of the real facts, embellished in my favour.
Thus Mr Huppert visited us in Kiel for four weeks per year, allegedly to use the assistance of me and other colleagues from Kiel. In reality this endeavour proved to be a marvellous and gratefully used opportunity for our seminar to thoroughly keep up with the latest developments. Moreover, this source of information broadened as our colleague Blackburn from Manchester - I am very happy that he is here as well today, despite severe disabilities - contributed the wealth of his knowledge to volumes 2 and 3 as co-author and mentor.
Now, going back to my starting point, I had become so accustomed to this close and convenient collaboration with Mr Huppert, that, with my propensity to sedentism, I stayed in the seminar in Kiel, which I had grown fond of. I hope to have hereby explained myself as an oddball, who never left Kiel once on his scientific path from the first semester to my retirement. With my way of working I never perceived this as a shortcoming, particularly because Mr Huppert never held my decision against me. Afterwards our friendship strengthened even more. The talk to which he wants to treat us today, despite numerous commitments, is proof of this.
Perhaps others now see me as one of those pieces of furniture whose springs push through the padding as they age. I would like to ask all my colleagues and students to excuse me if they had to - sometimes grudgingly - follow my inconvenient advice. I hope that my advice was not seen as a professor's delusion, but as an attempt to serve the cause. Often my advice could only be understood if one had known the circumstances at Kiel for a long time.
I gladly step down from my post as director of the mathematical seminar. The duties of our alma mater have changed considerably over the last forty years. But I am relieved to see how younger colleagues do an excellent job of serving our Christian-Albrechts-Universität in a more modern manner, with scientific achievements and dedicated teaching. May my blessing accompany their work.
Prof Dr Dr h. c. Wolfgang Gaschütz
Projensdorfer Str. 220