Is string theory “the new calculus”?

Well, no… it cannot be… the first calculus I know, defined by Newton and then refined by Leibnitz was rather cumbersome to work with but otherwise well defined… You cannot say the same thing about string theory. Its mathematical foundations are shaky at best and there are consistent imprecisions in the use of terms (to quote a few: flux compactification, compact spaces, string quantization, world sheet integral, perturbative expansion terms, topological series, closing conditions, etc.) In fact I am not sure there is anything well defined in string theory except the idea that there should be strings… While the basic idea of dimensional extension has found some very specific applications (see dimensional regularization, dimensional extension, retraction, etc.) I doubt quite a lot about the “mathematical consistency” of string theory whatsoever… 


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