I agree with you that the relationship between math and physics is complex and interwined. Some times we should force maths to follow physics.

Differential equations are a very blunt tool of modeling. What I am surprised about is that you did not mention fractional calculus, as a way of revisiting evolutionary equations. While the Schrodinger equation is a reliable work horse, the addition of fractional derivative terms to the Schrodinger DE may allow for exploring as an example Bohmian quantum mechanics from a non linear stand point. We in science have a fixation on the Harmonic oscillator because its a standardized DE , which is easier to solve than say the Van Der Pol equation.

So here is my question. Why the neglect of fractional calculus ?

22 days later

Certainly on topic. A very broad consideration of it. There is no background evidence, or references, or conclusions from argument, The overall impression is of a wish list, That we should avoid subjective bias based on our own preferance ,eg. For beauty is an interesting point. Às is the directions science may have taken without pressure from finding funding,

20 days later

Mohit Das
Important and interesting essay. But I have questions about the problem of foundations of fundamental sciences.
You write:
<<Mathematics provides a language for expressing physical theories, and it allows physicists to make precise predictions and calculations.>>

Why did "trouble with physics" (Lee Smolin "Trouble with Physics"), "crisis of interpretation and representation" (Romanovskaya T.B. "Modern physics and contemporary art - parallels of style" ), "loss of certainty" (Kline M. "Mathematics: Loss of Certainty"), "crisis of understanding" (J. Horgan "The End of Science", Kopeikin K.V. "Souls" of atoms and "atoms" of the soul : Wolfgang Ernst Pauli, Carl Gustav Jung and "three great problems of physics")?

Maybe Whitehead and Wheeler are right after all?
A.N. Whitehead: “A precise language must await a completed metaphysical knowledge.
John A. Wheeler: "Philosophy is too important to be left to philosophers."
Philosophy - the most rigorous Science?
Have you ever dealt with the "problem of the millennium No. 1" - the ontological justification of mathematics (ontological basification)?

<<For example, Euclidean geometry and non-Euclidean geometries use different axioms, but both have applications in physics and engineering.>>

Have you tried to find a single axiom (Meta-Axiom) not only for geometry, but for the entire system of knowledge? (The problem of ontological justification / substantiation of knowledge)

<<...but the concept of STRUCTURE is atrans-disciplinary concept.>>
and then build an ontologically justified single Super Structure as the basis of knowledge (Primordial Generating Structure, "la Structure Mère")?

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