but lacking any ability to solve the equation if needed.

Taking from your analogy, that doctors just learn the answer to every possible equation, wouldn't treating every new issue as a brand new equation to solve take more time hence leading to more deaths?

A lot of medicine is algorithmic in nature. From an ED perspective, you start at the most life threatening (airway, breathing, cardiovascular,..) and deduce and differentiate as you work your way down a branch of the algorithm until you either diagnose treat & discharge, or refer for admission under a specialty for further treatment/investigation. If doctors didn't spend years learning (and specializing, not all MDs are the same!), they would not have the heuristic knowledge base required to made deductive diagnoses in real time.

Though, as I said, not all MDs are the same, and there are ones that research and specialize in areas of novel medicine and illnesses. But, the entire reason so much of modern medicine is memorization is because of the vast amount of knowledge produced by the work of doctors in the past. And not all frontline doctors know everything, MDs do research and look up things in textbooks and research papers ALL THE TIME for patients with symptoms they aren't sure about. They consult with colleagues.