my forty years on his shoulders - Department of Mathematics

55statements represents an inevitable general expansion of mathematical activity.This, I conjecture, will apply to any standard mathematical context.This program has been carried out, to some very limited extent, by BRT –as can be seen in section 10 above.This may seem like a ridiculously ambitious conjecture, which goes totallyagainst the current conventional wisdom of mathematicians - who think thatthey are immune to the incompleteness phenomena.But I submit that even fundamental features of current mathematics arenot likely to bear much resemblance to the mathematics of the future.Mathematics as a professional activity with serious numbers of workers, isquite new. Let’s say 100 <strong>years</strong> old – although even that is a stretch.Assuming the human race thrives, what is this compared to, say, 1000more <strong>years</strong>? Probably merely a bunch of simple observations in comparison.Of course, 1000 <strong>years</strong> is absolutely nothing in evolutionary or geologicaltime. A more reasonable number is 1M <strong>years</strong>. And what does our presentmathematics look like compared to that in 1M <strong>years</strong> time? These considerationsshould apply to our present understanding of the Gödel phenomena.We can of course take this even further. 1M <strong>years</strong> time is absolutelynothing in astronomical time. This Sun has several billion good <strong>years</strong> left(although the Sun will cause a lot of global warming!).Mathematics in 1B <strong>years</strong> time? Who can know what that will be like. But Iam convinced that the Gödel legacy will remain very much alive – at least aslong as there is vibrant mathematical activity.