How much better current day physics would have been if it had a axiom set in year 1900, the Maxwell Equations as axioms.
Axiom systems for physics, the 20th century had none and thus physics is at least a 100 years behind of where it should be. That in 1911 with Onnes discovery of superconductivity, if he had known that the Maxwell Equations were the axioms over all of physics, it is highly likely that he would have discovered the true theory of superconductivity-- Malus law theory.
Why would Onnes have discovered the true theory of superconductivity? Because when you have a axiom set over your science, you measure all ideas and facts of the science against that axiom set. That is what we do constantly in mathematics, everytime we wish to make a mathematical proof. So that if Onnes had accept the 1860s Maxwell Equations as the axioms of physics, he would have wanted to peer into the Maxwell Equations to derive Ohm's law, since it talks of resistance. Onnes would then have followed up on all the laws known of photons and matter and would have quickly come upon the Malus law which speaks of a "resistance" to the passage of photons. Onnes would then have derived not only the Ohm's law from Maxwell theory but the Malus law. And in a final step, Onnes would have connected the R, resistance in Ohm's law with the entire Malus law.
When a science has a axiom set hanging over it, then the science is guided to the truth, not misguided by thousands of cranks of physics, each with their own silly likes and favoritism-- some like springs, some like strings, some like toruses, some like "wading in mud to gain mass", some like being on a space elevator to imitate gravity, and all of that is some cranks love of irrelevances to physics.
When physics has a axiom set, then every cranks love of silly things is thrown out the window, and the real work begins-- get it and derive it out of the Maxwell Equations. So that when Onnes discovered superconductivity, if the Maxwell Equations had been the axioms, Onnes would have been compelled to search through the Maxwell Equations.
Now can we compare how retarded mathematics would be if they had no axiom system? Well, we would not have Euclidean geometry, nor the NonEuclidean geometries because we need axioms to pinpoint what is missing. Mathematics would not be coherent, nor consistent, nor tied together in large part. There would be no proofs in mathematics since you eventually have to refer to an axiom set for justification. A mathematics without proofs is like a physics without doing experiments. We did have physics without experiments during Ancient Greek times. I forgotten who is credited with experimentation for physics, was it Roger Bacon in the 1200's?
So what I am saying is that I admit and subscribe to Physics being a experimental science, but that in order for it to be true physics, it must be experimental and arising from a axiom set.
It is hard to say how much stunted and crippled would be mathematics without an axiom system. It would still be a useful and powerful science but mostly a science of rules for calculations and a cottage industry type of science, not unified under a few roofs but tiny cottages of mathematics all over the place.
Physics without axiom system is easy to predict how stunted in growth, because until 2012, physics was without an axiom system and physics was at least 100 years stunted in growth, that it should not have been stunted. Now if someone wanted a axiom system for physics before Maxwell of 1860s, they could have used Newton and in fact they did use Newton, even up to 2012 with a minor fix of relativity. But the sad case of the matter, is that when Maxwell discovered the unified Maxwell Equations, the best in physics should have started the earnest debate of throwing out the Newton axiom system and replacing it with the Maxwell Equations. It was probably premature from 1860s to that of 1900, but when the Michelson experiment ended with the Lorentz transformations and the Poincare Special Relativity noting that the Maxwell Equations were relativistic in the first place. That the Maxwell Equations should have become the axioms of physics by year 1900.
Now if physics had adopted the Maxwell Equations as the axiom system in 1900, the 20th century would not have had a Big Bang theory, nor black holes, nor neutron stars, nor quarks, nor strings, nor Higgs boson, nor Doppler shift of light, nor BCS theory.
There are two major ways that a science is stunted and stalled in growth, 1) it lacks a axiom system to guide it, 2) because it lacks a axiom system, then a lot of fake science is accepted, since it has no true measuring rod of consistency to place it against when experiments could not be made to test those wild ideas masking as physics. For example, if the Maxwell Equations as the axioms of physics had been taken in year 1900, then later in that century, when some physicists crowed about black-holes they would have been tarred and feathered, since black-holes contradict the Maxwell Equations via the Pauli Exclusion Principle which is derived from the Maxwell Equations.
So when a science like physics does not have a axiom set, it leaves itself wide open to poppycock inconsistencies and contradictions and nothing to guide it out of that nonsense.
Google's archives are top-heavy in hate-spew from search-engine- bombing. Only Drexel's Math Forum has done a excellent, simple and fair archiving of AP posts for the past 15 years as seen here: