Word: statement
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Dates: during 1990-1999
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...thus, in one of the keenest insights in the history of mathematics, Godel devised a remarkable statement that said simply, "X is not an M.P. number" where X is the exact number we read when the statement "X is not an M.P. number" is translated into Martian math notation. Think about this for a little while until you get it. Translated into Martian notation, the statement "X is not an M.P. number" will look to us like just some huge string of digits--a very big numeral. But that string of Martian writing is our numeral for the number...
...thinking of theorems as patterns of symbols, Godel discovered that it is possible for a statement in a formal system not only to talk about itself, but also to deny its own theoremhood. The consequences of this unexpected tangle lurking inside mathematics were rich, mind-boggling and--rather oddly--very sad for the Martians. Why sad? Because the Martians--like Russell and Whitehead--had hoped with all their hearts that their formal system would capture all true statements of mathematics. If Godel's statement is true, it is not a theorem in their textbooks and will never, ever show...
...STATEMENT "I was a small-business person, a home builder...
...STATEMENT] "I'm a Vietnam veteran--one of the lucky ones...
...STATEMENT] "I lived on a farm...[My father] taught me how to clean out hog waste with a shovel and a hose...