## Sitting down with Arthur T. Benjamin

*in*Sitting Down With

*Professor Arthur T. Benjamin, popularly known as the Mathemagician, is an American mathematician specialising in combinatorics. He occupies the chair of the Smallwood Family Professor of Mathematics at Harvey Mudd College. His adept techniques explore and simplify mathematics’ fun, quirky side. Often regarded as the Bob Ross of Mathematics, learn more about Professor Benjamin’s’s conversation with our team.*

**As one of the most renowned “mathemagicians”, spectators are in awe of what you do. Do you think of it as “just math”, or is it somehow magical to you too?**

I guess I approach it as a skill. I think of it as performing a magic show. Maybe similar to someone who has practised playing the piano and performing in front of a large audience. They are not composing music on the spot; they are just performing something that they have gotten to do very well over the years. So for me, mental math is like my instrument that I am playing for the audience.

**What inspired your interest in the domain of combinatorics?**

Mathematics has many different facets, including those that have nothing to do with numbers, like Geometry, Topology, but the math that I love is very number oriented. Combinatorics is the mathematics of counting. In how many different ways can we seat 20 different people? How many ways can we seat them if there are certain restrictions? Questions like those. I find questions like those very fun and very number oriented. It allows you to think about problems very creatively. I guess it was the mathematics that tickled my brain the most; hence I continue to study it because I like to be tickled, mentally, not physically.

**When it comes to mental maths, how do you think one can train their cognitive faculties to achieve a desired level of speed and accuracy?**

Accuracy comes from understanding the process, and speed comes from lots and lots and lots of practice. Accuracy comes from the technique of squaring a number. You do this, and as you practice more, for example, if someone said what’s 300 times 300, the first time you say that it’s, oh, is it nine thousand? Is it ninety thousand? But after a bit of practice, you know that’s around 90 thousand. But in the beginning, you’re trying to figure out what the sizes of things are; after a while, that’s not a problem; you know the size of the things, and now you have got to get to the exact answer.

**You’ve also been a vocal proponent of creative visualisation as a means to understanding mathematics. To what extent do you think that’s applicable, especially when one moves on to higher studies, for instance, if we take higher-order matrices?**

I think one of the best things about mathematics is that it can be done in a very creative way. There are often many, many different ways to solve them. Whether we’re talking about an arithmetic problem, algebraic problems, or real-life problems, often there are many promising approaches to a problem, and what’s fun about mathematics is that if you can do a problem in different ways, you’ll get the same answer. That’s true for arithmetic as well as for a lot of real-life problems as well. I found that consistency of mathematics to be absolutely beautiful, which I still do now as a mathematician. Again, I think the ability to look at problems from multiple angles is important; it gives you depth. If you can see from different angles, you’ll see different sides of it. You’ll get the big picture of what you got, and I think that’s true, in all areas of mathematics, from arithmetic to matrices to calculus, and I certainly want to send the message that when people see me, they just see the mental math, they don’t see me doing algebra or calculus. I want to send the message that arithmetic is just the beginning, but it’s the beginning for everybody, and if people get turned off even at that first step, then they probably never going to like mathematics at all. If you give them a good first step, I hope they would take the second and third and fourth and fifth steps.

**What would you like to leave as food for thought for the younger generations to ponder upon?**

There is a fun and beautiful side to mathematics that you are probably not exposed to in school. It would be as if in school if the only music they played for you was opera, and that’s all you’ve ever heard of music. You might like opera, but you wouldn’t know about the variety of other music out there. Just because you don’t like opera doesn’t mean you dislike music. Just because a lot of math in school doesn’t interest you, there’s a gigantic part of the fun and beautiful mathematics out there that I hope you get to experience.

**As students of mathematics, we crack a good number of math jokes. How often do you find yourself indulging in some?**

I have certainly heard a lot of math jokes, like, what do you call a hen that counts its egg? A “Mathmachicken”. You know what I’d like to do? I probably have never said this in an interview; I love the musical Hamilton. What I love about Hamilton, you know, is that my daughters learnt the entire musical, including the cabinet meetings between George Washington and Thomas Jefferson, and I was thinking, wow! These kids learn a slightly fictionalized version of American History and get into it. I mean, Alexander Hamilton, before Lin Manuel Miranda, was just some boring guy on a 10-dollar bill, and no one ever knew anything interesting about this guy unless you were a history major. Because of that musical, a whole generation of kids learnt to love a portion of American History. I would love to do and try something like that for mathematics. When I retire, that is one of the things that is on the back of my mind: can we do something that would be interesting enough, cool enough, or popular enough?

I watch kids who invest thousands of hours in memorising rap lyrics, and cricket statistics, and I wonder if only that energy could be channelled into something like mathematics. Oh my God! How brilliant they could become and how good that would be. If I could create something like that or if I create a musical or a book that a generation of kids knew how to prove that there are infinite prime numbers and found that to be astonishing. There is a beautiful side of mathematics that they are not showing you in school. I think that love of mathematics pays so many dividends for science, technology and for the world! Anyway can’t remember what the original question was, but that is something I would love to do for mathematics, that is, create something that is Hamilton-like.

By the way, I think everyone should learn multiplication tables till 10. Do you really need it? Yes. Especially at a young age, you have that. What is an 8-year-old or 9-year-old going to think about anyway? You can use some of their brain cells to master a skill that will be useful for them for the rest of their lives. But make it fun. Don’t make it monotonous. The worst thing that could happen is for people to take my mental math ideas and say, “Now we are gonna make people learn this every night for hours and hours”, and everyone will hate mathematics.

**Given the rise of ChatGPT and Google Bard, do you think that somewhere computational mathematics may find itself somewhat stagnant as human-paced developments would give way to instant artificial intelligence?**

I think we should give it time to evolve. I mean, people made fun of the internet and Google Searches in their infancy. With Wikipedia, they used to be like look at what this says about Mathematics. I think I am not worried about ChatGPT putting mathematicians out of work because they cannot think creatively. It just thinks, “What are the most likely words that can appear out of words that are already here?” and it doesn’t understand what it is saying. It is just saying. You can ask some very basic questions, questions that a child would get right, and ChatGPT would just bluff its way very authoritatively. But again, to succeed in mathematics requires you to think differently. Think outside the box, and think from an angle that has not been explored before, whereas ChatGPT is all about doing what seems to flow the best from what has been written before.

I think as far as technology and mathematics are concerned, no, your advances come from thinking in a new direction, not just thinking in the old direction. I think it is a wonderful tool. It is a wonderful starting point. Let’s say I am trying to write a song about the infinity of prime numbers; I may ask ChatGPT to give me some ideas and rhymes. It’s like asking a friend. At least I am not using it as the authoritative, that this is THE answer. It surprised me that ChatGPT is being used for software development. You can ask, “give me a computer program that will do this.” and maybe partly. This is why we see layoffs in software companies. What took software developers months to develop, you get it instantly, and now you can tweak it. Again it won’t put the entire company out of business because you need people to think in new directions, but a lot of the routine work, forget about mental arithmetic, think about writing code; I think in the past, you could have Googled things and found things around the internet but this thing just gives it to you. It is exciting and scary at the same time.

All these big tech companies, we keep hearing- Microsoft is laying off people; Google is laying off people, and Facebook is laying off people. I don’t think I have heard the full reason.

In the same way, this generation grew up with iPhones and the internet as a way of life. What would the next generation who grew up with ChatGPT be like? Whatever the next big thing is, that is based on these models that are at their fingertips since they were born. People are thinking, how is it going to affect education? It can write a college essay that could get a B. You don’t learn from that.

We academics are wrestling over things anyway; I mean, there are enough sites out there where we can buy answers to homework problems which makes professors say, “What is the purpose of homework?” I hope the purpose is that it makes people think and solidify the concepts better, but do you make it required? Do you give it weight? Ultimately you’ll have to be given tests, offline exams showing what you know at your fingertips, even though that is not very realistic.

**Sir, you’re someone who’s been working with patterns, sometimes recognising some which would otherwise go unnoticed. Have you ever contemplated applying it to the share market?**

Well, there are certainly people who do and there’s a lot of money paid to people who can discover patterns and correlations. Now, if everybody knows that fact, you can’t make money off of it but if you’re one of the first people to make that connection then yes it can be very rewarding. One of the greatest geniuses in financial math was Edward Thorpe, and he had analysed a card game that was played in the casinos called Black Jack and he figured out how to play the game to have an advantage, and the casinos had to change the rules because he’d figured these things out. He later also applied the same ability to optimize to finding things in the stock market to say certain things are worth this much and if people are selling that much then you can make some good money. I am not trained in finance and macroeconomics but I know some people who are very strong mathematically and who’ve gone on to do very well in the financial sector, and it’s really good for people in that sort of field. I used to say if I hadn’t gone into teaching I might’ve gone into financial mathematics and now I’m saying if I hadn’t gone into teaching I might’ve gotten into data science because it defines a lot of things I like to do.

**When one reads about you, one comes across the fact that you’ve been deeply involved with scepticism. ****With due respect, what do you believe is more true about scepticism, is it a constant state of questioning widely accepted standards, or a temporary suspension of belief?**

You know what, I was greatly influenced by another magician by the name of James Randy. He performed as the Amazing Randy. A very successful escape artist and illusionist, but like Houdini, was disappointed in seeing magicians deceive the public using magic tricks represented as legitimate science. Millions believe in communicating with dead people and would spend money on these magicians (or worse). I met him early in my career, as I was starting to perform shows. He got very excited because it allowed him to say that these people are full of it and are not telling the truth, they are making you believe in things that are not true whereas this guy is not cheating. He’s doing amazing things with his mind but he’s not claiming supernatural powers to do it. This is what we should be paying attention to, science is beautiful all by itself and it doesn’t need supernatural mumbo jumbo. If there are things out there that we don’t understand, let’s study and research them.

For instance, in parapsychology, there is not a single repeatable experiment in that field. Does the Extrasensory Perception exist? Probably not, but no one’s been able to measure anything for a little bit of time. As I was transitioning from doing magic onto mentalism, I thought this was magic and I can really pull it off, but after meeting Randy and a few others, I felt guilty that I might be spreading misinformation. After my show, if people thought “Oh my gosh look at that guy he really could read your mind”, I wouldn’t want people to start thinking that was legitimate. I’ve always performed things that for the most part I was willing to explain afterwards. Most magicians would never do that but when it comes to mathematical magic it should be open, there should be no secrets. I think the explanation can be more fascinating than the effect.

Hi, This is Siya!

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