18/09/24 13:14:03.75 b5cCvILu.net
>>62
つづき
i.e., that
substantial progress in understanding IUTch always requires discussions
over an extended period of time, typically on the order of months.
Indeed, the issue of lack of time became especially conspicuous during the afternoon
of the final day of discussions. Typically, short periods of interaction center around
reacting in real time and do not leave participants the time to reflect deeply on
various aspects of the mathematics under discussion. This sort of deep reflection,
which is absolutely necessary to achieve fundamental progress in understanding,
can only occur in situations where the participants are afforded the opportunity
to think at their leisure and forget about any time or deadline factors. (In this
context, it is perhaps of interest to note that Scholze contacted me in May 2015 by
e-mail concerning a question he had regarding the non-commutativity of the logtheta-
lattice in IUTch (i.e., in effect, “(Ind3)”). This contact resulted in a short
series of e-mail exchanges in May 2015, in which I addressed his (somewhat vaguely
worded) question as best I could, but this did not satisfy him at the time. On the
other hand, the March 2018 discussions centered around quite different issues, such
as (Ind1, 2), as will be described in detail below.)
§3. On the other hand, it seems that the March discussions may in fact be regarded
as constituting substantial progress in the following sense. Prior to the March
discussions, (at least to my knowledge)
negative positions concerning IUTch were always discussed in highly nonmathematical
terms, i.e., by focusing on various aspects of the situation
that were quite far removed from any sort of detailed, well-defined,
mathematically substantive content.
(引用終り)