Why Learn Mathematics in the Age of AI?
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| Image by Bkrmadtya Karki from Pixabay |
Question: “Why learn maths when AI can solve all the problems?”
In this post, I will be writing my thoughts on the topic and giving my answer, as it currently stands. Spoiler: My answer is “It is still worth our while learning maths, not because we can find the answer to any particular problem, but because of the person it helps you become.” Note that I am writing from the point of view of a secondary school teacher who works with students in Grades 7 to 12. Whether you are in my shoes, those of a learner or of a parent, I invite you to come up with your own answer and share it in the comments.
Humans are curious
As human beings, we are innately curious about the world in which we live. We want to observe the repeating patterns of fern leaves and we want to know whether this phenomenon is unique to them or if it exists elsewhere.
Humans have always wanted to study the locations of stars relative to the earth. They have calculated the trajectories of planets. Centuries later, we used this knowledge to place objects in space.
Previous generations asked “How could we represent all numbers using only zeroes and ones?” They had no practical reason to do that. When time came for us to create an electronic computer, we found that using strings of zeroes and ones to represent every number and every letter was very efficient, and that this representation lent itself to the use of electronic on-off switches.
Others among our ancestors pondered the properties of prime numbers. Again, they did so out of sheer curiosity. Then came the need for secure communications between government agencies, banks and their customers and social media users with Instagram servers. Prime numbers and their properties became part of modern-day cyber security. Every time you log on to see your social feeds, the security of your communication with the site is achieved using mathematical insights. One of them is the fact that it is easy to multiply two large prime numbers, but it is terribly difficult for a hacker to work out what primes we used by looking at the result of the multiplication.
Enjoyment in difficulty
If your idea of an enjoyable day is one spent fishing, you may buy a boat, maybe sonar equipment to help you locate the fish, but would you buy a robot to take the boat out, do the fishing and return home with a boat-load of fish?
In the same way, curious people have invented games like chess, sudoku and cryptic crosswords. In such games, the difficulty is the point. Imagine reading the clue “Icon distributed money (4)” and having AI tell you the answer. Where is the fun in that? Compare this with thinking:
‘Distributed’ is asking me to rearrange the letters of ‘icon’. The resulting word must mean money. I got it, the answer is ‘COIN’.
In the same way, we can solve maths problems for the joy of it. If you don’t believe me, take a pencil and paper and attempt to answer this question, then take a look at this full explanation to see if you got it right.
A rabbit can hop either 1 or 2 steps at a time. Faced with 10 steps, in how many ways can the rabbit reach the top of the stairs?
To understand the world and, most importantly, to avoid being misled by political and commercial interests, it is imperative to understand statistics. We need to know how biases can be introduced, whether deliberately or through carelessness, at the point of choosing survey respondents or in the way that data is presented with graphs. We need to be able to challenge conclusions based on some knowledge of how statistics are carried out.
Needless to say, some nimbleness with numbers can help us shop better. A colleague of mine, Caroline, once bought an item at Myer in the Melbourne CBD. Since I don’t remember the exact numbers, let’s say that the item’s price was $100. It was on a 20% sale that day and my colleague had a $50 voucher on her. The teenage register attendant deducted the $50 voucher from $100 and then proceeded to apply the 20% discount to the remaining $50. Caroline gently pointed out the erroneous method, but the young attendant insisted that it wouldn’t make a difference! Being a skilled maths teacher came in handy to Caroline! She helped the teenager understand that the discount would be halved if applied to half of the item’s price, resulting in a final price of $90 rather than the correct $80.
The addition of AI to our lives adds another reason: Can you tell whether an answer provided by AI is reasonable? Unless you have some idea of the range of reasonable answers, you won’t be able to tell when AI makes a mistake.
Like all human endeavours, mathematics involves tradition: The art of passing the practices of one generation to the next. In a moving interview about the impact of AI on mathematics, Cornell professor, Steven Strogatz, holds back tears as he describes the following photo of Hungarian mathematician Paul Erdős with the then ten-year-old Terence Tao, in Adelaide, Australia. It is much more powerful to listen to the next minute from where this link starts off, but here is an excerpt of Strogatz’s words:
There’s a picture of little Terry Tao, who is often called the Mozart of math because he was a child prodigy … It’s so sweet, this generational passing. You see the picture of old man Erdős with his grey hair. The two of them are sitting together with their paper and pencil, such nerds with very serious faces. Terry Tao is like eight-years-old [sic]. Two great mathematicians working together, happy as clams, on some real world, inconsequential problem, for the pleasure of being together.
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| Photo of Paul Erdős (left) and Terence Tao (right), CC BY-SA 2.0, via Wikimedia Commons |
Our forebears discovered much mathematics. Thanks to their work, we now trust the bridges on which we drive and the buildings in which we live and work. Thanks to them, I can type this article and you can read it. You are feeling happy to be reading my post, aren’t you?!
In my opinion, the best answer to the question, “Why learn something as hard as Calculus or Algebra?” is “Because it is one of the greatest achievements of the human mind!”
Mathematics for human flourishing
The heading of this paragraph is the title of a beautiful book written by mathematician Francis Su. In the book, Su states, “If you ask me, ‘Why do mathematics?’ I will say this: ‘Mathematics helps people flourish’.”
A feature of Su’s book is that it includes letters, written from prison, by Christopher Jackson. In them, Jackson describes teaching himself mathematics from the basics to university level. As the book progresses, we see the discoveries that Jackson makes: The creativity, friendship and empowerment that come with the discipline of learning mathematics.
Su’s argument is that learning mathematics is a great way to develop habits of mind, which he calls virtues. In an article on his Substack, entitled The enduring value of math in an age of AI, Su writes:
If your future job depends only on skills, that job is in jeopardy in the AI revolution.
Virtues, on the other hand, are aspects of character that you build. These are habits of mind or dispositions that become second nature as a result of doing math regularly—like being creative, or seeing a problem from multiple points of view, or being persistent in problem-solving, or being less fearful of getting stuck and knowing how to chew on a hard problem for a while. Or experiencing joy when you see a beautiful idea.
What else can I possibly add after those wise and beautiful words? I simply repeat my invitation to share your own thoughts in the comments.
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