Interview: Problem solving with the world’s greatest mathematician

Published Sep 29, 2022, 6:30 PM

Professor Terence Tao is regarded as the world’s greatest living mathematician. Originally from Adelaide, he was doing university level maths by age 9.

He joins Sean Aylmer from the US to discuss how problem solving can help business, and what we need to do to improve Australia’s mathematical prowess.

Welcome to the Fear and Greed daily interview. I'm Sean Aylmer. Something very different today. My guest this morning is a maths genius, simple as that. Professor Terence Tao was a child prodigy in Australia who then completed his PhD in mathematics at UCLA in the United States at the age of 20. At 31, he received the Fields Medal regarded as the Nobel Prize of Mathematics, and has been the author or co- author of more than 350 research papers and 18 books. Students travel from around the world to learn from him at UCLA. He's regarded as one of the great mathematicians alive today, but he's on a mission to simplify maths, to make it more accessible, and to show exactly how it can be used for problem solving and creative thinking. He's recently been named Global Australian of the Year for 2022, recognizing the influence of Australian expats who are leading the way on the global stage. Professor Terence Tao joins me this morning. Professor Tao, welcome to Fear and Greed.

Thank you. Nice to meet you.

That is quite an incredible story. You were studying university level maths by the age of nine. When did you realize that you were really good at maths?

Well, I've always enjoyed maths. Apparently when I was two years old, this is before I actually could remember anything, my parents told me that they caught me at friend's place trying to teach some older kids, like four or five, how to count using number blocks. And apparently I had taught myself this from watching Sesame Street.

Wow. Obviously you had a very accelerated maths education, but you learned it the traditional way. Counting blocks, watching Sesame Street, et cetera. Just probably younger than most of us, but it was the traditional way.

Pretty much. My mother was a high school maths teacher before she moved to Australia, and so she did teach me a little bit of maths when I was growing up. But I devoured maths workbooks and so forth. I remember when I was seven or eight, if I was getting rowdy or something, my parents would give me a book of sums to do, and I just liked filling in all the boxes. Seven plus eight equals... I always liked numbers and symbols and things with a right answer and a wrong answer.

Yeah. What was that like growing up that good at maths? Because what I really want to get on to is education, maths education in Australia, at school level and also beyond. Undoubtedly, if Australia can be great in those STEM subjects, Australia can be great as a nation. I think no one's going to dispute that, and I think part of what you are trying to do is help that along. But as an individual in a country like Australia, going to high school, being good at maths probably wasn't cool, shall I say, Professor Tao?

Well, I was too young to really notice what was cool and what was not. But my maths teachers, I think, quickly realized that the material they were teaching in my year was not advanced enough for me. So they talked to my parents and the parents talked to the headmaster and so forth, and they eventually arranged this complicated scheme where I would take some classes in my home year, and then I would take some advanced maths and science classes three, four, five years ahead. Which meant that when I was in primary school, I would take some classes at the local high school. And when I was in high school, I would take some classes at the local uni. So that worked out well for me. So I was in classes that most of the other kids were maybe four or five years older than me. I remember when I first took Year 12 maths, they had to keep a special cushion in the classroom, because I couldn't reach the desk without it.

What a great story. So just going from that, you are obviously a true believer in mathematics. How important is it that Australia gets good at maths and science and engineering and technology?

Well, I think maths is now pervading every area of human endeavor, really. Like for example, if you take advertising. It used to be that if you want to create a good ad, you can eyeball it and maybe do a few surveys to see whether your ad is resonating with this target audience and so forth. But now it's become a really precise science. You can do all kinds of machine learning and data crunching and you can put out test versions of your ad, slightly different changes in different audiences. It's kind of scary actually, just how much more effective it becomes. But that's just one example. I think every field has become more quantitative, and you need people who have some idea of how numbers work.

As we become more quantitative, which is a great way of putting it, it means that we need people to understand numbers, as you put it. Do you think the way we teach maths at the moment in primary school, in high school can get us there? Or do we need to change the way we do it?

I think we do need to move with the times. There's a traditional list of topics in mathematics. So there's arithmetic, and then there's algebra, and there's calculus, and trigonometry and so forth. And these are still important. But nowadays, a lot of maths used in the real world, we use statistics, we use probability, there's something called discrete maths. The type of maths that shows up is a little bit different. Already at the uni level, the curriculums are slowly changing. At the primary school level, I'm not sure. Part of the problem is that the teachers won't have advanced maths training themselves often. So it's the teachers that really make all the difference.

Stay with me, Professor Tao. We'll be back in a minute. I'm speaking to Professor Terence Tao, mathematician and Global Australian of the Year. I have children in high school at the moment, and when I went through high school, maths was my thing, not English. You were either maths or English, and maths was my thing. It's funny, my kids are much more English oriented, and their ability in maths is pretty much totally proportional to the teacher, whether or not they liked the teacher. And it's a worry, in a sense.

Yeah, well, that's our culture. In some other countries, parents put more pressure on their kids. Like in Asia where these tiger mom stereotypes, where if you get anything less than an A or something in your class, there's a disaster. One thing I've certainly noticed when teaching in Australia is that kids follow their interests. And if they find that the teacher is boring or something, you can't just tell them, " Oh, this would be good for you later." It has to appeal to them. My favorite teacher in high school was my physics teacher. He cracked jokes and he turned all his exams into stories. He was obsessed with ants, actually. At least in his exams. So all the stories would be like, there's an ant climbing this hill at a certain slope, at a certain speed. What happens to the ant? And so forth. I actually looked forward to his exams just to read the stories.

Yeah. What he's doing is doing something very identifiable with what can be a fairly abstract art, which is maths, making it quite identifiable to someone sitting there in a classroom.

Right. Yeah. It's all too easy to view maths as some sort of sorcery. We have all these formulas that almost seem like magic spells from a Harry Potter movie, like the quadratic formula or something. And that can make you kind of terrified when you use maths and you're worried that you're going to get the spell slightly wrong and it will be a big disaster. If you want to make something your own, you have to play with it. So at home I would play with my calculator and try to find patterns in numbers and so forth. Once you tinker with something, then it doesn't seem scary. So I guess it's just to make it seem familiar and connected with the real world.

Professor Tao, earlier this year you started teaching an online masterclass on mathematical thinking, how to apply it to problem solving. Can you give us a taste of what that covers?

Yeah. So it's about two hours long, into little bite- sized pieces of 10 minutes of me talking and maybe working through some, not so much maths problems, there's no equations or anything scary. But just to give one example. So one of the things I talk about in the class is how mathematicians use analogy. If you have a problem which is alien and you don't know how to start, if you can find an equivalent problem in a different context, but it's more familiar to you, you can solve that problem. So for example, the US Army in the 50s had this issue. They wanted to test soldiers for, I think, syphilis. And there was a blood test for this, but it was quite expensive. So a hundred soldiers administering a hundred blood tests for syphilis was very expensive. And they wanted to know if there was a more efficient way to do it. They eventually realized that what they should do is what is called group testing. Instead of testing each sample separately, they mix the samples, maybe 10 or 20 samples together at a time, and test the entire group as a whole, as a batch to see if one of the soldiers in that group had the disease. And then if they do, you can just focus on that group and then subdivide it again. This problem is equivalent to that of guessing a number. So suppose one of these 100 soldiers has a disease, but you don't know which one. That's like you have a number from one to 100 and you have to guess what it is. And that's a game of 20 questions. That's something that we know how to do. I think there's even these board games, like Guess Who? So if you have a number from one to 100, you can ask, " Is it less than 50?" And that corresponds to taking the first 50 soldiers and just testing that as a batch. And then if it is less than 50, you ask, " Is it bigger than 25? Less than 25?" And it turns out that you can basically identify the people with the disease in only seven or so tests this way.

Okay, Professor Tao, I want to bring this to business. What can business learn from this way of thinking, this way of thinking about mathematics?

So every so often, sometimes there are these business fads, like these (inaudible) models and so forth, where people try to be quantitative and actually not just follow their instinct, but try to make some precise process to arrive at their decision. And it's well intentioned, but I think sometimes these formulas, they're teaching maths where you're taught the formulas, but you're not really taught why they work. So you have this 12- step procedure to arrive at a decision and you just follow all the steps. But sometimes in some context, these steps are not actually relevant. But if you don't actually have quantitative training and quantitative thinking, you can't really examine the assumptions, and you're just following these rules because that's what some authority told you to do. So having quantitative thinking skills, it's a toolkit that allows you to understand why things are the way they are.

Which is good for every business.

Yeah. Yeah.

Professor Tao, thank you for talking to Fear and Greed.

Yeah, no, you're welcome.

That was Professor Terence Tao, mathematician and Global Australian of the Year. This is a Fear and Greed daily interview. Remember, this information is general in nature and you should seek professional advice before making any investment decisions. Join us every morning for the full episode of Fear and Greed, Australia's most popular business podcast. I'm Sean Aylmer. Enjoy your day.