This workshop marks the 75th birthday of Eugene Gordon. The anniversary of a scholar is his opportunity to hear what his colleagues, friends and students think of him. The adversaries rarely speak about the hero of the date. Hence, appreciations might seem and often are indeed exaggerations. Today, nothing of the sort will happen, as Eugene is undoubtedly an excellent mathematician and charming person.
Anatoly Kusraev and I became acquainted with Eugene in 1977, which as the bifurcation point of our worldlines. We had begun plunging into the flood of nonstandard methods of analysis. This was an uneasy but irreversible process. We started with mastering the methods of Boolean valued models of set theory. It was Yurii Manin who revealed the methods to the mathematicians of this country in the mid-1970s. I happened to be at his talk on the Cohen solution of the continuum hypothesis at the meeting of the Moscow Mathematical Society in Lomonosov Moscow State University. The room was overcrowded and many, me inclusively, listened Manin's talk on feet. I understood nothing. But I saw Serge Novikov and Vladimir Arnold in the first rows and thought that I am a complete dummy but the genuine mathematicians do understand everything (at present we know that not all great mathematicians comprehend anything about Boolean valued models).
Eugene's talk at our seminar in Novosibirsk demonstrated that it is impossible to be professional in studying Dedekind complete vector lattices, aka Kantorovich spaces, without some knowledge of Boolean valued models. As time elapsed, we acquired some understanding of the place of nonstandard models as a revolutionary step forward to the future of mathematics which is tied with the rejection of illusions of categoricity and universality of the axiomatic method.
Kurt Gödel wrote about analysis of the future, implying nonstandard analysis of Abby Robinson. There are sufficient grounds to see much deeper and essential meanings of his forecast. The aim of science is to make tricky simple. To achieve this aim we split any situation or problem in the parts we can handle, which is in fact the general nature of analysis. Synthesis is tied with the application of the fragments of knowledge and techniques to any practical issue. The analysis of the future lacks the blinds of canonizing whatever axiomatic theory or methodology. It is free of mysticism and primitive attacks against infinity.
Eugene Gordon is an alien of the future, a sherpa of the new mathematics that humankind is trying to construct.
Anatoly and I are very greatful to Eugene for science, friendship, partnership, and cooperation. Thanks, Eugene!
September 17, 2024
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