On $E_\infty$-spaces and $E_\infty$-ring sectra:
On the relation between the practice of mathematics and physics (for historical context see Hitchin 20, Sec. 8):
Arthur Jaffe, Frank Quinn, “Theoretical Mathematics”: Towards a cultural synthesis of mathematics and theoretical physics, Bulletin of the AMS, Volume 29,Number 1, July 1993 (arXiv:math/9307227)
we claim that the role of rigorous proof in mathematics is functionally analogous to the role of experiment in the natural sciences (Jaffe-Quinn 93, p. 2)
On rigorous mathematics and formal proof:
Frank Quinn: Proof Projects for Teachers (2009) [pdf, pdf]
Frank Quinn, A Revolution in Mathematics? What Really Happened a Century Ago and Why It Matters Today, Notices of the AMS (2012) $[$pdf$]$
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