N1VUX is my FCC-issued ham radio callsign.
Most amateur scientists know Gödel and his (in)famous Incompleteness Theorem from Douglas R. Hofstadter's Godel, Escher, Bach: An Eternal Golden Braid http://isbn.nu/0394756827, one of the magnum opuses of popular math. A more technical introduction is From Frege to Gödel , which I got as "assigned reading" by a client once. http://isbn.nu/0674324498/ It is a "primary sourcebook" . The editor was perhaps more competent as a mathematical logician than as a bodyguard -- he was Trotsky's amanuensis. Van Heijenoort collected in this sadly O/P edition key seminal papers in mathematical logic, to which he added excellent introductions and segues.
[ Thanks to TorgoX for the New Yorker link and bringing this to my attention. ]
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