"My work is a fundamental extension of the work of Gödel and Turing on undecidability in pure mathematics." (Gregory J. Chaitin, "Conversations with a Mathematician---Math, Art, Science and the Limits of Reason", pp. 109-110, Springer-Verlag, 2003)
It is not up to me to say whether this is true or not---it is fair to say, however, that Chaitin's work is considered to be fundamental by many and will probably stay with us---, but is it up to the author himself? Would any of my readers claim in public that her/his work is fundamental?
My modest opinion is that the only judge of whether (the result of) some human endeavour is fundamental in any sense is Time.
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