Gödel's Lasting Legacy

Austrian logician Kurt Gödel’s incompleteness theorems showed us the limitations of mathematics within mathematics. While math is still useful for proving scientific theorems, Gödel transformed the perception of pure mathematics in a way that still makes modern mathematicians uncomfortable. Here, leading thinkers—a mathematician, a philosopher, and a physicist—wrestle, almost literally, with the implications of Gödel’s legacy.

Original Program Date: June 4, 2010

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[KingThallion]

I heard a short description of The incompleteness theorem, but nothing on lasting legacy.  

[arijit]

as Gödel also said the problem with us is we stipulate everything in a closed system..

we're inside the system, we belong to here..
we ask to follow a machine with a predefined statement a+b=b+a
so why it always satisfies the axiom

Simply, we used to prove the stability always, we never run for or worry about the instability..
this is why we had a chapter in higher mathematics, it's called inequality..

we truly don't know why can't we prove 2+2≠5
must be some limitations
limitations of algorithm

of course we are getting modern & advanced but still are the victim of parallax & conundrum ✓

[Neueregel]

Nice review of Gödel's theorem. In 1930, Kurt Gödel's just debunked Cantor, Hilbert and all other proponents of completeness .