A letter to colleagues

A letter to mathematics and computer science colleagues

Dear Colleagues,

Very recently I wrote to a few friends saying that I expected ChatGPT in its next version becoming able to solve every algebra and calculus problem in A Level (the end of school exams in England) and similar school exams in other countries. For that, ChatGPT simply should be shown how to identify what looks as an algebraic, logarithmic, differential etc. equation or a system of equations or inequalities and plug this thing into one of already existing maths problems solvers, for example, the Universal Math Solver, https://universalmathsolver.com/ — it does more than finding an answer, it produces a complete step-by-step write-up of a solution.

But this important symbolic threshold was passed much earlier than I expected. Conrad Wolfram posted on his blog on 23 March an announcement “Game Over for Maths A-level”, https://www.conradwolfram.com/writings/game-over-for-maths-a-level. A quote:

“The combination of ChatGPT with its Wolfram plug-in just scored 96% in a UK Maths A-level paper, the exam taken at the end of school, as a crucial metric for university entrance. (That compares to 43% for ChatGPT alone).”

This means that undergraduate pre-Calculus and Calculus undergraduate exams will follow quickly.
I think it is dangerous to sit and wait while we are overrun by events. I suggest that we have to address the issues on the global scale: changes in the technological and socio-economic environments of education will soon affect hundreds of millions of children in dozens of countries and later become truly global. It is the scale of the problem which is the issue.

There is nothing special in the ChatGPT, it is only one of a dozen AI systems of enhanced functionality which have suddenly appeared on the market. They are pushed by some of the mightiest transnational corporations to the market where, unlike many other markets, the rules of the supply-side economics apply in their full strength (remember the story of iPod? Or selfie sticks?). It does not matter, what we think and feel about the AI: very soon, it will be everywhere around us. It was Marx who said “supply takes demand, if necessary, by force”. A classical example, which is likely to be reproduced in the case of AI, is the multibillion pet food industry: the concept of pet food was invented and forced on people (now called, in TV commercials, “pet parents”) in the late 1950s by the American meat packing industry which by that time completely saturated the American market (for human consumption) and looked for new directions to expand. For billions of people around the globe, AI will become an intellectual pet food for the masses. And we have to take into account that the supply-side push of the AI on people, is likely to be a total assault, in all spheres of human activity, much wider than education.

In many countries, politicians, state bureaucrats, theoreticians of mathematics education, and school teachers led by them, made everything possible to turn students into a kind of biorobots trained for passing school exams. And here comes the moment of truth: if real robots pass exams with much better marks — what is the purpose of the current model of mathematics education?

And we should not be distracted by general philosophical questions of the kind “can machine learning produce sentient beings?” The real, and immediate issue, is the disruption which will be caused by still non-sentient AI in the human society (made of sentient beings).

It is interesting to glimpse a politician’s view of these issues. Please see below some examples of uses of mathematics as given by Rishi Sunak, Prime Minister of the UK, in his speech on improving attainment in mathematics, 17 April 2023, https://www.gov.uk/government/speeches/pm-speech-on-improving-attainment-in-mathematics-17-april-2023 . Interestingly, the speech was given at the London Screen Academy – this is why examples start with “visual effects”, etc.

You can’t make visual effects without vectors and matrices.

You can’t design a set without some geometry.

You can’t run a production company without being financially literate.

And that’s not just true of our creative industries. It’s true of so many of our industries.

In healthcare, maths allows you to calculate dosages.

In retail, data skills allow you to analyse sales and calculate discounts.

And the same is true in all our daily lives…

… from managing household budgets to understanding mobile phone contracts or mortgages.

With a possible exception of the first line (about visual effects¹), all that in 5 (or at most 10) years from now will be done by a combination of AI and specialist mathematics (or maybe accounting) tools — and done much better than 90% of people can do. For example, an app on a smartphone which has access to all financials accounts of the owner – bank accounts, credit cards, tax account, mortgage, etc. and linked to powerful AI servers on the Internet, will be able to take care of household budgets. This app will ask the user, after each contactless payment in the shop, under which heading this payment should be entered in the ledger of the household budget, offering most likely options (maybe deducing them from the shops’ names, like Mothercare or Bargain Booze).

It is widely accepted now that in most areas of human activity ChatGPT and other AI systems are no more than imposters faking answers to questions they do not understand.

However, routine mathematical by their nature tasks of household budgeting, etc. are likely to be important exceptions — because they are intrinsically well structured and less ambiguous. And AI paired with mathematical problem solving software will pass standard school exams better than students or their teachers can do.

I summarise the situation in three bullet points:

• What we see now is a slow motion car crash of the traditional model of mathematics education. Sunak (and practically everyone in the area of education policy) are asleep at the wheel and do not see the road ahead. But in the education policy, we have to look at least 14 years ahead – this is the length of school education (in the UK), from 4 to 18 years of age.
• Most politicians are able to think ahead only on the time scale of the election cycle, 4 or 5 years. They cannot comprehend the scale of quantities and magnitudes (the latter include time) involved in economic and social problems (and even less so in all the mess around the climate change).
• Most politicians lack basic skills of project management and do not understand that work on a serious project should start with the step-by-step reverse planning from the target to the present position.

This why I appeal to professional mathematicians and computer scientists:

Of all people involved in some way in mathematics /computer science education, you are perhaps the only ones free from mental handicaps listed in the three bullet points above. Let us discuss, at first perhaps only in our circle, this fundamental question:

What kind of mathematics education is needed in the era of AI?

Perhaps we have to split the question:

What kind of mathematics should be taught

(a) To future developers, controllers, masters of AI?

(b) To the general public, the users (and perhaps victims) of AI?

If these questions are not answered in our professional communities, we should not expect an answer coming from elsewhere.

Alexandre Borovik

18 April 2023

http://www.borovik.net/selecta

The Electrician, by Boris Eldagsen. This AI-generated image winning a prestigious Sony world photography award, https://www.theguardian.com/technology/2023/apr/17/photographer-admits-prize-winning-image-was-ai-generated.

 

1But perhaps this is no longer an exception, see a recent scandal: An AI-generated image winning a prestigious Sony world photography award, https://www.theguardian.com/technology/2023/apr/17/photographer-admits-prize-winning-image-was-ai-generated.