biology can’t proceed by deduction the way mathematics does. “Understanding the mechanism” in biology usually only goes down to a certain level: we know which target a drug acts on and which pathway it activates, but why that ultimately produces the therapeutic effect often can’t be fully explained. Metformin is a case in point: after decades of research, its mechanism is still debated. If “someone understands the mechanism” were a precondition for using a drug, many good drugs could never be used at all.
This exposes exactly where Tao’s analogy breaks down. The slide comes from his “Math 2.0” talk, and what he really cares about is mathematics: if AI generates proofs and Lean verifies them, do we still need human understanding? In mathematics, understanding is attainable, because mathematics is deductive and a correct proof can, in principle, be read and understood by a person. So in mathematics it is reasonable to require that “at least one person understands it.” But when he uses drugs as the analogy, he carries a standard that is feasible in mathematics over into a field where it often can’t be met. In biomedicine, what can substitute for “understanding” is not deeper mechanistic research but more empirical evidence.
Sous les ors des Bourbons, quelques braises veillaient ;
Dans la nuit des sociétés, on se jurait l'aurore.
Ils pensaient qu'un serment ferait trembler les palais ;
Mais la France était vaste, et la nuit tenait encore.
——GPT