That ignores/discounts scholarship, which is just plain stupid. It certainly leaves you at the bottom of the heap you are disparaging.

No one disparages the ability to derive functional equations that can stand the test of time. It takes great talent. The problem IMO is that the equations derived would be phenomenological rather than also being based upon logical theory.

Valid logic underpins all valid science. How illogical of you to disparage it.

I consider QM as valid science, but consider it incomplete, and for the most part IMO it is quite lacking in logic. As Richard Feynman said "if you think you understand Quantum Mechanics, then you don't understand Quantum Mechanics."

Name one theory that does that.

None, that's why I used the phrase "in principle."

So math is used to create problems rather than to solve them?

The purpose of math is to solve problems to as much exactness as possible. Problems can arise IMO if equations are derived from observations alone absent theory. The problem then is the practitioner does not know why the equations he is deriving or using should be valid.

Explain how this applies to Darwin, Mendel, Newton, Maxwell, Carnot, Balmer or Lorentz (just to pick a few at random)

Darwin went to the Galapagos as a zoologist. Based upon his observations he developed a clear mental picture of his theory of evolution, clearly explained his reasoning, and provided many great examples in nature concerning his theory and natural selection. Mendel, with his pea plants, also based his theory on solid logic, and showed through experimentation the validity of his theory based upon the probabilities involved while breeding pea plants. Newton was the ultimate scientist. Not only did he theorize in so many fields, but he designed many great experiments to show evidence for his theories, as well as improved equipment (mirrored telescope, prism, etc.) to test his hypothesis and to further gather improved observations and experiments.

Maxwell was a classical scientist. He did the studies and experiments, studied the history of such observations quantitatively and thus developed his theory of magnetism based upon the data and aether theory. His equations have stood the test of time and experimentation and are revered as part of "first principles" in physics along with Newton. His talents are held in the highest regards today. Carnot was both an Engineer and a physicist. He was not well known in his lifetime because he died so young (36), but today is considered the farther of thermodynamics. The core of his ideas and experiments were the bases for those that later developed steam engine technology and later resulted in the concept of entropy. He certainly was a great thinker. But IMO the theory of entropy today involves mistaken concepts.

Balmer was a mathematician and scholar. He didn't marry until age 43, taught at a school for girls until age 60. Both give a clue as to how smart he really was

(my kinda guy). According to my readings he stumbled into atomic physics upon his retirement based upon the suggestions of a friend. After retirement he made his fame based upon his experiments and mathematical talent applied to physics, both spectral emissions and absorptions of atoms resulting in his famous equations based upon atomic phenomenology. As to Lorentz, he was a scholar and scientist of the highest caliber. In school he showed his talents in many fields. After his PhD he took up theoretical physics and helped refine Maxwell's theory of magnetism and his now famous equations. He was an aether theorist like Maxwell and with aether theory developed Lorentz Transforms, the mathematical basis of Special Relativity. He also made significant contributions in the field of hydrodynamics that have stood the test of time.