Part of the reason that the formal, natural connections between mathematics and physics are rejected as significant by most physicists is because the the two fields are so firmly intertwined at the most basic levels that the epistemological becomes confused with the ontological.

In fact, it is not that mathematics underlies physics and it isn’t that they look the same because mathematics is only our tool to examine physics with. It’s that the same fundamental principles – laws which are both natural AND mathematical – underlie them both. But we shouldn’t be surprised at this.

Human concepts of number and maths developed from experience and observation of the real world: geometry can be developed from both theory AND by measuring the physical world; counting systems are based on measuring and comparing the physical properties of different groups of the same or equivalent physical objects.

It’s not so much that either maths or physics underlie the other, it’s more that they develop from the same first principles, and are parts of the same thing. There’s only a single ‘sum total of existence’: you can define the mathematical concept 1, physically. And the first law of thermodynamics can be expressed as 1a+2a=3a.

Issues of efficiency act as constraints on how mathematical complexities develop naturally from first principles into a physical spacetime. These constraints are the difference which leads to a separation of human abstract mathematics from physical mathematicality.

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