So there you have it. Hundreds of pages and more than 3000 diagrams later, we've told you (pretty much) everything we know about quantum theory and diagrammatic reasoning. So, where to now? Is it time for everyone to start covering blackboards and filling papers with diagrams? Of course!

But even better, what if someone else did all the diagrammatic proving for you while you sit back, relax, and have a beer? That's even better! The fact that the diagrams we use are essentially made up of a finite number of ingredients (namely, spiders) means they are particularly well suited to automated reasoning. In this subfield of artificial intelligence, one develops software that allows a computer to do a whole range of things often associated with human mathematicians: from simply checking mathematical proofs for correctness to automatically searching for new proofs or even new and interesting conjectures to then try and prove automatically.

In the past, automated reasoning has typically concerned traditional, formula-based mathematics built on formal logics and set-based algebraic structures, and there it has been very successful. It has provided us with tools called proof assistants, which allow us to automatically construct proofs of mind-bending results, such as Gödel's incompleteness theorems, and rigorously check proofs that are way too big for a human mathematician to get totally correct, like Kepler's conjecture, the four-colour theorem, and the Feit– Thompson theorem (famously massive proofs in geometry, graph theory, and group theory, respectively).

In addition to serving essentially as ‘robot teaching assistants’, which tirelessly check the work of human mathematicians, techniques from automated reasoning can actually tell us something new, via conjecture synthesis. Much as a human mathematician would discover features and behaviours of an unfamiliar mathematical creature by ‘poking at it’ (i.e. making educated guesses about how it will behave and trying to prove them), there exist automated techniques that do this at high speed. When it succeeds in a proof, the result is a freshly minted theorem that no human has ever seen or even thought to ask about.