Fine older review by Jaron Lanier of two books that have been out for awhile, and worth looking into if you've never read them: "Meta Math! The Quest For Omega" by Gregory Chaitin, and "The Lifebox, the Seashell, and the Soul: What Gnarly Computation Taught Me about Ultimate Reality, the Meaning of Life, and How to Be Happy" by Rudy Rucker:
http://www.americanscientist.org/bookshelf/pub/two-philosophies-of-mathematical-weirdness
Toward the end of the lengthy review, Lanier summarizes thusly:
"These two books are near opposites even though they appear to explore similar topics. Chaitin loves negative results and is thrilled by the prospect of future generations of mathematicians finding ever weirder math. The Chaitinesque intellectual future will be eternally youthful and anarchic. Neither mathematicians nor computer scientists will settle down into a single preferred pattern of thought. Rucker, in contrast, is reaching as high as he can to try to use available computer science and math metaphors to create a new, comprehensive, multidisciplinary sensibility. The Ruckerian future is one in which new guiding explanatory ideas will connect all areas of intellectual curiosity."(Of these two works, I enjoyed Chaitin's volume more than Rucker's, but it's largely a personal preference, and I've enjoyed some of Rucker's other books more than this particular one.)
And a bit more current, Murray Bourne's latest "IntMath Newsletter" is up here (with a little something for everybody who enjoys math):
http://tinyurl.com/2euddty
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