The analytic tradition failing to grasp properly mathematics, and its relation to physics, deterring people from conducting the most appropriate Friedmanian meta-scientific work. What stopped people realising that mathematics concerns ideas of space, symmetry, quantity, extension, classification, etc.? Between logic and physics
Its failure to take category theory seriously as a radical change of point of view. This is partly due to the idea that if something can be rewritten in an existing language, e.g., set theory, then it’s not new. Of late we see many ways in which higher category theory is revealing itself as a revolution.
The failure to see the proper value of type theory.
Maths and physics failing to talk (1930s-1970s).“I am acutely aware of the fact that the marriage between mathematics and physics, which was so enormously fruitful in past centuries, has recently ended in divorce”, Freeman Dyson, Missed Opportunities, 1972. Joint work since then often category theoretic, mirror symmetry, string duality (Kontsevich, Witten, etc.) “The marriage between gauge theory and the geometry of fiber bundles from the sometime warring tribes of physics and mathematics is now over thirty years old. The marriage brokers were none other than Chern and Simons. The 1978 paper by Wu and Yang can be regarded as the announcement of this union. It has led to many wonderful offspring.” (K. Marathe, Topics in Physical Mathematics, 2010, p. xi). “The love affair between math and physics has turned from a fling into a serious, committed relationship.” (Jeff Harvey, Strings 2011).
The idea of gruppenpest.
Quantum mechanics not being philosophically grounded by meta-scientific work
Weyl and von Neumann changing their minds on mathematical foundations