Conversations with members of the Harvard and Radcliffe Class of 1992.
Hosted by Will Bachman.

Episode: 93

Joshua Brandon Holden, Math Professor and Author of The Mathematics of Secrets

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Show notes

Joshua Brandon Holden, the author of The Mathematics of Secrets, Cryptography from Caesar Ciphers to Digital Encryption, graduated with a degree in pure math and went on to teach at the University of Massachusetts and Duke. He discovered that he was spending most of his time on teaching, so he sought jobs where they would reward teaching. He then worked at the Rose Hulman Institute of Technology, where he did both teaching and research. 


Common Misconceptions about Cryptography

Joshua discusses common misconceptions about cryptography and its connection to the internet. He explains that people often knew about cryptography in ancient times but don’t know about the throughline. Older theories of cryptography were implicitly mathematical but not explicitly, while new theories are very explicitly mathematical. Joshua aims to open up the connection between older forms of cryptography and the new ones, stating that everyone has some ability to do all of it in varying amounts. He talks about the current state of cryptography online, including public key cryptography, which originated in the 70s and gained popularity in the 90s with internet commerce. Public key cryptography allows users to send secret messages through a one-way key, which is only decrypted by the sender who has a different key. This is important for sending credit card information to companies like Amazon or Walmart. However, end-to-end encryption means middlemen are no longer able to decrypt messages, so it’s crucial to look carefully at providers’ policies to determine if they stay in the loop. Joshua talks about the networks and relationships within the cryptography field, including the opportunities for professionals to work in private camps, government agencies, and academia. He notes that while there is money and space in the field, there is also a lot of space for professionals to stay updated on the latest theories and developments.


Quantum Computers in Cryptography

The conversation turns to the potential of quantum computers in cryptography and the potential for breaking encryption systems. He believes that quantum computers are expected to be better at breaking the problems used in creating mathematical problems used in special public key systems, such as encryption used by browsers to protect credit card information and communications. He also discusses the development of quantum resistant cryptography, which is a more complex system but the basic principles of quantum resistance systems are still relatively graspable for anyone with high school algebra and a willingness to dig deep. By applying enough computing power to end-to-end encryption systems, it is possible to break them. The only way to achieve perfect secrecy is to have a secret key, which is as long as the conversation. This method was supposedly used for the famous red phone between the White House and the Kremlin during the Cold War.


Keeping Your Data Safe

In terms of security, Joshua advises people to know their threat model and consider the potential threats they face. Some people may worry about powerful governments trying to break their communications, while others may be concerned about corporate spies, children, or random people passing by. For those worried about corporate espionage, it is recommended to look for end-to-end encryption systems. While quantum computers may not be easy to break, they do not guarantee that someone can’t break the system with enough computing power.


Class Field Towers Explained

Joshua talks about his research in the field of mathematics, specifically in the area of class field towers. He explains why imaginary numbers are not square roots but rather arbitrary choices. He also discusses the concept of Galois groups, which track the number of ways complex numbers can be shuffled around without making a difference. He explains that class field towers consist of rational numbers, real numbers with irrational decimals, and complex numbers on top of them. These towers record the complexity of each jump made in the tower. Joshua talks about the role of computers in mathematical research, stating that there is more computer usage in this area due to improved software tools and more applications in cryptography. He identifies two traits that are most useful for being successful in mathematical research: perseverance and curiosity. Perseverance is the reason most people persist. In graduate school or postgraduate school, those who stick with their passion and interest in math may be more likely to succeed in mathematical research. He encourages students to not give up on problems that require a different kind of math, even if it’s not necessary for their career. He believes that having a sense of curiosity about everything comes from the fact that in mathematics, all one needs is to  just think hard about things and talk to others. This gives one a sense of confidence that they can figure things out without the need for special abilities or tools.


Influential Harvard Professors and Courses

Joshua mentions Math 25, an honors calculus course. He also enjoyed Professor McConnell, who he still maintains a friendship with. He also shares his experience with changing his name, which was the first of his non-professional wanderings. 



04:33 Cryptography and its applications in online security

11:57 Cryptography, public key systems, and quantum computing

21:07 Encryption, mathematics, and data security

27:49 Mathematical research and talent

33:41 Math education, career choices, and personal growth




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  1. Joshua Brandon Holden


Will Bachman, Joshua Brandon Holden


Will Bachman  00:02

Hello, and welcome to the 92 report conversations with members of the Harvard and Radcliffe class of 1992. I’m your host will Bachman and I’m here today with Joshua Brandon Holden, who many of you may have known in college as Josh Brandon. He’s the author of the mathematics of secrets, cryptography from Caesar ciphers to digital encryption, which we will chat about his most other things. Josh, welcome to the show.


Joshua Brandon Holden  00:31

Thanks very much. I’m happy to be here. Very happy to be here.


Will Bachman  00:35

So Josh, tell me about your journey since graduating from Harvard.


Joshua Brandon Holden  00:40

Right? Well, let’s see it started out. Probably not too surprising to anyone. I graduated with a degree in pure math, I went to grad school in pure math, I got a job at the University of Massachusetts teaching pure math, and theoretically, doing research. And then when I was at the University of Massachusetts, I discovered that even though I was supposed to be spending most of my time on research, I was actually spending most of my time on teaching. So I said, Okay, I should look for jobs where they actually rewarding me for that. Because research universities often don’t. So I, that was a two year position, I got another two year position at Duke, which is also a research university, but they had a group of people that were particularly interested in training people to teach at undergraduate institutions. And so I spent two years at Duke brushing up on my undergraduate teaching, and then got a job here at the Rose Hulman Institute of Technology, doing a lot of teaching and a little bit of research. And that’s where I’ve been since then. In the meantime, I got married and my wife found my wife, very patiently followed me around a lot of those places. She’s also here in Indiana with me. Okay,


Will Bachman  02:34

so So you were saying that you, when you got to UMass, you were you wanted to do more teaching or more research?


Joshua Brandon Holden  02:42

I thought I wanted to do more. Yeah, that’s, that’s a good question. I thought I wanted to do more research when I got there. And then I discovered, I was actually enjoying spending more time on my teaching.


Will Bachman  02:56

Oh, interesting. Okay. Some people view that as more of a annoying side by side distraction from what they really care about the research. But you found out you enjoyed the teaching part. What a part of that? Why, why was that? What part of teaching made you want to get up in the morning and go do it?


Joshua Brandon Holden  03:14

There were? Yeah, there were a number of pieces. There was the you know, there was the altruistic part of just the watching the the joy on somebody’s face, or the realization on their face, when they’re like, Oh, I get it, that makes sense. That’s just an incredible feeling that I love. There’s also the fact that, unlike research, you get up in the morning, and you know, by the end of the day, you’re going to have done something, you’re going to have gone and teach some classes and, and you can hardly avoid somebody learning something. Whereas in math, mathematical research, it’s very common to get up in the morning, and spend all day writing things on pieces of paper and then crumpling up on them throwing them away. Now


Will Bachman  04:17

tell me a bit about the origin and about some of the content in your book, which I will say has a 4.7 stars on Amazon pretty good. At seven rating. Yeah. Thanks. So tell me about the mathematics of secrets.


Joshua Brandon Holden  04:32

So when did this start? So I mentioned that my degree in college was in pure mathematics and my degree in grad school was in pure mathematics and cryptography was not included in either of those things. I mean, like many of us when I was a kid, you know, I did some playing around with secret codes with my friends and stuff, but then I, then I largely forgot about that for many years. And then the area of my discipline of mathematics, which I did specialize in, in graduate school is called number theory. It’s the theory of full numbers, primes. When a number divides and other number, and I wouldn’t say it was just getting going. But as I was graduating, well, yeah, when around the time I was graduating, grad school, internet commerce was starting to take off. And it turned out that the encryption that they needed for that was based on exactly the type of problems that I had been looking at exactly the type of problems, but definitely the same genre of problems that I was looking at, in, in graduate school. So as part of that first job, I mentioned, University of Massachusetts, I taught a course in number theory, with a small bit of cryptography in it. And then my second job, my department chair asked if I’d like to teach a course with a larger amount of cryptography in it. And then it just sort of started went from there, I taught more and more cryptography, and I enjoyed it enjoyed communicating with it. Discovered, you know, that not only did people enjoy thinking about secret codes, but it was a good way to sneak in some math to people who might otherwise not appreciate what the point of it was. And particularly some of the math that that I was trained in, which is traditionally the, for good or bad, the most considered the most useless kind of math, some people reveled in that. But as it happened, it’s, you know, indispensable for the internet.


Will Bachman  07:18

Talk to me about some common misconceptions that you encounter when you’re talking about cryptography cryptography, of even a reasonably educated intelligent person who’s not a math major, who hasn’t studied the topic in detail. What are some misconceptions out there about cryptography?


Joshua Brandon Holden  07:38

Well, I’ll start with a very uncommon misconception, which is that I once told somebody that I was a cryptographer, and they asked if I went, you know, underground, exploring crypts. Okay, that but that only happened to me once. People often know a little bit about cryptography in ancient times. And they know that there is cryptography out there on the internet. Most people really don’t know anything about the through line. And there definitely is a through line. But the old, older theories of cryptography, were implicitly mathematical but not explicitly. And the new theories are very explicitly mathematical. So that that connection is often very opaque to people. One of the things that I hope to do is to open that up connection to you how older forms of cryptography which were considered very linguistic. And I don’t believe that there are math people and language people. I believe that you know, everybody has some of the ability to everybody has some ability to do all of it in varying amounts. So I really enjoy showing people that that traditionally, linguistic area has its own mathematics to it.


Will Bachman  09:37

Talk to me about explaining sort of, to a layperson, me. Kind of the current state of cryptography online. For example, with WhatsApp, I think they advertised that it’s sort of fully encrypted on both sides. Are these other messaging apps like signal whatsoever? Just kind of what I rant? Yeah, vaguely here online. Is that is that? Are they actually like fully encrypted? Can the US government Spies Like, decode what you’re saying? Talk to me a little bit about like how, and actually, I’d love to also hear a little bit about how it currently works, you know, on with, with with


Joshua Brandon Holden  10:17

cryptolocker. Sure, well, we’re in enormous state of flux right now. So there are a lot of different things going on, which amount to a lot of different ways that cryptography can be used and a lot of different ways cryptography can fail. So one of the important things to talk about it to understand where we are, is something called public key cryptography, which is the idea and this was the idea that was just, it originated in the 70s, but really got booming in the 90s, with internet commerce, which is the idea that well, so we just, we just did it, or at least, could have done it, because I honestly don’t remember whether zoom, we probably didn’t set it up as encrypted. But you could have done that, just by sending me a link. And letting you look up, zooms certificate, which, you know, proves to me in some way, which we could get into that that Zoom is really zoom. But then it what it does is it provides what’s called a public key, which is really a one way key. I don’t need to know. Or rather, I can use that one way key to send a message through zoom to you. But just because, but you’re the only one who can decrypt it with a different key, you need a different key to decrypt it. So the traditional forms of cryptography, you know, you had two people talking back and forth. And everything that one of them knew the other one knew, in public key cryptography, there’s a piece of information that you know that I don’t, but nevertheless, I can still send you a secret message, even though I can’t decrypt my own message, and nobody else can decrypt my message. So this is important. If you want to send credit card information to Amazon or Walmart or whoever. Right, you don’t want to go to Amazon headquarters in Seattle, or Walmart headquarters in Arkansas, wherever, in order to establish what your secret is going to be. So I can just use that public key to send my credit card information. And despite the fact that anybody can send Walmart in that information, they’re the only ones that can break it. Or rather decrypted.


Will Bachman  13:20

Okay. So they’ll put that so like Walmart would put that public key out there. So they somehow create that, but they know how to decrypt it if someone has used that to encrypt it.


Joshua Brandon Holden  13:31

Exactly, exactly. Now, we’re thing, well, one of the places start, things start to get dicey. I can go a lot longer than an hour on this, if you let me but don’t let me. But one of the ways that this can start to get dicey is that I can use that to connect to zoom, then zoom can connect me to you, and then it’s up to the zoom, whether they’re going to stay in the loop or not. So end to end encryption, which I think that you mentioned, basically means the middleman is going to get out of the loop. And they’re not going to be able to decrypt things anymore. Okay. And it’s perfectly possible for them to do that. It’s also perfectly possible for them not to do that. So, you have to look very carefully at the policies of these different providers in order to know whether they are staying in the loop or not.


Will Bachman  14:37

Talk to me about what it’s like being in that field of cryptography today is give me a sense of the, the kind of the networks of people, the relationships that people have in that field. Is it you know, is there lots of dollars that people want to go work for, you know, private camp And he’s in that to do, you know, the developer encryption? Is there? You know, do people get recruited by the federal government to go work at the NSA? Just? What does it feel like to be a professional in that cryptography space?


Joshua Brandon Holden  15:12

Yeah. All of it. It is, it is all going on there is there is there’s a lot of money. But there’s also a lot of space. So some of us are academics. And, you know, I don’t, as I said, I don’t work at a research university. But I still keep my hand in a little bit. I go to academic conferences, mostly. But I overlap with those in academic conferences, with the people from industry who want to, you know, find out what the latest theory is going on. And the people from the NSA who want to find out what we think the latest theory is going on, which sometimes I imagine is news to them, and sometimes isn’t, but they don’t talk about which one it is.


Will Bachman  16:15

Well, what’s your intuition? My I mean, just given the amount of money that the federal government has, and I imagine, you know, China and Russia, same thing. I imagine that there must be some areas where the federal government has gone way ahead of what’s publicly known by academics and by industry people.


Joshua Brandon Holden  16:36

And I have no doubt there I had right now, way ahead, would mean having a working quantum computer. Okay. And that I would I would not even venture to give any sort of odds on whether the NSA or the comparable agencies and other countries, I would find it entirely believable if they did, and I would find it entirely believable if they didn’t


Will Bachman  17:09

know, why would a quantum computer help you with cryptography?


Joshua Brandon Holden  17:14

Great, great. So it turns out through what is either an odd coincidence, or some bit of theory that we don’t understand yet, it turns out that exactly the sort of problems that we’ve been using to make those mathematical problems that we’ve been using to make those special public key systems are exactly the sort of problems that quantum computers are expected to be good at breaking. So exactly the sort of encryption that that our browsers are using to protect our credit card information and our communications. That’s exactly the first thing that we expect to be broken when or if someone has a working quantum computer. So right now, and this is another really exciting thing that I’ve been trying to keep my hand in. People have been working on ways to make a new public key systems that rely on different mathematical problems that quantum computers find harder to break. The buzzword for this is post quantum cryptography, which is not really accurate, quantum resistant, cryptography might be better. And I’ve been writing some a couple of papers and things which I hope will maybe get into my next edition of the book about simplifying those systems down for undergraduates and other interested lay people to understand the these quantum resistance systems because they’re a little more complicated than the systems that are currently being used. But but there are some still some relatively graspable, basic, I mean, I wouldn’t even see relatively I think the basic principles are still quite graspable for for anyone, you know, with a really with with high school algebra and the willingness to dig in deep.


Will Bachman  19:44

With end to end encryption systems, if you apply enough computing power to it, is it possible to break those encryptions?


Joshua Brandon Holden  19:56

The short answer is yes. The only Only way to make it you know the the name for that is perfect secrecy. Impossible to break, the only way to do that is to have a secret key, which is as long as your conversation. So this was supposedly I don’t think the government has ever confirmed this but this was supposedly the method used for the, you know, the famous red phone between the White House and the Kremlin during the Cold War. They actually sent couriers with, you know, these huge reels of magnetic tape or something every month or whatever, in order to make sure there was enough key material so that they could use the red phone when they needed to. But very, very, very few other systems, if any, can afford to do that.


Will Bachman  21:06

Okay. What, what, what are you sort of just your tips on for, you know, the ordinary person about keeping your data safe? Are there things that a cryptographer knows about systems that we should be either using or that we should realize are much more hackable than we thought? What are some of your own personal practices?


Joshua Brandon Holden  21:35

Well, so the first thing that that I tell people is know your threat model, who are you actually worried about? There are going to be a few people out there probably a few people in the class of 1992, who really ought to worry about powerful governments trying to break their communications. They’re playing a whole different ballgame than the rest of us. The rest of us, some of us are going to be worried about corporate spies. Some of us are going to be worried about our children, you know, getting into things that they shouldn’t. And some of us are not, you know, going to be particularly worried, you know, maybe just try not to make it too easy for for random people passing by. I mean, so that’s going to determine, you know, and I so so if you’re worried about corporate greed. So first of all, if you’re if you’re worried about the the the the federal government or the Russian government, yes, some of you out there have good reason to be, you know, I have reasonable consulting rates. I’m not, I’m not going to try to go into that here. If you’re worried about corporate espionage, then yeah, you probably don’t want zoom. Or, and I don’t want to pick on Zoom, it’s just what we happen to be using right now. So the their logo is staring me in the face. But, you know, any, any intermediary which we use for our communication, Facebook, or, or, you know, whatever, Twitter direct messages, which is now called the X. Sorry, Elon Musk, don’t hurt me. Lord, what was I saying? I just sort of, yeah, so if you’re worried about big corporations, and you might be, then yeah, you want to look for things which have end to end encryption, and which promise, you know, not to be on the line. And if they’re not on the line during the call, they can’t turn over your messages, no matter what the government does, they just don’t have them. So signal is usually held up as the best example of that when you make a call using signal or send a text using signal. There’s, you know, they just, they don’t they don’t keep any of the information that that could be used to, they just don’t have it. So if the government comes asking for it, and they just they just don’t have it. Now, again, you know, with enough computing power, that doesn’t mean that that somebody can’t break the system, but it’s not going to be easy.


Will Bachman  24:57

Talk to me about the research your research. better, you know, as a grad student, and as an academic, tell me about some of the areas that you have written about.


Joshua Brandon Holden  25:10

Oh, boy, okay, yeah. Um, so like I said, I started out in a very pure area of mathematics. My first, my dissertation was about something called Class field towers, which I won’t even begin to try to explain to you. Oh,


Will Bachman  25:31

please do that. Oh, okay. Sure. Just, I know, I, yeah, I’m sure you try at cocktail parties and stuff. But I’m just math is interesting, because it’s one of the areas where it’s maybe the hardest for someone who’s even a STEM major to, you know, to kind of grasp it. So I’d love to take a shot. Glass field towers, what, what is that about?


Joshua Brandon Holden  25:53

So? So most? Most people have probably heard of imaginary numbers, whether or not you know what they’re


Will Bachman  26:04

yes, they’re not that square to negative one, square


Joshua Brandon Holden  26:08

root of negative one. Okay, so something you probably have never thought about. And most people also know that numbers really have two square roots. The square root of 25 is five, but it’s also negative five, because when you multiply the negative five with itself, the negatives cancel out, and you still get 25. I’m with you so far. All right. So but maybe you’ve never thought I never thought about the fact that there’s a positive imaginary square root of negative one. And there’s also a negative imaginary square root of negative one. And which one is which is really pretty arbitrary, because neither of them are greater than zero or less than zero, because they’re imaginary. They just don’t go on that. Number line. So you know, the conventional way of depicting a number line, like in grade school is you’ve got positive numbers, the left negative numbers to the right, well, then you’ve got these imaginary numbers going up and down, but which one is which? How do we decide what to put his up and what to put his down? And the answer is, Well, honestly, we just make an arbitrary choice. So what happens if you make the other choice and just flip that whole, you know, two dimensional picture upside down, you can’t flip it left to right, because positive things are definitely the same as negative things, or else my bank account would be in a lot better shape, or definitely not the same. But, but you know, the up is really the same as down. So what happens if you flip it? Well, you get something called a very simple example of what’s called a Galois group. So Galois groups keep track of the number of ways that you can shuffle around complex numbers, without it really being without really making a difference. And with more complicated system of numbers, you can shuffle them around in different ways. And there’s a whole algebra of these Galois groups. And that’s known as Galois theory. And you can then look at towers of numbers by which I mean, you you’ve got rational numbers, which are just fractions. And then you’ve got real numbers, where you have decimals that are irrational like pie. And then you’ve got complex numbers on top of that, and there are ways that you can make these towers. And you can look at Galois groups record at each step of the tower, how complicated a jump you’ve made. And so there are different ways of studying these Galois groups, and one of them is called Class fields. And the particular tower that comes out of that theory is called a class field tower.


Will Bachman  29:32

Now, if you are doing this kind of work, I’m curious what it actually looks like. Are you sitting down kind of with pencil and paper a lot and trying to write proofs or working with equations or are you using computer to do some sort of powered kind of brute force method like what what does it look like to be doing work in the space


Joshua Brandon Holden  29:59

so When I was in graduate school, it looked a lot like filling notebooks and notebooks full of attempts to prove things. Nowadays, there’s there’s much more computer usage in that area as well, two things. One is the tools have, the software tools have gotten better to work with these esoteric mathematical structures, which are esoteric, but still concrete, you still can actually, in this area of mathematics, describe these things to a computer. So so it is possible and techniques for doing that, as I said, have gotten better. But also, people have discovered more applications of these things, including but not limited to cryptography. So there’s a lot more interest in the concrete computation with these structures, and not just the theoretical proofs.


Will Bachman  31:13

Now, in terms of assessing talent and thinking about talent in this space, would you say that the intrinsics that are required for success at doing that kind of higher level math? Are they very different than the requirements to be good at just your basic, you know, high school or early college math, your, you know, algebra, trigonometry, calculus, linear algebra, sort of stuff, where you’re, you know, solving problems from textbooks is, you know, someone who’s, like, awesome at calculus and loved it in high school? Are they often is that the same skill set? Is this? Or is it like, very different, it’s, you know, like, they may or may not be good at doing class field towers, but it’s like a different a different kind of talent on


Joshua Brandon Holden  32:07

the two traits that I have observed, that are most useful for being successful in mathematical research are number one, and primarily perseverance. Um, and number two, I think a close second, I would say curiosity. Although honestly, that’s the reason most of us persevere. So they’re late. But it was definitely not the fastest people who succeeded. In graduate school or postgraduate school, it was not, you know, it was not the most successful people in college classes necessarily, or even graduate school classes, necessarily. Who, you know, it’s the people who stuck with it, that ended up you know, still there. A lot of my friends for, you know, very good reasons of their own have, have decided, you know, people that I was a math major, constantly got to get back into the Harvard mode of math concentrator with at Harvard. A lot of those people are not doing pure math research anymore. They’re doing other things more or less related to math. For perfectly good, you know, and I don’t want to, I don’t want to, in any way, make a value judgment. I really don’t. But some of us just, I don’t know, we’re just too stubborn and too interested in what was going on, to give it up.


Will Bachman  34:13

So curiosity, perseverance doesn’t make total sense. What about other things? Do you find that people in your field? Do they tend to have very strong spatial reasoning skills? If you give them some sort of 3d lock problem or something they’re going to just see through it? Or? Luckily for


Joshua Brandon Holden  34:32

me, no. I actually tell my students that I am surprisingly bad at spatial reasoning. 3d geometry is a branch of math that I really have to work very hard out. And struggle. Yeah, I’ll say I’ll say it. I struggle with it. I have to And that’s not the only branch of mathematics that I struggle with. But, you know, one of the things I also tell math students is, if math is going to be your career, even if it’s not, but your career is going to involve math, you don’t always get to pick the kind of math that solves the problems you want to solve. So I try not to give up on a problem just because I discover it requires a kind of math that I’m bad at.


Will Bachman  35:38

How would you? How would you say that? Your professional study of math and research and math has shaped the way you think about the world, the French have this term depth Amasian. Professor now, which, like the idea, you know, like a Taylor would look at someone and they would judge them. Okay, they’re 38 short? Yes, the first thing that comes to mind, do you is it changed the way that you think as you kind of walk down the street or take care of your family? Or just, you know, wash the dishes or something? Or you or walk past the convenience store? Are you kind of thinking about, does it influence the way you perceive the world in any way?


Joshua Brandon Holden  36:18

I think it does. People telling me, I’m a very pedantic person, and I will, I will own that, I like to be extremely precise, I like to be very clear about what I mean, when I’m speaking, if I can be, I like to understand things very deeply. If I can, if I’m really interested in something, I, I go, I go deep, even you know, whether it’s a mathematical subject or not, if I get into it, I can, I can really go deep into it. And, um, you know, and I try to have a sense of curiosity about everything. And I really think that, that comes from the fact that in mathematics, you really just need your brain. You know, you really just need to think hard about things. And, and talk to other people, but you know, and get other people to help you. But you, you, you don’t need to be able to draw well, you you, you don’t need to be able to shoot a basketball, you just need to be able to think and that gives one a sort of confidence that they can figure things out. If I try hard enough and spend long enough on it. And I’m sure I’ll never have enough time in my lifetime to figure out all the things I’d like to figure out. But I have confidence that if I had worlds enough in time, I could I could unravel whatever I tried hard enough to unravel.


Will Bachman  38:35

Talk to me about any courses or professors that you had at Harvard that continue to resonate with you.


Joshua Brandon Holden  38:42

Yeah, so one of my very first Harvard experiences was an example of excellent math teaching. That was in math 25, which apparently has gone many variations over the year, but years, but when I was we were there. It was a sort of an honors calculus. They generally assumed that we’d seen calculus before. And they were going to teach it to us, again, with all of the theory. And I love that. And I loved Professor McConnell, who I’m still Facebook friends with and occasionally actually look at my Facebook page and see him. I just did last week actually. He was a post a post doctorate fellow, or a senior lecturer, I suppose. At Harvard, Cool I heard later was told by his colleagues that he was spending too much time on teaching. But he was a great guy. And just a really clear, motivating and relatable teacher. So a lot of that attitude that, you know, yes, if things are presented the right way, you can learn it, whatever it is. A lot of that came from him as well as you know, really great examples of how to be a good teacher.


Will Bachman  40:40

Amazing. One final question I have Oh, okay.


Joshua Brandon Holden  40:44

All right, which


Will Bachman  40:45

was, tell us about how you ended up changing your name. Ah, okay. Yeah, some of our classmates one week might be curious. And they’ll be like, Well, why didn’t you ask that? So,


Joshua Brandon Holden  40:55

yeah, that was the first of my non professional wanderings and turns, which is when my wife and I got married. I would hardly, I was a liberal firebrand without the Firebrand. Yes. But I was I grew up on free to be you and me, which, which was also in the news lately, for an anniversary. I really felt it was completely unfair for her to take my name, which is actually what she had intended to do. But I told her that we could do anything other than that, and gave her a long, you know, we could keep our own names. We could hyphenate our names, we could swap names, I could take hers, and she could take them off. You know, I


Will Bachman  42:04

have never heard of that swapping.


Joshua Brandon Holden  42:05

I’m not sure I’d actually ever heard of anybody who had done it either. But it seemed as you know, why not? We’re


Will Bachman  42:13

being we’re being we’re being collectively exhaustive.


Joshua Brandon Holden  42:18

So so what we what we settled on, was combining our names. So she was looking at homes. And I was Joshua Brandon. So we combined them into Holden. All right, yeah. We had a friend who suggested whole brand, but we didn’t go with that. All


Will Bachman  42:39

right. I have not heard of that. Option two. That is pretty cool. So invented a new line where you merge is like a merger.


Joshua Brandon Holden  42:49

Yep. Very cool. Exactly. Josh,


Will Bachman  42:52

where can people find you online?


Joshua Brandon Holden  42:55

Yeah, go to www dot math of That’s the homepage for my book, but also my professional homepage, and also has contact information for me.


Will Bachman  43:11

Fabulous. Josh, thank you so much for being on the show today. This is a great discussion. Thanks


Joshua Brandon Holden  43:17

very much. I really enjoyed it. Hope to talk to you again sometime.