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“Mirror symmetry is concerned with counting the number of holomorphic curves on Calabi-Yau manifolds, i.e. compact Kähler manifolds X with trivial canonical bundle KX.”

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Robbert Dijkgraaf

[Mirror symmetry and elliptic curves by Robert Dijkgraaf, The moduli space of curves, 149–163, Progress in Mathematics, vol. 129, Birkhäuser Boston, 1995, 10.1007/978-1-4612-4264-2_5]

“The last two years have seen the emergence of a beautiful new subject in mathematical physics. It manages to combine a most exotic range of disciplines: two-dimensional quantum field theory, intersection theory on the moduli space of Riemann surfaces, integrable hierarchies, matrix integrals, random surfaces, and many more. The common denominator of all these fields is two-dimensional quantum gravity or, more general, low-dimensional string theory.”

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Robbert Dijkgraaf

[1992, Intersection Theory, Integrable Hierarchies and Topological Field Theory by Robbert Dijkgraaf, Fröhlich J., ’t Hooft G., Jaffe A., Mack G., Mitter P.K., Stora R. (eds.), New Symmetry Principles in Quantum Field Theory, NATO ASI Series (Series B: Physics), vol. 295, 95–158, Springer, Boston, MA, 10.1007/978-1-4615-3472-3_4]

“I would be willing to bet that whatever formulations of quantum field theory we have now are preliminary ...”

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Robbert Dijkgraaf

[The Universe Speaks in Numbers: Robbert Dijkgraaf and Edward Witten in Conversation, 30 May 2019, YouTube, https://www.youtube.com/watch?v=RjthuCDzAnY] (quote at 7:18 of 21:39)