Can you name some? Preferably in analysis.
https://ncatlab.org/nlab/show/list+of+lost+manuscripts+in+ca...
Further is it any relevant theorem, which has been cited many times?
John Beck's Monadicity Theorem is cited in "many sources" but a manuscript has been found and "The proof is reproduced for instance in (MacLane, p. 147-150, Riehl 2017, 5/5/)".
Fred Linton cites Michael Barr for a "Universal property of the Kleisli construction" and no copy has been found.
I don't know enough about the subject to say how difficult these proofs would be to recreate or whether they exist elsewhere, but these definitely seem to be specific theorems.
I'd like to see a specific theorem in any field that was once proven and accepted but all existing proofs have been lost. That would be extremely tantalizing
The first one isn't lost at all, the second is just a single lost citation.
All of this is very far away from mathematicians building upon thr shaky grounds of mythical theorems. Also, in all my mathematical experience (going up to recent research in analysis) I never encountered something like this. In all textbooks I ever read either everything was proven or was cited to other works, which every time I checked included the proof.
