A letter to mathematics and computer science 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.
Added on 19 April 2023:
I got a response to my text from a good colleague of mine, Bill Lionheart, a brilliant, and really applicable, applied mathematician (inverse problems and mathematical tomography, with a fantastic range of applications, from medical stuff to control of any kind of industrial bulk material flows in pipes, say, grain in grain pumps, to airport security scaners to land mine clearance) .
Bill run some bits of my my text by ChatGPT and got this reply:
ChatGPT and Wolfram Alpha are two technological innovations that have had a significant impact on mathematics education, particularly in A-level math. These tools have revolutionized the way students learn and solve mathematical problems, providing them with a wealth of information and resources to help them excel in their studies.ChatGPT is a large language model that has been trained on a vast corpus of data, including textbooks, articles, and other relevant information. It is designed to understand natural language input and generate human-like responses to queries. ChatGPT has made it easier for students to access information about mathematical concepts, theories, and formulas quickly. It can answer questions on any topic related to mathematics, from algebra and geometry to calculus and statistics.With ChatGPT, students no longer need to spend hours flipping through textbooks or browsing the internet for answers. They can simply ask the tool a question, and it will provide a detailed explanation or solution. This has made math more accessible to a wider audience, including those who previously struggled with the subject.Wolfram Alpha, on the other hand, is a computational knowledge engine that provides answers to a wide range of mathematical questions. It uses a vast database of algorithms and data to provide accurate and reliable answers. Wolfram Alpha can perform a wide range of mathematical operations, including symbolic and numerical computations, solving equations, and graphing functions.Wolfram Alpha has made it easier for students to visualize and understand complex mathematical concepts. For example, students can enter an equation, and Wolfram Alpha will generate a graph of the function, making it easier to see its behavior and understand its properties. This has helped students to better understand the relationship between different mathematical concepts and apply them to real-world problems.The impact of ChatGPT and Wolfram Alpha on A-level mathematics has been significant. These tools have helped to democratize access to mathematics education by providing students with easy access to information and resources. They have also made math more engaging and interactive, allowing students to explore mathematical concepts in a more meaningful way.Moreover, these tools have also helped to improve student performance in math. With ChatGPT and Wolfram Alpha, students can quickly and easily check their work, ensuring that they have not made any errors. This has helped to reduce the number of mistakes made by students, leading to better grades and more confidence in their abilities.
In conclusion, ChatGPT and Wolfram Alpha have had a significant impact on A-level mathematics education. These tools have made math more accessible, engaging, and interactive, helping to improve student performance and understanding. As technology continues to evolve, it is likely that we will see even more innovations that will further enhance the teaching and learning of mathematics.
18 April 2023
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.