An Interview with Gaurav Suri
We interviewed Gaurav Suri, author of A Certain Ambiguity, by phone on November 9, 2014
G – Gaurav Suri, W – William Campillo, S – Steven Mijajlovic
S - One of the first things that comes to our mind is, what essentially motivated you to write this book?
G - For me the motivation of the book was a childhood love of mathematics and a strong interest in philosophy. And philosophically, I became more and more interested in questions about epistemology, which is a field that thinks about how do we know the things that we know, and as I thought about what we really knew, I realized that probably one of the fields of knowledge which we are most certain is mathematics. That early love of mathematics had undoubtedly influenced me into thinking that way, but I thought if I’m interested in really saying something about what do we know and how do we know it, mathematics is a great way to investigate that question or to think about that question. That was the motivation for the book. When I started the book I did not even know that we would publish it as a novel, it started as an examination about what do we know and how do we know it.
W - The novel format widens your audience, and I wonder who this book was intended for?
G - The audience of this book is anyone who has the openness to perceive the beauty and importance of mathematics. But, we came with no conception of people having a sense of prior training in mathematics. My co-author Hartosh (Hartosh Singh Bal) and I thought that It should be accessible to anyone with a middle school background in mathematics, but we wanted people who were interested in ideas and who weren’t averse to mathematics. So I would say the audience is people who are open to mathematics and philosophical curiosity. We realized that this could span kids from 15 years old all the way to people getting into mathematics after a long time gap. It was not an age sort of thing we had in mind, but much more an openness to mathematics and philosophical curiosity.
W - There seems to be an idea of the limitless, a theme of infinity, why choose that theme for the book?
G - Actually there are two themes going through the book. One is a theme on Euclidean Geometry, and the other is infinity, set theory and infinity. The reason to choose the Euclidian geometry piece is that human notions of proof started with geometry, and it’s really interesting to play with that because if there is something that is certain it is that the angles of a triangle equal one hundred eighty degrees, for example, as Euclid proves. The reason to choose the infinite part of the book, was that as mathematics was developed we have been able to find or seek certainty in ideas that are more abstract, or seemingly more abstract than triangles on paper. It is also a beautiful theory of mathematics, and I also thought that it connected with some philosophical and religious ideas that we were setting up in the book. So for those reasons it made sense to include infinity as a parallel theme.
S - To build on that idea, was there any intention behind the cover art of an infinity symbol, or depending on interpretation a Mobius strip, and a cyclist?
G - I’ve always liked that symbol. It was intended to be the infinity symbol, but can be interpreted as a Mobius strip. It was a design that said, look, we are thinking about infinity in this book, and in some sense this quest for knowledge and understanding is also a long term infinite quest. There was definitely that angle.
W - There is also the figure of a bicycle rider in that graphic which must be the main character, Ravi, who rides a bike in several parts of the book. Are any of his experiences based on your life or are any of the other characters from the book based on some of the people you have run into in your lifetime?
G - You might say that some of Ravi’s experiences are ones of my own. Any character that you write about is an amalgamation of people you have encountered, because how would we know people otherwise.
W - The teacher is an interesting character and seems to be very influential. Did you have a mathematics teacher like that - a person who helped mold who you are and helped you make decisions?
G - I did. This was at Purdue University in Indiana, he was professor C. D. Alaprantis, who taught me real analysis, a branch of mathematics, and his style and aesthetics about mathematics really profoundly influenced me. I kind of modeled the character of the teacher after that real life teacher. In a sad kind of twist what had happened about two years after the book came out, professor Alaprantis’ daughter called me and told me he was very sick and he was dying, but he had a chance to read through the book and often she would read him the book. Yes, professor Alaprantis was the model for the character Nico Alaprantis and I’m glad the real inspiration behind the character saw some image of himself however imperfect in the book.
W - Are you currently a teacher?
G - I am a researcher at Stanford University. it’s a part of my job to teach, but my main function is, my interest in philosophy and decision making has led me to study neuroscience and research neuroscience, and that’s what I do currently. And it’s also at Stanford University which is also the setting for the book.
W - Somewhere in the epilogue there is mention of being the best teacher you can be and I wonder if through this book you are also looking at teaching important mathematical ideas which have shaped us and shaped important philosophies?
G - Yes, this is most relevant to our conversation. My own experience with mathematics came about from other people, teachers and friends Teachers because they have inspired me to see mathematics for almost being an art form, for being profoundly beautiful and profoundly meaningful. And friends because we did mathematics together. I think other people, especially teachers are really important in helping kids see that this is one of the heights of human pursuits. It’s the hallmark of civilization in some ways. I’m not saying it’s the only hallmark. There are many hallmarks - science, art, music and many other things in our culture. But one of the hallmarks, in my eyes, of civilization is mathematics, Teachers being able to open students to perceiving this as the beautiful and meaningful and worthwhile journey I think is really important. I’m grateful to my teachers and we certainly hope that we have enough of a feel for this so that younger readers of this book would feel inspired to be open to mathematics and especially if it is done in a context of teaching, where they have support from teachers. That would be great.
S - It’s interesting that you speak of the younger readers. After I read the number trick from Bauji in the first chapter, a few days later our math team met and I presented that problem which the students thoroughly enjoyed, there were a few students who figured it out after thirty minutes but most of them left feeling that frustration. Many of them came in throughout the week and shared their thoughts and it was interesting to see their thought processes. To see that perseverance and problem solving reminded me of how it developed in the character Ravi.
G - That’s really great to hear, and that’s a nice little puzzle. I think you bring up a point that I think is often missed in mathematics and the teaching of mathematics. It is that mathematics should be given as problems and the role of a teacher is, I think, to figure out how much scaffolding each student must be given. So some students may require a great deal of scaffolding, because of their background, there can be many reasons. So a teacher saying let’s think about the factors to one kid and saying what happens when you multiply something by one thousand and one to another kid, I think is entirely right and proper and in fact is the role of a teacher. I’m delighted that you had that experience which I think is an important one.
S - I’m curious about “Bauji’s” character. Was he based on your own grandfather? Were there different characters who were woven together to make him up?
G - My maternal grandfather, he was referred to as “Bauji”. I never knew him, He died when I was three years old, but what I heard about him was an inspiration for the mathematician character, but he wasn’t a mathematician he was a medical doctor. Parts of him, I guess, were based on perceptions of what my grandfather must have been like.
W - I wonder how long you thought about these mathematical ideas before you decided to write about the thoughts that are in this book?
G - I think the curiosity about whether mathematical questions are certain, meaning, if there are people in other planets would their mathematics look exactly like ours, or is mathematics a human enterprise, varied with culture, and that mathematical truths are a product of human biology. This question has been with me for a long time. I always used to talk to friends of mine, including Hartosh, the co-author, and ask is it true in some sense that there is an infinite number of primes in every universe, meaning all alien civilizations must come to the same conclusion that there is an infinite number of primes? The answer is tantalizing and I never quite figured it out. In a sense we thought about the book for a long time. The actual writing of the book was surprisingly efficient. Once we decided this was going to be a book it went really fast. I think we wrote it end to end in a year and a half maybe two years.
W - What other kinds of things do you wonder about?
G - Well when I do mathematics it seems really natural. It seems that I’m thinking about real things, just like you can think about bridges or engines and cars and whatnot. When I do mathematics it feels like a real thing, like you’re working with real notions and yet when I think about doing mathematics it seems a lot more tied to our brains and who we are as a species. Thinking about that led me to thinking about the nature of our brains, how we see patterns - how we see connectedness in things and thinking about us. What does it mean for something to be true? What is the nature of truth and how is it connected to our biology? These are things that I wonder about.
W - I was instantly interested in your book as soon as I opened the front cover to find a foreword by Keith Devlin. I recently read his book The Math Gene in which he writes about some of the ideas you just talked about, especially how the mathematician’s mind works. He equates mathematics to gossip. Is this how your mind processes mathematical ideas?
G - I’ve read the math gene and I’ve had the opportunity to spend some time with Keith. He has a really terrific idea. I think the notion of mathematical concepts, some people see them as gossip, it’s interesting because that notion is a fluid notion, it almost always varies with people. Richard Simon, the American physicist, he used to say when someone was describing a model to him he would construct the reality of that model in layers. He would imagine a truck and he would see the properties of the truck, so - one property would be the color is blue and another property is the yellow stripes on the side and then pretty soon he would be building this picture. Then a person would say something that would counter the model, the properties and the model that he already had, and he would say something like, “no, but that’s yellow”. The guy would have no idea of what Richard was talking about, but Richard was building the physical model of abstract ideas So people think about mathematical ideas differently, and what’s fascinating is how predictive mathematics is, how beautifully mathematics works in the universe, there would be no real reason for mathematics to work in the universe but it does.
W - A big moment in the book is when Bauji, the grandfather, receives a news report of Eddington’s expedition to a remote island so that he could observe light coming from stars around the sun during an eclipse. Was it this event, this time period, meant to coincide with the year for the grandfather’s jailing?
G - Yes, it was an exciting time in human history. Einstein had come out with his theory of general relativity, it was the first time that general relativity was tested, and general relativity was basically a theory which was based on mathematics. The mathematics around general relativity is beautiful. In fact somebody had asked Einstein, “what would you have done if it turned out that Eddington’s measurements around the eclipse showed that general relativity was not true”. Einstein said, “well I would have felt sorry for God. The meaning of that statement is that Einstein saw the beauty of the mathematics and would have been disappointed if that beauty did not describe the actuality of how the universe works. I think that’s a really interesting insight into the nature of mathematics and how people do mathematics.
S – I’m interested in how you inspire students you encounter, your colleagues, and children with mathematics. How do you motivate them and peak their curiosity about mathematics?
G - I think that this is a crucial question because in mathematics education there are two sort of orthogonal things that need to be done. One of the vectors is that if you learn mathematics, one needs to learn the language of mathematics, that one needs a lot of drilling in mathematics. I have an eleven year old son and I often will sit down with him as he does his math homework and I realize that kids have to be drilled into learning how to add fractions, figuring out what decimals really mean, how percentages work. These are the tools, the basic tools of conceptualizing and learning the language of mathematics - so that’s one way. The other vector which is equally important, maybe more important, is to see that mathematics is beautiful, and you do that with puzzles and you do that with games. You do that in a way that really captures the interest. You have to do both and one can be a lot of fun, but if you haven't done the first one, meaning the drilling, then you can’t have the fun. So, I think the challenge in inspiring young people is to realize that mathematics requires a foundation, not to ignore that foundation but also not to ignore what makes it beautiful. I think it must be both and a good teacher, or somebody who wants to inspire people (to study math) should be aware that there are these two dimensions of learning and appreciating mathematics.
G – Gaurav Suri, W – William Campillo, S – Steven Mijajlovic
S - One of the first things that comes to our mind is, what essentially motivated you to write this book?
G - For me the motivation of the book was a childhood love of mathematics and a strong interest in philosophy. And philosophically, I became more and more interested in questions about epistemology, which is a field that thinks about how do we know the things that we know, and as I thought about what we really knew, I realized that probably one of the fields of knowledge which we are most certain is mathematics. That early love of mathematics had undoubtedly influenced me into thinking that way, but I thought if I’m interested in really saying something about what do we know and how do we know it, mathematics is a great way to investigate that question or to think about that question. That was the motivation for the book. When I started the book I did not even know that we would publish it as a novel, it started as an examination about what do we know and how do we know it.
W - The novel format widens your audience, and I wonder who this book was intended for?
G - The audience of this book is anyone who has the openness to perceive the beauty and importance of mathematics. But, we came with no conception of people having a sense of prior training in mathematics. My co-author Hartosh (Hartosh Singh Bal) and I thought that It should be accessible to anyone with a middle school background in mathematics, but we wanted people who were interested in ideas and who weren’t averse to mathematics. So I would say the audience is people who are open to mathematics and philosophical curiosity. We realized that this could span kids from 15 years old all the way to people getting into mathematics after a long time gap. It was not an age sort of thing we had in mind, but much more an openness to mathematics and philosophical curiosity.
W - There seems to be an idea of the limitless, a theme of infinity, why choose that theme for the book?
G - Actually there are two themes going through the book. One is a theme on Euclidean Geometry, and the other is infinity, set theory and infinity. The reason to choose the Euclidian geometry piece is that human notions of proof started with geometry, and it’s really interesting to play with that because if there is something that is certain it is that the angles of a triangle equal one hundred eighty degrees, for example, as Euclid proves. The reason to choose the infinite part of the book, was that as mathematics was developed we have been able to find or seek certainty in ideas that are more abstract, or seemingly more abstract than triangles on paper. It is also a beautiful theory of mathematics, and I also thought that it connected with some philosophical and religious ideas that we were setting up in the book. So for those reasons it made sense to include infinity as a parallel theme.
S - To build on that idea, was there any intention behind the cover art of an infinity symbol, or depending on interpretation a Mobius strip, and a cyclist?
G - I’ve always liked that symbol. It was intended to be the infinity symbol, but can be interpreted as a Mobius strip. It was a design that said, look, we are thinking about infinity in this book, and in some sense this quest for knowledge and understanding is also a long term infinite quest. There was definitely that angle.
W - There is also the figure of a bicycle rider in that graphic which must be the main character, Ravi, who rides a bike in several parts of the book. Are any of his experiences based on your life or are any of the other characters from the book based on some of the people you have run into in your lifetime?
G - You might say that some of Ravi’s experiences are ones of my own. Any character that you write about is an amalgamation of people you have encountered, because how would we know people otherwise.
W - The teacher is an interesting character and seems to be very influential. Did you have a mathematics teacher like that - a person who helped mold who you are and helped you make decisions?
G - I did. This was at Purdue University in Indiana, he was professor C. D. Alaprantis, who taught me real analysis, a branch of mathematics, and his style and aesthetics about mathematics really profoundly influenced me. I kind of modeled the character of the teacher after that real life teacher. In a sad kind of twist what had happened about two years after the book came out, professor Alaprantis’ daughter called me and told me he was very sick and he was dying, but he had a chance to read through the book and often she would read him the book. Yes, professor Alaprantis was the model for the character Nico Alaprantis and I’m glad the real inspiration behind the character saw some image of himself however imperfect in the book.
W - Are you currently a teacher?
G - I am a researcher at Stanford University. it’s a part of my job to teach, but my main function is, my interest in philosophy and decision making has led me to study neuroscience and research neuroscience, and that’s what I do currently. And it’s also at Stanford University which is also the setting for the book.
W - Somewhere in the epilogue there is mention of being the best teacher you can be and I wonder if through this book you are also looking at teaching important mathematical ideas which have shaped us and shaped important philosophies?
G - Yes, this is most relevant to our conversation. My own experience with mathematics came about from other people, teachers and friends Teachers because they have inspired me to see mathematics for almost being an art form, for being profoundly beautiful and profoundly meaningful. And friends because we did mathematics together. I think other people, especially teachers are really important in helping kids see that this is one of the heights of human pursuits. It’s the hallmark of civilization in some ways. I’m not saying it’s the only hallmark. There are many hallmarks - science, art, music and many other things in our culture. But one of the hallmarks, in my eyes, of civilization is mathematics, Teachers being able to open students to perceiving this as the beautiful and meaningful and worthwhile journey I think is really important. I’m grateful to my teachers and we certainly hope that we have enough of a feel for this so that younger readers of this book would feel inspired to be open to mathematics and especially if it is done in a context of teaching, where they have support from teachers. That would be great.
S - It’s interesting that you speak of the younger readers. After I read the number trick from Bauji in the first chapter, a few days later our math team met and I presented that problem which the students thoroughly enjoyed, there were a few students who figured it out after thirty minutes but most of them left feeling that frustration. Many of them came in throughout the week and shared their thoughts and it was interesting to see their thought processes. To see that perseverance and problem solving reminded me of how it developed in the character Ravi.
G - That’s really great to hear, and that’s a nice little puzzle. I think you bring up a point that I think is often missed in mathematics and the teaching of mathematics. It is that mathematics should be given as problems and the role of a teacher is, I think, to figure out how much scaffolding each student must be given. So some students may require a great deal of scaffolding, because of their background, there can be many reasons. So a teacher saying let’s think about the factors to one kid and saying what happens when you multiply something by one thousand and one to another kid, I think is entirely right and proper and in fact is the role of a teacher. I’m delighted that you had that experience which I think is an important one.
S - I’m curious about “Bauji’s” character. Was he based on your own grandfather? Were there different characters who were woven together to make him up?
G - My maternal grandfather, he was referred to as “Bauji”. I never knew him, He died when I was three years old, but what I heard about him was an inspiration for the mathematician character, but he wasn’t a mathematician he was a medical doctor. Parts of him, I guess, were based on perceptions of what my grandfather must have been like.
W - I wonder how long you thought about these mathematical ideas before you decided to write about the thoughts that are in this book?
G - I think the curiosity about whether mathematical questions are certain, meaning, if there are people in other planets would their mathematics look exactly like ours, or is mathematics a human enterprise, varied with culture, and that mathematical truths are a product of human biology. This question has been with me for a long time. I always used to talk to friends of mine, including Hartosh, the co-author, and ask is it true in some sense that there is an infinite number of primes in every universe, meaning all alien civilizations must come to the same conclusion that there is an infinite number of primes? The answer is tantalizing and I never quite figured it out. In a sense we thought about the book for a long time. The actual writing of the book was surprisingly efficient. Once we decided this was going to be a book it went really fast. I think we wrote it end to end in a year and a half maybe two years.
W - What other kinds of things do you wonder about?
G - Well when I do mathematics it seems really natural. It seems that I’m thinking about real things, just like you can think about bridges or engines and cars and whatnot. When I do mathematics it feels like a real thing, like you’re working with real notions and yet when I think about doing mathematics it seems a lot more tied to our brains and who we are as a species. Thinking about that led me to thinking about the nature of our brains, how we see patterns - how we see connectedness in things and thinking about us. What does it mean for something to be true? What is the nature of truth and how is it connected to our biology? These are things that I wonder about.
W - I was instantly interested in your book as soon as I opened the front cover to find a foreword by Keith Devlin. I recently read his book The Math Gene in which he writes about some of the ideas you just talked about, especially how the mathematician’s mind works. He equates mathematics to gossip. Is this how your mind processes mathematical ideas?
G - I’ve read the math gene and I’ve had the opportunity to spend some time with Keith. He has a really terrific idea. I think the notion of mathematical concepts, some people see them as gossip, it’s interesting because that notion is a fluid notion, it almost always varies with people. Richard Simon, the American physicist, he used to say when someone was describing a model to him he would construct the reality of that model in layers. He would imagine a truck and he would see the properties of the truck, so - one property would be the color is blue and another property is the yellow stripes on the side and then pretty soon he would be building this picture. Then a person would say something that would counter the model, the properties and the model that he already had, and he would say something like, “no, but that’s yellow”. The guy would have no idea of what Richard was talking about, but Richard was building the physical model of abstract ideas So people think about mathematical ideas differently, and what’s fascinating is how predictive mathematics is, how beautifully mathematics works in the universe, there would be no real reason for mathematics to work in the universe but it does.
W - A big moment in the book is when Bauji, the grandfather, receives a news report of Eddington’s expedition to a remote island so that he could observe light coming from stars around the sun during an eclipse. Was it this event, this time period, meant to coincide with the year for the grandfather’s jailing?
G - Yes, it was an exciting time in human history. Einstein had come out with his theory of general relativity, it was the first time that general relativity was tested, and general relativity was basically a theory which was based on mathematics. The mathematics around general relativity is beautiful. In fact somebody had asked Einstein, “what would you have done if it turned out that Eddington’s measurements around the eclipse showed that general relativity was not true”. Einstein said, “well I would have felt sorry for God. The meaning of that statement is that Einstein saw the beauty of the mathematics and would have been disappointed if that beauty did not describe the actuality of how the universe works. I think that’s a really interesting insight into the nature of mathematics and how people do mathematics.
S – I’m interested in how you inspire students you encounter, your colleagues, and children with mathematics. How do you motivate them and peak their curiosity about mathematics?
G - I think that this is a crucial question because in mathematics education there are two sort of orthogonal things that need to be done. One of the vectors is that if you learn mathematics, one needs to learn the language of mathematics, that one needs a lot of drilling in mathematics. I have an eleven year old son and I often will sit down with him as he does his math homework and I realize that kids have to be drilled into learning how to add fractions, figuring out what decimals really mean, how percentages work. These are the tools, the basic tools of conceptualizing and learning the language of mathematics - so that’s one way. The other vector which is equally important, maybe more important, is to see that mathematics is beautiful, and you do that with puzzles and you do that with games. You do that in a way that really captures the interest. You have to do both and one can be a lot of fun, but if you haven't done the first one, meaning the drilling, then you can’t have the fun. So, I think the challenge in inspiring young people is to realize that mathematics requires a foundation, not to ignore that foundation but also not to ignore what makes it beautiful. I think it must be both and a good teacher, or somebody who wants to inspire people (to study math) should be aware that there are these two dimensions of learning and appreciating mathematics.
