18

Andre Nikolaevich Kolmogorov, Mathematics of the 19th Century (Birkhauser, 1998).

19

Deane Yang (Polytechnic Institute of New York University), e-mail letter to author, April 20, 2009.

20

Mlodinow, Euclid's Window, p. 205.

21

Brian Greene, The Elegant Universe (New York: Vintage Books, 2000), p. 231.

22

C. N. Yang. “Albert Einstein: Opportunity and Perception,” speech, 22nd International Conference on the History of Science, Beijing, China, 2005.

23

Chen Ning Yang, “Einstein’s Impact on Theoretical Physics in the 21st Century,” AAPPS Bulletin 15 (February 2005).

24

Greene, The Elegant Universe, p. 72.

25

Robert Greene (UCLA), interview with author, March 13, 2008.

26

Lizhen Ji and Kefeng Liu, “Shing-Tung Yau: A Manifold Man of Mathematics,” Proceedings of Geometric Analysis: Present and Future Conference, Harvard University, August 27-September 1, 2008.

27

Leon Simon (Stanford University), interview with author, February 6, 2008.

28

Greene, interview with author, March 13, 2008.

29

Cameron Gordon (University of Texas), interview with author, March 14, 2008.

30

Robert Geroch (University of Chicago), interview with author, February 28, 2008.

31

Edward Witten (Institute for Advanced Study), interview with author, March 31, 2008.

32

Edward Witten, “A New Proof of the Positive Energy Theorem,” Communications in Mathematical Physics 80 (1981): 381–402.

33

Roger Penrose, “Gravitational Collapse: The Role of General Relativity,” 1969, reprinted in Mathematical Intelligencer 30 (2008): 27–36.

34

Richard Schoen (Stanford University), interview with author, January 31, 2008.

35

Demetrios Christodoulou, The Formation of Black Holes in General Relativity (Zurich: European Mathematical Society, 2009).

36

John D. S. Jones, “Mysteries of Four Dimensions,” Nature 332 (April 7, 1998): 488–489.

37

Simon Donaldson (Imperial College), interview with author, April 3, 2008.

38

Faye Flam, “Getting Comfortable in Four Dimensions,” Science 266 (December 9, 1994): 1640.

39

Ibid.

40

Mathematical Institute at the University of Oxford, “Chart the Realm of the 4th Dimension,” http://www2.maths.ox.ac.uk/~dusautoy/2soft/4D.htm.

41

Grisha Perelman, “The Entropy Formula for the Ricci Flow and Its Geometric Applications,” November 11, 2002, http://arxiv.org/abs/math/0211159vl.

42

Eugenio Calabi (University of Pennsylvania), interview with author, October 18, 2007.

43

Robert Greene, interview with author, April 17, 2008.