Over some 20 years, we have developed a diagrammatic quantum formalism, sometimes referred to as quantum picturalism. We showed that this formalism enabled secondary school students to perform exceptionally well on an Oxford University post-graduate quantum exam. It was, in fact, John von Neumann himself who denounced ‘his own’ quantum formalism that relies on Hilbert space. Alternatives had been proposed, including by von Neumann himself, but none play a role in quantum theory today. Quantum picturalism; on the other hand, is not widespread in the quantum industry. The same formalism has been used as the basis for interpretable AI, and even music.