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268
Lothar Goettsche, “A Conjectural Generating Function for Numbers of Curves on Surfaces,” November II, 1997, arXiv.org, Cornell University archives, http://arxiv.org/PS_cache/alg-geom/pdf/9711/9711012vl.pdf.
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269
Ai-Ko Liu, “Family Blowup Formula, Admissible Graphs and the Enumeration of Singular Curves, I,” Journal of Differential Geometry 56 (2000): 381–579.
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270
Bong Lian (Brandeis University), interview with author, December 12, 2007.
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271
Michael Atiyah, “Pulling the Strings,” Nature 438 (December 22–29, 2005): 1,082.
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272
Glennda Chui, “Wisecracks Fly When Brian Greene and Lawrence Krauss Tangle Over String Theory,” Symmetry 4 (May 2007): 17–21.
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273
Sean Carroll, “String Theory: Not Dead Yet,” Cosmic Variance blog, Discover online magazine, May 24,2007, http://cosmicvariance.com.
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274
Edward Witten, quoted in К. C. Cole, “A Theory of Everything,” New York Times Magazine, October 18, 1987.
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275
Ibid.
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276
Alan Guth (MIT), interview with author, September 13, 2007.
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277
Brian Greene, The Elegant Universe (New York: Vintage Books, 2000), p. 261.
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278
Max Tegmark (MIT), interview with author, October 23, 2007.
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279
Faye Flam, “Getting Comfortable in Four Dimensions,” Science 266 (December 9, 1994): 1, 640.
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280
Cumrun Vafa (Harvard University), interview with author, January 19, 2007.
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281
Robbert Dijkgraaf (University of Amsterdam), interview with author, February 8, 2007.
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282
David Morrison (University of California, Santa Barbara), interview with author, May 27, 2008.
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283
Allan Adams (MIT), interview with author, May 23, 2008.
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284
Joe Polchinski (University of California, Santa Barbara), interview with author, August 31, 2007.
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285
Edward Witten (Institute for Advanced Study), e-mail letter to author, January 30, 2007.
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286
Adams, interview with author, May 23, 2008.
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287
Turnbull WWW Server, “Quotations by Gauss,” School of Mathematical Sciences, University of St. Andrews, St. Andrews, Fife, Scotland, February 2006, http://wwwgroups.dcs.st-and.ac.uk/-history/Quotations/Gauss.html.
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288
Ibid.
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289
Brian Greene, “String Theory on Calabi-Yau Manifolds,” lectures given at Theoretical Advanced Study Institute, 1996 session (TASI-96), Boulder, June 1996.
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290
К. C. Cole, “Time, Space Obsolete in New View of Universe,” Los Angeles Times, November 16, 1999.
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291
Andrew Strominger (Harvard University), interview with author, August 1, 2007.
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292
Morrison, interview with author, May 29, 2008.
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293
Brian Greene, Elegant Universe (New York: Vintage Books, 2000), pp. 268, 273.
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294
Paul Aspinwall (Duke University), interview with author, June 6, 2008.
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295
Morrison, interview with author, May 27, 2008.
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296
Andrew Strominger (Harvard University), February 7, 2007.
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297
Chris Beasley, Jonathan Heckman, and Cumrun Vafa, “GUTs and Exceptional Branes in F-Theory — I,” November 18, 2008, http://arxiv.org/abs/0802.3391; Chris Beasley, Jonathan Heckman, and Cumrun Vafa, “GUTs and Exceptional Branes in F-Theory — II: Experimental Predictions,” June 12, 2008, http://arxiv.org/abs/arxiv:0806.0102; Ron Donagi and Martijn Wijnholt, “Model Building with F-Theory,” March 3, 2008, http://lanl.arxiv.org/pdf/0802.2969v2; and Ron Donagi and Martijn Wijnholt, “Breaking GUT Groups in F-Theory,” August 17, 2008, http://lanl.arxiv,org/pdf/0808.2223vl.
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298
Strominger, interview with author, July 23, 2007.
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299
Cumrun Vafa (Harvard University), interview with author, November 2, 2007.
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300
Leonard Mlodinow, Euclid's Mirror (New York: Simon & Schuster, 2002), p. 255.
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301
Edward Witten (Institute for Advanced Study), e-mail letter to author, February 12, 2007.
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302
David Morrison (University of California, Santa Barbara), interview with author, May 27, 2008.
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303
Ravi Vakil (Stanford University), interview with author, May 28, 2008.
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304
Strominger, interview with author, August 1, 2007.
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305
Piers Bursill-Hall, “Why Do We Study Geometry? Answers Through the Ages,” lecture, Faulkes Institute for Geometry, University of Cambridge, May 1, 2002.
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306
Donald Zeyl (University of Rhode Island), interview with author, October 18, 2007.
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