Dear Andrei Petrovich!

I want to thank you sincerely for this most unexpected invitation to such in many respects
uncommon meeting of specialists. I like the idea of this meeting very much, although I have no clear
understanding of its possible concrete results. Almost every question from the preliminary list has
some philosophic hue – one can hardly get unambiguous and final answer to them. Among the
topics proposed the most close to me is the topic 3. Of course, the way it’s formulated it is equal to
the question “What to do with the given mathematical problem?”, because any problem apparently
can be considered as a special case of a problem so general that its undecidability would be
apparent. At the same time, decision algorithms are sometimes so complex that there is no sense in
applying them to a single problem.

Seemingly, it is already late to express my opinion about the second list – the one of invited to
participate, but I was very surprised by the absence of Prof. Shanin’s name. Together with his
teacher A.A. Markov (who, because of his illness, most probably will not come) he is a founder of
constructional approach in mathematics – the approach that assumes as its basis not the notion of set
but the notion of algorithm. Today there are representatives of constructivism in many countries
including the USA. Unfortunately (or fortunately?) today’s constructivism is represented by several
different schools, and the discussion of perspectives and future development directions of
constructive mathematics could become one of the symposium’s topics. Among invited Soviet
mathematicians, besides A.A. Markov, G.S. Tseitin represents constructivism; among foreign ones
the closest one to constructivism is S.C. Kleene. Although N.A. Shanin tends to overload his papers
with technical details, which seriously complicates comprehension of his presentations, Nikolai
Aleksandrovich always takes the most lively part in discussions. I think it will nbe a good idea to
invite N.A. Shanin to Urgench.

…

With best regards, Yu.Matijasevich

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