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spend more than 100 billion dollars each year on basic research: I’ve based this assertion on chapter 4 of a report from the US National Science Foundation [144]. According to numbers included in that report, the US government spends 39 billion dollars each year on basic research. The report does not directly compute total worldwide governmental spending on basic research, and so the figure of 100 billion dollars is an estimate, based on several other numbers from that report.

p 206: The Daniel Hillis quote “there are problems that are impossible&0;. . .” is from page 157 of Stewart Brand’s book The Clock of the Long Now [27].

Appendix

p 211: A gentle introduction to the density Hales Jewett (DHJ) theorem, including on explanation of the concept of combinatorial lines, may be found in [66].

p 212: For Szemerédi’s theorem, see [218]. The Green-Tao theorem is proved in [84].

p 212: The original proof of DHJ was in [66].

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