Recreational Mathematics in the Age of AI
AI is changing mathematics very fast. I personally write papers faster and make far fewer typos. My friends, who are research mathematicians, are scared that they might soon become irrelevant. But what about math majors?
A math degree is extremely versatile. Math majors find jobs in finance, insurance, cryptography, computer science, and so on. Not to mention teaching. Once a lawyer told me that mathematics was the best preparation for arguing cases. Funnily, when I teach my STEP students proof writing, I tell them to imagine that I am a skeptical judge and they want to convince me they are right.
I personally worked as a specifications writer and an analyst. I did that at two different companies, but I was doing the same thing. I had to figure out what the client wanted, then translate it into a precise, high-level specification that programmers could implement. That experience seems especially relevant to working with AI. Before asking for a solution, we need to figure out what the problem is. After receiving a solution, we need to decide whether it actually solves that problem and how to present the solution to other people.
Mathematics is great because it structures the mind. I’ve seen many mathematicians who decided to become programmers and became strong programmers very fast. Being precise and knowing how to follow the logic was great help. I think the value of mathematics is this structured mind.
AI makes answers easier to obtain. But what is left? We still need to learn new things, pose questions, and understand answers. It is also good to be able to explain them. Another very important thing is the process of finding the answer. Here is where recreational mathematics comes in, as it was never primarily about producing new answers.
If these are the goals, then why would students take classes in advanced algebraic geometry that require 3 semesters of prerequisites? Well, I can think of many reasons to take advanced algebraic geometry. However, back to my point: Recreational mathematics allows for serious mathematical thinking without much background. Moreover, recreational mathematics is accessible to more students. In addition, while learning recreational mathematics, people can learn things they would really need in life. Optimal stopping problems, for example, help us understand how to buy a better house. They discuss when we should make an offer and when we should continue looking. Just as importantly, they make us formulate our goals and assumptions. Actually, the experience of recreational mathematics would be great for students beyond math majors.
Plus, recreational mathematics is so much fun! That is not a minor advantage. When outsourcing a solution is easy, we need problems that make us want to do the thinking ourselves.
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