Scientists have a history of trying — and failing — to link biology and quantum mechanics. The real connection between them may be in the math.

T wo decades ago, scientists seemed on the verge of understanding biology in a new, quantum way.

Life unfolds over an incomprehensible span of scales, from our planet-enveloping biosphere at one end, to individual cell-building biomolecules at the other. Even at its most microscopic, though, biology doesn’t really reach down to the quantum realm, in which particles act like waves, become entangled with one another, and exist in superpositions of multiple states at once.…