God and Math: Embracing Mystery

Bryan:

Well, it's Tuesday and that means we have a very special bonus topic for our listeners today. On the show today, I've got my, one of my best friends in the whole world, Dr. Sathyan Devadas. Now we call him Sadi. He, he and his family, Sadi, you and your family still laugh whenever we call you this, but it's what we called you in college

Satyan:

That's right.

Bryan:

and it's what we still call you today. So what here, before I get into introductions and Sadi, you can explain who you are and why you're so smart. I think. our listeners need to understand what we're going to be talking about today. Today's topic is great for skeptics. It's great for people who are trying to understand God. You're still trying to decide if you believe in Jesus, if you believe in God. Now we're not going to specifically get into that. What we're going to talk about today is how math is really a metaphor for a pursuit of God. In fact, more specifically, how a pursuit of mathematics, which is what Sadi has done your whole life, you've pursued mathematics. You are a. one of the best professors in math in the whole country, the smartest guy that I know. And yet, in your pursuit of math, you have understood a few things that we're going to unpack today. You've understood, number one, that there will always be mystery. As smart

Satyan:

That's

Bryan:

as

Satyan:

right.

Bryan:

you are, that pursuing math is a journey, not a destination, and the same is true for a pursuit of God. Number two, that it's beautiful, it's not just useful. that it's not just about a utilitarian, like what does it matter for me and how can it impact my life today? Even though both of us are really into utilitarianism, it's beautiful and that's true of math and it's also true of a pursuit of God. And then really the last thing we're probably gonna get to if we even get there today, Sati, is that math can't prove the existence of God. You know, that it's not because of math that you're a follower of Jesus and maybe we'll get to all of those things. But before we do that, Why don't we start with the technical stuff, Sadi, and tell us who you are and why are you the smartest guy that I know?

Satyan:

Yeah, I think that's maybe because you don't know too many people, right? That's my that's my background, but I That's

Bryan:

All of my

Satyan:

right.

Bryan:

other friends are dumb.

Satyan:

I grew up in India I was born and raised there and then I eventually landed in the Chicago area where you and I went to college together where we Went to high school in different high schools But then met met up in college and then you went to grad school In math and I went to grad school math and I I went to Johns Hopkins in Baltimore got a PhD there and then taught at Ohio State for a little bit. There's a college called Williams College, which I think is one of the best schools in the nation. I was there for about 15 years, and I really learned the line between teaching and creating. What does it mean to create new mathematics? And what does it mean to teach mathematics? Not just teach to students, but to bring the unsolved, the wonder and the mystery that mathematicians do as a professional to create new mathematics, to bring it to students and to anybody in the world. And so that line I really learned when I was in the East Coast for about 15 years. And then during that time I bounced around, I was a visiting professor for a year at Berkeley, I was at Ohio State for a year. I'm right now at UC San Diego, University of California at San Diego for a year on sabbatical. I was at Harvey Mudd, I was at Stanford for a year. And then over time after Williams, I just landed in San Diego now. And I'm a professor at the University of San Diego. I have a kind of a long title associated to my name, but it just means that I can play. I'm allowed the chance to play, which is what my dream is.

Bryan:

And that's what I love about you, Sadi, is that for as smart as you are, you are one of the most playful, inquisitive, hilarious, I would almost say bordering on immature people I've ever met. And I love that about you that, that you've got this incredible brilliance. And I think our listeners are going to see that. And yet you and I can just revert back to our college days, whenever we're hanging out. And I

Satyan:

Yeah.

Bryan:

love that about you. A couple more things I need to fill in. on your CV and it's that you're an inaugural fellow of the American Mathematical Society. And you've won two national teaching awards from the Mathematical Association of America. So you really are kind of a big deal. And any of your former students that are listening, I'm sure that you were their favorite professor. I know that anyone that's listening today would probably wish that they would have had you as a math professor, because I know for me and for you both, I think the reason we both took to math isn't just because we were... We were... kind of naturally good at it. It's because we had great teachers.

Satyan:

That's

Bryan:

And you

Satyan:

right.

Bryan:

know, your dad was a math professor, was one of our math professors. He was a great teacher. And you and I have both had great teachers in junior high and high school and in college. And a lot of our listeners probably didn't have great teachers.

Satyan:

Yeah.

Bryan:

Not to blame the teachers, but I do think the way we present matters. I think the way, you know, I think that math kind of like faith is... is something that you can catch more than it can, it can be caught more than it can be taught.

Satyan:

Yeah.

Bryan:

That the buy-in that the teacher has or the preacher has or the disciple has, or your parents have or your friends have or whatever, whatever they buy into, is something that you tend to buy into if it seems attractive. And that's what I love about your approach to math, as far as accomplished as you are, that really your goal is to provide access to all of math, right? Your goal is

Satyan:

Yeah.

Bryan:

to make math attractive and joyful. And for some of our listeners, those words are not words that they would associate with math.

Satyan:

Yeah, I mean, I'm surprised that anybody's actually still listening to this podcast after they saw the word math, you know, appear in the title, because it is, I mean, it could be just you and me and my mom, you know, who knows who's listening to this right now. But it's just more than any discipline I know more than any subject I know. It has caused the most pain and the most bitterness in people, because I think going back to what you're saying, Brian, it's very much like like a language that you learn. And imagine you're taking Spanish, right? You took the first year of Spanish, it was great. And somehow you missed like part of the second year of Spanish for some reason, like it didn't click for you. And then if you're in Spanish three and Spanish four and the fifth year, the fact that you didn't have that good second year, you always feel like you're an outsider, right? Like everybody else is doing something. And it could be something simple. Like your teacher could say like pass the bread and everybody else in the class is doing it because they had second year Spanish. And then you're just out for that one year, maybe you had a poor teacher for second year. And then you don't even know what they're saying. Hey, what do you mean past? It's a simple action, just past the bread, right? And because of that, you feel like a failure. You feel like, oh my gosh, I don't know this at all. And then society just pounds you with the fact that how important math is in so many ways and how some people get it and some people don't. And it's just that one poor year. Most of almost anything like history, it doesn't build so intensely. If you didn't understand the Cold War, hey, you could still get the Civil War. Things still kind of go on. But somehow in math, you feel like you're kind of out of that loop and you feel like you're not in the thing. So my goal is to realize that there's so much brokenness in the world today when we talk about math. And you and I, that's right, you and I and your brother, the three of us, we're kind of lucky once we had this great sense of community and we had great teachers. who even if we had those holes in our lives, were very merciful and graceful to us and kind of walked with us to plug those holes. And they just made us feel like, hey, it's okay, man. You'll make it to the next step. Just cover these things rather than just push ahead.

Bryan:

Yeah. In fact, one of those holes for both of us is when we are first class that we took together our freshman year of college was calc three.

Satyan:

That's

Bryan:

And

Satyan:

right.

Bryan:

as we sat in that, do you remember this study? As we sat in that class, we realized that the professor was talking about things that we didn't, we had never studied before because we basically are, are AP testing. landed us into calc 3, but little did we know that we'd never really technically taken calc 2. And so we had to go back and fill in those holes, but

Satyan:

That's right.

Bryan:

it was good that we could do it together, that we could do it in community. But so many people, if they feel like, I don't get what you're saying right now, they just give up on it. You know, and this isn't

Satyan:

That's

Bryan:

just true

Satyan:

right.

Bryan:

in math. I think this is true in faith. I think some people

Satyan:

Yeah.

Bryan:

might try church, they might go to church or might try to go to a small group or mentor or whatever. And they're in it and they're like, there's something that it seems like everyone else picked up on and I missed.

Satyan:

That's right. I

Bryan:

And

Satyan:

think

Bryan:

a lot

Satyan:

especially-

Bryan:

of people then just stop pursuing because

Satyan:

Yeah.

Bryan:

they feel like they're missing something. They've got a gap. And I would, whether it's math or faith, I would say don't, don't give up so easily on it, right? Like

Satyan:

Yeah, I think it's especially

Bryan:

hang

Satyan:

true.

Bryan:

in there and figure it out.

Satyan:

Yeah, sorry to interrupt, man, but it's especially true if you go to a new place, right? You walk into a new church building, you walk into a new small group of friends, and then it feels like they have a history there. Like somebody reads something and says, well, the book of Matthew says this, and you're like, wait, what? And you just feel like you're an outsider and that you're the idiot in the room. And the great thing about community is that you realize that the room's filled with idiots. Like there are tons of people who don't know what those words mean. And this is for you and I, right? Like we were thinking we were kind of hot shots in high school because we actually did an AP class in calculus, right? Those are the nerdier ones you get up there. And then at college, we got put into this class. We were thinking, dude, we're the best, you know, some of the best kids that are in high school about the math world. And we soon realized, oh, we are idiots. But the great thing was to know that you, me, your brother, like a few other ones out there too, and that gave us such confidence to know. that the struggle that you want to do, whether to struggle to think about something like math or struggle to think about something far bigger like who God is or what does that mean in life or how do you live a good life? All of those struggles are commonplace.

Bryan:

Yeah, that leads to really the first thing I want to talk about. It may be the main thing we're going to talk about today because there's so much to cover. But, Sati, help us with understanding this idea that there will always be mystery. When it comes to math,

Satyan:

Hmm.

Bryan:

and it's true for faith also,

Satyan:

Yeah.

Bryan:

there will always be mystery. And the reason this is important is because if people think they're going to get all the answers,

Satyan:

Yeah.

Bryan:

then maybe they'll be disappointed in their study of math or in their pursuit of God. That really, whether it's... whether it's pursuing math or pursuing God, it's a journey, it's not a destination.

Satyan:

Yeah.

Bryan:

And one of the ways to understand this is in the idea of infinity. Help our listeners to understand the types of infinity.

Satyan:

Oh man, yeah, it's interesting because in most of the times you're in a math class, there's always answers in the back of the book. Right, so it feels like everybody knows everything, and I just need to figure out what those answers in the back of the book are. So like when you're doing chapter five, chapter seven, chapter nine, somebody's figured it out and I just need to kind of pave the way. And I'm just thinking of this from bigger perspectives too, right? It's like... it feels like, well, everybody has understood, or like the great ones have understood what the gospel of Matthew's about, you know, when they're talking about the life of Jesus. And I just need to check that box and I'll be able to get everything. And so what are the few classes I need to take? And if you just pull back for a second and think about that, you realize that this is ridiculously silly, because the moment any one of us have creatively thought about one question. Say the question is, hey man, if I plant a tree next, you know, if I plant, if I'm starting my own garden, if I plant like mint and basil next to cilantro, I wonder what that's gonna look like. The moment you figure out the answer to that question, you don't get everything. You realize there are 10 new questions you're coming up with. Oh, if I get that, I wonder what a peach tree would do to this stuff, right? Like, your brain is bursting with new questions and it doesn't close the door. Every question you figure out opens 10 other doors, right? Of other mystery. And if you're a welder, and if you're trying to figure out how metal works, how aluminum can be welded to titanium, and you figure it out, that doesn't mean you've now gotten it. Then you wonder how copper does it. Or 23% copper with 18% titanium. The questions just become infinite. So in the math world, same thing is true. And the concept of infinity, you know, a while ago, like hundreds of years ago, felt just things that mathematicians couldn't deal with. You know, we knew how to add numbers, but if somebody, you know, the game you play as a friend, right, like, well, I'm 30 times better than you are, well, I'm 70 times better than you are, I'm infinite times, and then I'm two infinity, and you just kind of make up stuff because you just run out of things. And so we wanted to, as mathematicians, we're always trying to measure things. That's one of the cool things math does, we're trying to find patterns in things. So people wanted to measure infinity. And some people said, dude, that's a realm of God. We're not strong enough to handle that yet, because you're talking about huge things. We'll never get there. But the notion of calculus that you just started with today when you talk about our Calc III class that we did in college and then the AP Calc in high school, the entire goal of that class is to try to hold infinity in your hand. That's what calculus is, because you're trying to say, hey, if... If something is like a mountain that goes up, you know like rise over run is a slope, what happens if something is curvy and you're trying to zoom in as much as you can to find out how curvy it is at an infinitesimal spot? Like what does it look like at that one dot? Or you're trying to add area, not 13 bits of area, but infinitely many pieces of strips and you're adding it together. And the most powerful thing about calculus with Newton and Leibniz at that time was they were able to find a way that they can kind of begin to measure infinity a little.

Bryan:

And

Satyan:

To

Bryan:

so.

Satyan:

me that's ridiculous, right? That's amazing.

Bryan:

And so when you are talking to your buddy on the playground and they say infinity and you say infinity times infinity,

Satyan:

Yeah.

Bryan:

like, did you just win or is there something

Satyan:

Yeah.

Bryan:

even beyond that? Like what did try to explain this in a way that, uh, that

Satyan:

Mmm.

Bryan:

a non mathematically minded listener, what, what did they discover about infinities?

Satyan:

So there are two pieces about infinities that were really important in math. One is just talking about the notion of zooming in as small as possible, right? Like if you, now in the normal human world, we have limitations like atoms and molecules, like things come in discrete chunks, right? So I can say I'm at the atomic level. And you know, Ant-Man, it's like this Marvel thing that you could watch on TV now in the movie theaters. Like there, he's in a subatomic level and he's at these finite states. But in mathematics, you can just keep, for example, how many numbers are between the number one and two? Well, there are tons, infinitely many. Like let's zoom in. How many are between one and 1.1? You can zoom in. You can keep zooming in forever. And so how do you figure that out? That was the calculus part of it, Bri. When you're zooming in down at the small level. But then if you kind of pull back and go the other end, which is now you're gonna go to big infinity stuff, right? Like you're fighting on the playground. Well, then you have things like this, one, two, three, four, five, six, seven, eight, dot, dot, dot, right? That thing goes on forever, right? That's an infinity there. What if I then take all the fractions, I'm counting that infinity, one, two, three, put it all in the bag, one, two, three, four, five, six, seven, dot, dot, dot, put it in the bag. What if I take all the fractions, like one, a half, a third. two, three, you know, take all that stuff, put that in a bag. What if I take the negative numbers also, one, negative one, negative two, negative three, put that in a bag. What if I take negatives and fractions? I put that in a bag. You have all these different bags, and then how do you know which of these bags is bigger? It feels like the one, two, three, four, five is okay, but if you add the fractions in, that feels like way more, right? You got, you don't, you not only just have one, two, three, four, five, but you also have fractions in the bag. And this guy named Gregor Cantor said, actually it turns out all these bags are the same size. All right, he's like, wait, how'd you do that man? He has this cool way of doing it, we could talk about that another time, but like, he just basically matches them up. He's like, you know, what you call a two thirds, it's just another way of saying the number eight over here. He's just matching up the balls in the bag and saying you got the same number of matchings going on. And so people first thought, well, that's kind of weird. And then they thought, you know what? That makes sense, cause they're all infinity, dude. Of course they're gonna match up, they're all the same thing. And then he did something that was mind blowing. He says, now I'm gonna throw in all the real numbers, not just the fractions, but I'm gonna throw in like square root of two, or pi, or any of the 1.8, the things that don't have patterns, right? Just like, let's throw that stuff in there too. And now people go, well, that's just gonna be like your old trick. You're gonna be able to match it up. It's gonna be just like another infinity. He goes, no, no, no, this is a different kind of infinity. And you will never be able to match up any of those bags to this bag. In fact, you'll always have more stuff left over on this bag, which means this is not only another kind of infinity, it's a bigger infinity. So now this is the time when he actually got kind of knocked down in the math community because it was so radical that mathematicians weren't ready for it. It was just people thought everything was going to be the same kind of infinity. He now introduces a new infinity that was different. And then he goes on to establish the fact that there's even an infinity beyond that. and he tells you how to build that new infinity, and he tells you how to build infinities as many times as you want. So in other words, there are infinitely many kinds of infinities, each one bigger than the other one. Ridiculous.

Bryan:

So again, we, some of our listeners just tuned out and now they're onto an easier conversation.

Satyan:

That's

Bryan:

But, but

Satyan:

right.

Bryan:

this

Satyan:

You know,

Bryan:

is

Satyan:

hey,

Bryan:

really,

Satyan:

good for them. Good for them. Ha ha ha.

Bryan:

this is really, again, this is, this is, we're talking about math and mystery is the more, I love how you said it, Sati, the more you study something, the more you realize how much more there is to study.

Satyan:

That's right. That's right.

Bryan:

And if that's true for math, which it is. How much more true is it for God as we try to understand God? And this is what I want to say to our listeners who maybe are, let's say they're doubters or let's say they're skeptics. And they just say, look, I'm not going to buy into this

Satyan:

Yeah.

Bryan:

unless I can get all my questions answered.

Satyan:

right.

Bryan:

Then I would, I think we would both say to them, then you're not going to buy into anything.

Satyan:

anything, that's right. In fact, math, I would say, is the cleanest of the disciplines. If you think of any thing in the world, we talked about gardening a little bit, you know, I kind of threw that gardening analogy on, or like welding. Compared to all that stuff, math is the cleanest stuff, and we got equations that talk about stuff, you know, Pythagorean theorem and quadratic formulas. That is so clean. You know, you talk about somebody's marriage, you talk about how to raise kids, you talk about what it means to like, create a new, cool idea of a... you know, of how metal works, all those are complicated things compared to the sides of a triangle. You know, a squared plus b squared equals c squared. And so you think math should be the easiest of the stuff. And I think it is, to me, it's the simplest of it, of all the complicated stuff. And even then there's so much mystery. Even then, I mean, I'm telling you all the things we know. Like we know about these infinities and we know about Newton and how they figured it out. But that's all the stuff we know, brother. Like there are. And we could talk about all the mysteries in math that are so simple that we don't even know about. And if that's just a math world to say that you fully understand things about how humans work, how we feel, how we love, how we forgive, how we bring community together, much less a possible entity, a creature or a, or a thing, not even created who might've made us. And to say that I'm not gonna buy into something until I fully get that, that's ridiculous. Because there's most of mathematics, 99.99% of mathematics is unknown, right? As you said, Brian, like every time you figure something, there's 10 things that doesn't, you know, that you don't get, which means all the things we know, we know a lot of stuff, but it means like most of it is unknown. It's just filled with all these questions that nobody knows about. But yet we buy into math, we get on a plane based on mathematical constructs of how the planes created, how wind turbulence works. Right? How fluid dynamics happens. We get that. We do it. We take risks all the time with the belief in mathematical truths. How could we possibly not take such risks in bigger things as well? You will never get big questions. Nobody will. But that doesn't mean we can't have faith and push ahead.

Bryan:

You wrote a book Saudi called mage Merlin's unsolved mathematical mysteries. I'll put a link to it below in the show notes, but you talk through 16 unsolved problems in the book. And I thought it'd be fun just to talk about a cup. Now try to dumb it down for us,

Satyan:

Yeah.

Bryan:

Saudi, but there are a couple of examples in there that I've sort of picked out that maybe you can explain these mysteries that are. What I love about the book is it's saying these are mysteries. It's someone with a grade school understanding of math. can understand the question.

Satyan:

Yeah.

Bryan:

And yet the smartest math minds for centuries haven't figured out a proof for it.

Satyan:

Yes.

Bryan:

And one of the examples is has to do with one by one tiles. Explain that mystery to us.

Satyan:

.: 000000

Bryan:

Yes. So I know some of our listeners might be like, well, just try every possible combination,

Satyan:

Yes.

Bryan:

but with our discussion of infinities,

Satyan:

Yes.

Bryan:

there's no way to try. So you can't actually prove this

Satyan:

Yes.

Bryan:

by just doing a million examples. Now I'm sure we have computers working on this

Satyan:

Yeah.

Bryan:

and we've got,

Satyan:

But if

Bryan:

you

Satyan:

you

Bryan:

know,

Satyan:

think

Bryan:

we

Satyan:

about

Bryan:

can

Satyan:

it, yeah,

Bryan:

just

Satyan:

let's

Bryan:

set.

Satyan:

actually talk about computers for a sec, right? That's a great

Bryan:

Yeah.

Satyan:

point, right? So, you know, every time you rotate a tile, you know, that's a turn of an angle, right? Then you can go zero degrees. And the turning, by the way, doesn't come in one degree angle chunks. It's not like one degree, two degree, three degree. It's like between zero and one, we talked about there are infinitely many turns, right? So just turning it is gonna give you infinitely many possibilities. But now you have six tiles to turn. That's already six kind of. kinds of infinities you're holding in your hand, and you can place them on the plane, right? Like you have an X-Y coordinate, that's actually two dimensions of movement. It could be like, you know, zero, one, and tons of numbers between zero and one. So you have all of these options, and a computer, the great thing about a computer is it's really fast. It's way better than you are. It's way better than I am in computing things, right? It could do like a terabyte, or whatever, a teraflop, or all of these kind of words of like things per second, right, of calculations. And the problem is though, You know, 200 trillion calculations a second is nothing compared to infinity. You know how many 200 trillions you need? You need infinitely many of them to actually check everything. So a computer is great to give you intuition. You know, you can kind of like smell things out for you and be like, oh, that, that those, those combinations might or might not work, but it can't ever prove anything because I'm trying to do it for everything. And a computer will only do finite things. And even if the finite number is big, Infinity is so much bigger. I think so many times we fool ourselves into thinking we get it because 100 trillion is like you're still at the starting block compared to infinity. 100 trillion raised to the 100 trillion power. You're still at the starting block brother. Infinity is so big. So this is why mathematicians when we actually prove something when I can tell you something about the truth of every triangle it is unimaginably cool. We can do something no physicist can. I could tell you. that the sum of the angles of three, of any triangle is 180 degrees. Now let's just think about that, Bri. How many triangles are there? There are infinitely many triangles. I mean, literally the sides of the triangles could be long and it could be as big or small and all these weird shapes as you want to, there are infinitely many triangles out there. If I'm a physicist or a biologist or a chemist, like if I'm a scientist sitting around, do you know like there's the scientific method of how you have to like find something and test it? Well, there are finitely many humans that have lived on the earth. And if each human is spending every second measuring a different triangle and checking out the angles, that's still a finite many triangles that have been checked. Right? So, so from a physics perspective, there might be a new triangle out there that we haven't checked yet. You know, there's a theory of physics, right? But like, maybe that'll break the model. Maybe, but math, we can guarantee the sum of the angles of a triangle is guaranteed to be 180. even though I haven't checked every triangle. And that's the power of mathematics.

Bryan:

And that's because the proof isn't the proof that you're using isn't exhausting every possibility

Satyan:

Exactly.

Bryan:

because you couldn't ever do that.

Satyan:

Exactly.

Bryan:

The proof, the mathematical proof uses a different, and could you just explain that in a simple way

Satyan:

Yeah,

Bryan:

for our listeners to understand what would

Satyan:

and

Bryan:

a mathematical proof be?

Satyan:

so a mathematical proof could use things like how geometry works. So Euclid, the old granddaddy of all geometry, came up with things like parallel lines and how angles worked. And so mathematics, going back to a word he used at the very beginning of our chatting brah, is about community. It's not the fact we sit here and then we immediately come up with an idea. It's people have come up with mathematical truths. over thousands of years and we're using them as like hammers and saws and screwdrivers as different weapons to build this other house of truth. So I know that if you have two parallel lines they can intersect. I know that if you have another line that does this it has this property. So over time there's all these geometric truths, there's algebraic truths. If you add two numbers together you get a new number. And if the two numbers are positive, the new number is gonna be a bigger positive number. So we have these algebraic truths and we have geometric truths and we have analytic truths. So mathematics has built up this entire language of stuff that I could use to create and build upon and come up with a new truth. And that truth is, if you add up all the angles, it's gonna be 180 degrees. So we're building up on these things. It's not proof by exhausting the thing, it's proof by building on these other truths that exist.

Bryan:

Yeah, that's good.

Satyan:

And

Bryan:

All

Satyan:

even

Bryan:

right, let's.

Satyan:

then, yeah, even then we realize that truth is it's not like we're now, it's not like we're closing the door on things, right? It's not like, oh, my gosh, now it's converging and we're going to eventually get all the truth out there. We realize we're at the base of Mount Everest. And every mathematical knowledge put into one box will give me one step towards the march to the top of Everest, right? We're nowhere close to getting it. We're just the opposite.

Bryan:

Okay, do one more example from your book. And then we'll just have, if people want to find the other 14, you'll have to pick up the book. Talk about twin primes and the unsolved problem related to them.

Satyan:

That's it. You know, the first problem that we talked about about the tile and, uh, and covering it up with, you know, with, with six other tiles is it's kind of a hidden puzzle. A few mathematicians know about it in different worlds, but this problem, the twin prompts is kind of on the opposite end of the spec bri. This one. almost any mathematician knows, right? Like anybody who's anything has heard about this thing. So here's how the story goes. If you look at the numbers like three, four, five, six, seven, eight, just the classic old school numbers we're talking about, some of those numbers are prime. Prime means you can't, they're not made up of other numbers put together. Like four is made up of two times two, six is made up of two times three, but seven isn't made up of two numbers multiplied, two whole numbers multiplied together, seven just is. Right, and eight is made up of four times two, and and 12 is made up of three times four, but then 13 is just is. And so one question is, the prime numbers are almost like stars in the sky. They're like, there's this blackness of all the numbers and then these things are sparkling. Something's cool about 13, man. It just is, something's cool about 19. Something's cool about these other primes that just show up. So one question is, are there infinitely many stars in the sky? Are there infinitely many primes? And as an old result, that was said by Euclid that was said that there are infinitely many primes that no matter how far out you go You will always find new prime numbers out there that if you take 200 trillion There's gonna be new primes after that that primes never end. There's nothing you know, they're special They're gonna be always out there and the proof of this bright going back to you know, how this was done It wasn't they found every prime number because you know, they're infinitely many of them, right? It's just this cool mathematical way of logically working out stuff And so you clearly did this thing and the proof is, it only took like four or five lines to prove it. It's really beautiful and gorgeous. And technically for those nerdy ones, proof by contradiction is a cool thing. Great, all right, so now the question is, okay, this was done thousands of years ago. Now somebody started noticing this interesting thing. If you actually look at the stars of the sky, sometimes the stars come in pairs. So look at three and look at five, right? They're both prime numbers. Now, you know every even number. can't be prime, right? Cause you could divide it by two. So that's not a prime number at all. Four is made up of two times two. Eight is made up of two times four, right? 16 is made up of two times eight. There's always these two times. So forget those. But twins means they're right next to each other. Like three and five are basically the closest you can get and be prime numbers, right? And then like if you, well, seven and nine, well, nine's not a prime. What about 11 and 13, right? 11's a prime and 13, like these are like stars that are kind of clustered together. And then they started noticing, dude, these twin primie things, the primes that are right next to each other basically, there are also a bunch of them. Right? They keep, it feels like they keep going, just like the primes keep going, that these twin primes also feel like it keeps going. And then the question was, are there infinitely many twin primes? If you go to 200 trillion, will you eventually find a pair of primes that are kind of right next to each other? And this question is unsolved. It's one of the... biggest questions in the world of number theory, the people, the mathematicians who study the theory of numbers, the property of numbers, no one has a clue. So

Bryan:

Okay.

Satyan:

it's remarkable, remarkable.

Bryan:

So, and this is what's crazy about it is it's provable. It's proven that proof by contradiction, like you said, it's proven that there's no end to the prime numbers.

Satyan:

Yes.

Bryan:

And yet it is not all the most brilliant minds in the world working on this. And it's still not something that simple. It's still not proven, even though instinctively it seems like it's true that there's no end to twin primes. we have no actual proof. You can't use the same proof by contradiction for the primes that you can for twin primes. And again, that's a tension that's just so beautiful to think that there's this tension with math. It's so easy to articulate the problem, and yet we don't know the solution. And there's something in us, and I think this is true, especially for American Christians, there's something in us that says, I hate the tension. I hate

Satyan:

Mmm

Bryan:

living with the tension,

Satyan:

Mmm

Bryan:

and yet there's incredible tension that you have to live with in math, you'll always have to live with, and I think the same is true in faith. And one example, Sati, really is, like, if you read the book of Proverbs, there's all these principles, it seems like it's so clear. It's like the easily provable, if you do this, this will happen, if you don't

Satyan:

Yes.

Bryan:

do this, this will happen.

Satyan:

If

Bryan:

And

Satyan:

you do X, then you get Y, right?

Bryan:

that's

Satyan:

That kind

Bryan:

right.

Satyan:

of stuff.

Bryan:

And Proverbs tends to be like that. Proverbs are principles. They're not promises, by the way, but they're

Satyan:

Yeah.

Bryan:

principles that for the most part are a good guide for how to live your life. I encourage

Satyan:

Yeah.

Bryan:

people to read the Proverbs and yet not very far away in the Bible from Proverbs is the book of Job. And if you compare Job, and again, a skeptic might do this. They might read Job and read Proverbs and say, look at all these contradictions. Look at all this tension because Jobe was a godly man. Jobe lived,

Satyan:

He

Bryan:

really.

Satyan:

was doing all the X's going back to,

Bryan:

Yeah.

Satyan:

right? Like he was doing all that X and he wasn't getting the Y's.

Bryan:

Yeah.

Satyan:

Yeah,

Bryan:

In a cr-

Satyan:

you look at, I'm sorry, I'm sorry, man, keep going.

Bryan:

It creates this tension that some people just find hard to live with, and therefore they've deconstructed their faith.

Satyan:

rs ago, a thousand years ago,: 2000

Bryan:

Beautiful. Sadi, I feel like people, if they're still listening, their minds might be about ready to explode. I know I like to listen to podcasts on 2X or 1.5X speed. This is one you might need to slow down to 0.75 or 0.5 because what you've shared with us is just so thought provoking, so insightful. And I know that a lot of listeners are going to want to go back. and listen again, not for the math. I'm sure the math is interesting, but really for how it's a metaphor for pursuit of God. And here's what we've really landed on today. And we're out of time. I think we're going to have to pick this up next week because I still want to talk about how math is beautiful. It's not just useful. And I want to connect

Satyan:

Mmm.

Bryan:

that to faith. I

Satyan:

Yeah.

Bryan:

still want to talk about how math isn't really even the best discipline. You know, you're a math professor. But math really even isn't even the best discipline to prove the existence of God. It's too simple, it's too

Satyan:

Yeah,

Bryan:

measurable

Satyan:

that's right.

Bryan:

that actually there are some other disciplines that are more useful for those skeptics who are out there really trying to wrestle with this. But for today, really, I think we should leave it at this that as with math, so with God, there will always be a mystery. That it really is a journey, and I hope our listeners would have heard this and would have said. This guy, Sadi, seems to have this incredible joy along the journey. And that's really, you know, our paths diverged after grad school.

Satyan:

Mm-hmm.

Bryan:

You know, I got my master's in math and you went on and got a PhD and you've made an incredible career out of teaching math to some of the brightest students in the country. And I'm a pastor, but both of us, I think we've both understood just this,

Satyan:

Mmm.

Bryan:

the joy in the journey. that

Satyan:

Y'all.

Bryan:

it's not about a destination necessarily. And obviously we have a, and we'll talk about this maybe next time, that there is

Satyan:

Yeah.

Bryan:

a destination, there is heaven. And we'll talk about what that's even gonna look like. But more than anything is that the journey is where it is. It's all about embracing the mystery. It's all about embracing the tension. It's all about understanding the axioms on which our lives are built. Because that doesn't mean that we can have no sure thing.

Satyan:

Yo.

Bryan:

You know, our faith isn't blind. There's a reason that we trust in Jesus. There's a reason we believe the Bible. But, but just because we don't have blind faith doesn't mean that we're going to have all of our questions answered. It's still faith and it's still, there's always going to be a mystery when it comes to pursuing God or even really trying to understand math. So, thanks for talking with us. I can't wait for the next conversation we're going to have. I'm sure it's going to be just as insightful for those listeners. who want to talk about this with a family, with your small group or even one-on-one in a mentoring relationship, you can find all of these conversations that we're gonna have at pursuegod.org forward slash math. But Sati, I wanna leave by giving you the last word. Speak to us one more time.

Satyan:

I just want to say that don't be afraid of the unknown. Don't be afraid of the mystery. Everything's mysterious and the joy of pursuing it will make you more fulfilled. And the only way to do that, I think I love the way you closed up, Rai, is by bringing in community. Don't do this alone. You're not going to explore the unknown mysteries of mathematics, which formulas and equations and stuff might be daunting, but that's nothing compared to the mysteries of living life well. or the mysteries of seeking someone who might be our creator. Don't do that alone. These are huge things that people of wisdom have done before in space and time and people in your own community are struggling with. You are an idiot, just like everybody else around you. Embrace the idiocy.

Bryan:

Yeah, that's what I learned, Sati, when we were studying all those years ago in our undergrad, you know, we were, I know I was, I was way over my head,

Satyan:

Absolutely

Bryan:

in over my

Satyan:

man,

Bryan:

head with the

Satyan:

yeah.

Bryan:

math studies. But what made it so fun and memorable is that we did it together. And I'm so grateful for that and that friendship lasts. Can't wait for the conversation next week. And so for you listeners, share this podcast with a friend and join us next time as we continue to talk about math and God.