Still in CBM Denial as Computers Take Over Another Step of the Maths Process?
Humans and Maths: From 4/4 to 3/4 to 2/4 of the Process?
I characterise the computational or maths process as 4 step. (If you haven’t come across this central theme of The Math(s) Fix before, here’s a quick description.) And the central problem with our mainstream maths education has been the failure to recognise that step 3—compute—has been almost completely taken over by computers in real life…and that totally changes the what, when and how.
Big news for 2023 is that ChatGPT and, more generally, LLMs are rapidly computerising step 2—abstract—too. Up to now, abstraction has been largely a human activity of turning what you defined in English (if that’s your chosen language) into “maths” or, nowadays, computer code. But what’s remarkable is how ChatGPT is doing an impressive job of this step, at least for smaller cases for the moment, but already beyond the level that most citizens can operate at.
(In fact, ChatGPT or FactGPT, as we increasingly call ChatGPT + Wolfram, may also increasingly assist with step 4—interpret—too but I’ll concentrate on step 2 for this post.)
Good News, If We Don’t Botch the Educational Changes
This is a dramatic moment for universalising deployment of the computational process and it’s critical we don’t botch handling it. If we do it right, it’s really rather good news.
Here’s why. At the moment, ChatGPT does a pretty good job of writing programs, though not perfectly and not necessarily precisely what you had in mind. So rather than you writing code or maths expressions from scratch, our new-found AI capability can often give you at least a good first pass (and this will only improve as LLMs develop and become seamlessly hybrid with other technologies, like our Wolfram ones). Therefore, in the future, you may need to fulfil more the role of an “abstraction editor” than a code writer to use the powerful computational problem-solving system.
Early stage “Chatbooks” combining ChatGPT, Wolfram Language and abstraction editing.
This in turn means that many more people in society will be able to use the power of coding, abstraction, and therefore the computational process; even if they’re already such users, they’ll be able to use it more often and at lower time/cost.
Competently used, the computational process often achieves higher-fidelity decisions (or indeed an answer at all). This can be hugely empowering, both economically and societally significant. But like all powerful tools, if misused or misunderstood, it can be dangerous. Education and realistic experience are key.
Maths v. Maths Chasm Gets Deeper
There’s nothing new in that message. It’s exactly what I said in The Math(s) Fix but now the chasm between maths in education and maths or computation in the real world is even more pronounced (and blindingly obvious). It made no sense 20 years ago to have students expend huge effort on learning how to solve quadratic equations by hand, out of any practical context to their lives, when they should have been taking harder real-life problems, deploying computer-based maths on them with whichever abstraction was needed.
By last year, when most were learning online some of the time through a computer, it was obviously crazy: the computer is central to doing the maths, so it shouldn’t be there to instruct the student how to do maths that assumes it’s not there! If you have a computer, use it for computing!
By 2023, with ChatGPT, now even the abstraction can be assisted, if not done entirely by the computer, opening up far more real-life context far earlier—a completely different subject. Every effort is now needed for steps 1 and 4 of the process and much on managing step 2, alongside step 3.
More pressure for change. More urgent to move. Every curriculum authority, every university needs to be evaluating this change now.
Yet most of the educational establishment remain in CBM denial. Time to face down the hand-calculating maths brigade.