In pure subjects like math/logic, you have no observations, at least not really. Everything is abstract. Theorems follow the nomenclature of "hypothesis" and "conclusion" as if it's mimicking science, but every provable/disprovable statement in math, though it can be observed, formalized, and proved or disproved with enough effort or luck, is nevertheless merely a logical consequence of the axioms you started with. Theorems may provide insights, but they don't discover anything new. The conclusions of theorems are logically equivalent to the axioms. That's the essence of what it means to prove, mathematically.
Whereas, in a science, there is no underlying theoretical truth. The only truths are quasi-truths that you develop based on observation and experiment, but they can all change tomorrow with a new experiment that is not beholden to any historical science precedent.
Math/logic: everything is entirely based on axioms. The notion of "discovery" and "testing" of theorems is a cognitive fiction. Observation is merely the human process of deciding what things to try to prove. Everything is backstopped by abstract axioms and logic.
Science: everything is entirely based on observation. The claim of scientific "truth" is a human fiction. We can never be absolutely sure of anything in science. There is no abstract truth backstopping science.
Caveat: this does not imply anyone should be disputing scientific truth for practical purposes in everyday life. Disputing scientific consensus because it's not philosophically true is the refuge of spiritual quacks, religious apologists, and even rational people who are too in love with philosophy to take a step back and consider whether their philosophy is practical. "Oh, gravity isn't really true; quantum field theory isn't really true." Okay then, have fun not being able to move because you're floating in the air, and have fun without all modern electronics because they depend on the physics you're disputing, and have fun trying to find water with your dowsing rod.
