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episode icon Idea Machines
Managing Mathematics with Semon Rezchikov [Idea Machines #44]
In this conversation, Semon Rezchikov and I talk abo... more
May 30 2022 57m
Chapter 1 59 sec
Chapter 2 59 sec
day of
Chapter 3 40 sec
abstraction, doing extremely hardcore math while at the same time, paying attention to how he's doing the work and the broader institutional structures that affect
Chapter 4 18 sec
Ben
Chapter 5 13 sec
you find some problem
Chapter 6 45 sec
Semon: Okay. I don't think that's a complete description. So definitely people spend time in front of blackboards. I think the length of a typical length of a project can definitely
Chapter 7 59 sec
sort of stability to allow for that
Chapter 8 4 sec
mathematical construct to kind of make real on their own or with smaller groups of people. So all of those
Chapter 9 3 sec
Ben: happen. And how did these collaborations. Like come about and
Chapter 10 50 sec
Semon: how do you structure them? That's great
Chapter 11 24 sec
hopefully that guess works. So that's one way to start a collaboration
Chapter 12 27 sec
Ben: Can I, can I interject, like, I think it's actually realizing that you are confused about the same problem as someone who's coming at it from a different direction is actually hard in and of itself. Yes. Yes. How, how does, like, what is actually the process of realizing that the problem that both of you have is in fact the same problem?
Chapter 13 6 sec
Semon: you probably have to understand a little bit about the other person's work and you probably have to in some
Chapter 14 59 sec
way, have some basal amount of rapport with the other person first, because. You know, you're not going to get yourself to like, engage with this different foreign language, unless you kind of like liked them to some degree
Chapter 15 17 sec
intuitions through which you can grapple with this sort of object
Chapter 16 17 sec
Ben: Yeah. But I think the cruxy thing for me is that it is at the end of the day, it's like a really human process. There's not a way of sort of colliding what both of, you know, without hanging out
Chapter 17 23 sec
Semon: So people. And people can try to communicate what they know through texts. So people write reviews on
Chapter 18 59 sec
meeting this subject into existence
Chapter 19 15 sec
the problems or the theorems, ideally down to something that you don't need a huge superstructure in order to engage with, because then people will different, like techniques or perspective can engage with the same thing
Chapter 20 43 sec
Ben: do you think that mathematics is. Unique in its ability to sort of have those both like clean problem statements. And, and I think like I get the sense that it's, it's almost like it's higher status in mathematics to just declare problems
Chapter 21 9 sec
problems is fairly low status, unless you simultaneously point out the problem and then solve it
Chapter 22 49 sec
Semon: Potentially. So I think, yeah, anyone can make conjectures in that, but usually if you make a conjecture, it's either wrong or on. Interesting. It's a true for resulting proof is boring. So to get anyone to listen to you, when you make problem, you state problems, you need to, you need to have a certain amount of kind of controllers
Chapter 23 10 sec
similar process. And I do think that pointing out, like, look, here's a protein that we don't understand. And you didn't know about the existence of this protein. That can be a fairly high status work say in biology
Chapter 24 9 sec
Ben: Yeah, no, I like that a lot that math does not have, you could almost say like the substrate, that the context of reality
Chapter 25 25 sec
Semon: I mean it's there, right? It's just that you have to know what to look for in order to see it. So, right. Like, you know, number theorists, love examples like this, you know, like, oh, everybody knows about the natural numbers, but you know, they just love pointing out
Chapter 26 2 sec
Ben: It's not my thing really been around for a few thousand years. It's
Chapter 27 1 sec
Semon: old. Yeah
Chapter 28 2 sec
Ben: W w what would you
Chapter 29 1 sec
Semon: this is just curiosity
Chapter 30 2 sec
Ben: you call the first
Chapter 31 2 sec
instance of number theory in history?
Chapter 32 34 sec
Semon: I'm not really sure. I don't think I'm not a historian in that sense. I mean, certainly, you know, the Bell's equation is related to like all kinds of problems in. Like I think grease or something. I don't exactly know when the Chinese, when the Chinese remainder theorem is from, like, I I'm, I'm just not history
Chapter 33 21 sec
Ben: Okay. Yeah. So then going, going back to collaborations I think it's a surprising thing that you've told me about in the past is that collaborations in mathematics are like, people have different specializations in the sense that the collaborations are not just completely flat of like everybody just sort of
Chapter 34 7 sec
stabbing at a place
Chapter 35 51 sec
Semon: Yeah. So I think different people are naturally drawn to different kinds of thinking. And so they naturally develop different sort of thinking styles. So some people, for example, are very interested in someone had there's different kinds
Chapter 36 33 sec
people who do geometric analysis. Kind of geometric objects defined by partial differential equations and they want something very concrete. And there are relations between questions about areas. So I've spent some time trying to think about how one can kind of profitably move from one to the other
Chapter 37 1 sec
Ben: that was originally dice
Chapter 38 23 sec
Semon: And maybe I'm not sure, but it's certainly a very helpful framework. I think some people really want to take a single problem and like kind of stab at it. Other people want to see the big picture and how everything fits. And both of these types of work can be useful or useless depending on sort of the flavor of the, sort of the way the person approached it
Chapter 39 4 sec
of more birdlike and more frog like, and that can be a very productive
Chapter 40 13 sec
Ben: And how do you make your, like let's, let's let's date? Let's, let's frog that a little bit. And so like, what are the situations
Chapter 41 40 sec
Semon: frocks. Great, good. This is, I feel like this is somehow like very clearly known. So the success so-so what frogs fail at is they can get stuck on a technical problem, which does not matter to the larger aspect of the larger university
Chapter 42 59 sec
engaging with kind of the lower level details of mathematical reality. So. They can show the birds something they could never see and simultaneously they often have a lot of technical capacity. And so they can, you know, there might be some hard problem, which you know, no one, a large perspective can help you solve
Chapter 43 50 sec
ultimate bird success. The failure mode is that you spend a lot of time piecing things together, but then you only work on problems, which are, which makes sense from this huge perspective
Chapter 44 4 sec
Ben: yeah
Chapter 45 3 sec
Semon: too general, almost. That's very often a
Chapter 46 59 sec
problem. So so you know, one thing that one bit of mathematics that is popular among non mathematicians for interesting reasons is category. So I know a lot of computer scientists are sort of familiar with category theory because it's been applied to programming languages fairly successfully
Chapter 47 59 sec
framework of categories, There's a very general theorem and category theory, which implies what you wanted, what that tells you in some sense of that. Your question was not interesting because it had no, you know, it really wasn't a question about the concrete objects you were looking at at all
Chapter 48 26 sec
are kind of not necessarily developed in a way to be made relevant to the rest of mathematics and that there is a sort of natural tension that anyone is interested in. Category theory has to navigate. How far do you go into the land of abstract nonsense? So, you know, even as the mathematicians are kind of viewed as like the abstract nonsense people by most people, even within mathematics is hierarchy continues and is it's factal yeah
Chapter 49 32 sec
Ben: And actually that actually goes back to I think you mentioned when you're, you're talking about the failure mode of frogs, which is that they can end up working on things that. Ultimately don't matter. And I want to like poke how you think about what things matter and don't matter in mathematics because sort of, I think about this a lot in the context of like technologies, like people, people always think like technology needs to be useful for, to like some
Chapter 50 25 sec
but like some end consumer
Chapter 51 33 sec
Semon: how do you think about, so it's definitely not true that people decide which mathematics matters based on its applicability to real-world concerns. That might be true and applied with medics actually, which has maybe in as much as there's a distinction that it's sort of a distinction of value and judgment
Chapter 52 59 sec
understand
Chapter 53 59 sec
obviously important because it turns out to be connected to other questions and all of mathematics. So that's one perspective, kind of the, the, the simplest, like the questions that any mathematician would kind of find interesting
Chapter 54 54 sec
any physical belief about our world
Chapter 55 4 sec
Ben: but as you were saying that there, there are these like narrative arcs
Chapter 56 3 sec
Do something that is both like correct and defies the narrative
Chapter 57 24 sec
Semon: That's an interesting, that means there must be something there, or maybe not. Maybe it's only because there was some technicality and like, you know, the technicality is not kind of, it doesn't enlighten the rest of the narrative. So that's some sort of balance which people argue about and is determined in the end, I guess, socially, but also through the production of, I don't know, results and theorems and expect mathematical experiments and so forth
Chapter 58 24 sec
Ben: And to, to, so I'm gonna, I'm going to yank us back to, to the, the, the collaborations. And just like in the past, we've talked about like how you actually do like program management around these collaborations. And it felt like I got the impression that mathematics actually has like pretty good standards for how this is
Chapter 59 1 sec
Semon: do you mean by program management? Meaning
Chapter 60 3 sec
Ben: like like you're like, like how, like
Chapter 61 15 sec
how you were basically just managing your collaborators, like you you're talking about like how, what was it? It was like, you need to like wrangle people for, for. I, or yeah, or like, yeah. So you've got like, just like how to manage your collaborators
Chapter 62 2 sec
Semon: So I guess
Chapter 63 1 sec
Ben: we were developing like a theory on that
Chapter 64 11 sec
Semon: Yeah, I think a little bit. So on one hand, I guess in mathematics and math, every, so in the sciences, there's usually somebody with money and then they kind of determined what has. Is
Chapter 65 1 sec
Ben: this, is this a funder or is this like
Chapter 66 24 sec
Semon: a, I would think the guy pie is huge
Chapter 67 22 sec
then a bunch of creative work happens at lowest level. But you know, you're very constrained by what's possible in your lab in mathematics. There aren't really labs, right. You know, there are certainly places where people know more. Other places about certain parts of mathematics. So it's hard to do certain kinds of mathematics without kind of people around you who know something because most of the mathematics isn't written down
Chapter 68 2 sec
Ben: that, that statement is shocking in and of itself
Chapter 69 32 sec
Semon: The second is also similar with the sciences, right? Like most things people know about the natural world aren't really that well-documented that's why it pays to be sometimes lower down the chain. You might find something that isn't known
Chapter 70
Ben
Chapter 71 4 sec
like resolving, resolving. The confusion in a legible way
Chapter 72 54 sec
Semon: it sort of pushes the field. So that's, but also because everyone kind of can work on their own, you know, coordination involves, you know, a certain amount of narrative alignment
Chapter 73 44 sec
larger, but that's like kind of one on a single project collaboration to do larger collaboration. You have to kind of, you know, give you have to assign essentially you have to assign social value to questions, right? Like math, unlike sort of the math is small enough that it can just barely survive
Chapter 74 4 sec
Ben: do you know, like roughly how many mathematicians. I can, I can look this
Chapter 75 9 sec
Semon: up. I mean, it depends on who you count as a mathematician. So that's the technique I'm asking you. The reason, the reason I'm asking
Chapter 76 36 sec
that is because of course there's the American mathematical society and they publish, like, this is the number of mathematicians
Chapter 77 7 sec
Ben: a compared to, to most other disciplines then, especially compared to even. Science as a whole like research
Chapter 78 14 sec
Semon: has a whole. Yeah. So yeah, I think like if you look at like, you know, all the, if you say like, well look at the Harvard Kennedy school of business, and then they have an MBA program, which is my impression is it's serious
Chapter 79 14 sec
And then you also look at like all the math pieces. Graduates and like the top 15 kind of us schools are kind of like, you know, I think the MBAs are like several times lecture. Yes. So that's, maybe I was surprised to learn that
Chapter 80
Ben: that's also good. Instead of
Chapter 81 43 sec
Semon: like, you can look at the output rate, the flow rate, that's a very easy way to decide
Chapter 82 37 sec
things, then it'll be better for you because they fit into a larger context. So therefore your work is more significant that you're actually doing them a service by explaining some larger context. And simultaneously by sort of pointing out that maybe some problem is easy or comparatively, easy to some people that you, you might not do
Chapter 83 21 sec
Ben: And actually speaking of the social nature of mathematics I get the impression that mathematics sort of as a discipline is. It feels much closer to what one might think of as like old academia then many other disciplines in the sense that my, my impression is
Chapter 84 10 sec
that your, your tenure isn't as much based on like how much grant money you're getting in
Chapter 85 48 sec
Semon: gay. Yeah. There's definitely pressure to publish. There, the expected publishing rate definitely depends on the area. So, you know, probability publishers more, in some ways it's a little bit more like applied mathematics, which has more of a kind of paper mill quality to it
Chapter 86 49 sec
worried. But yeah, it's definitely not determined based on grant money because essentially there's not that much grant money to go around. So that makes it have more of this old-school flavor. And it's also true that it's still not, it's genuinely not strange for people to graduate with like just their thesis to graduate from a PhD program
Chapter 87 1 sec
Ben: what sort of, what, what does that work
Chapter 88 7 sec
Semon: actually look like? Well, I think it's true that it is actually true that grad students are not required to like publish a paper a year
Chapter 89 42 sec
that's true. And that's great that people, I think, do defend that kind of position and they are willing to put their reputation on the line and the kind of larger hiring process to defend that SAC separately. It's true that, you know, You know, work that is not coming out of one of the top three people or something is can still be considered legitimate
Chapter 90 7 sec
Ben: helpful
Chapter 91 8 sec
Semon: yeah, I think that a lot of it comes from teaching. A certain chunk of it comes from grants. Like basically people use grants to, in order to teach less. Yeah. That's more or
Chapter 92 37 sec
less how it works. You know, of course there's this, as in, you know, mathematics has this kind of current phenomenon where, you know, rich individuals like fund a department or something or they fund a prize
Chapter 93 7 sec
Ben: If it's, for some reason, it's every mathematician magically had say order of magnitude more funding
Chapter 94 13 sec
Semon: when it matters. Yeah. So it's not clear that they would know what to do with that. There is, I thought a lot about the question of, to what degree does the mathematics is some kind of social enterprise and that's maybe true of every research
Chapter 95 51 sec
program, but it's particularly true in mathematics because it's sort of so dependent on individual creativity
Chapter 96 7 sec
Ben: that's, that's like structurally baked into almost the entire world where there's just a ton of it's, it's
Chapter 97 14 sec
very hard to do something completely different than the things that you have done. Right? People, people, boat, people. Our book more inclined to help you do things like what you've done in the past
Chapter 98 11 sec
Ben: And, and sort of speaking of, of money in the past, you've also pointed out that math is terrible at capturing the value that it creates in this
Chapter 99 18 sec
Semon: Well, yeah. You know, math is, I mean, it may be hard to estimate kind of human capital value
Chapter 100 10 sec
Ben: sort of downstream, like basically every, every technical anything we have is to some extent downstream
Chapter 101 2 sec
Semon: th there is an argument to be made of that kind. You know
Chapter 102 59 sec
I don't think one should over I think, you know, there are extreme versions of this argument, which I think are maybe not helpful for thinking about the world. Like you shouldn't think like, ah, yes, computer science is downstream of the program
Chapter 103 59 sec
before a totally different community can really engage with them
Chapter 104 6 sec
clearly on this sort of path in a way that you kind of, it's very hard to imagine removing a completely. Yeah
Chapter 105 19 sec
Ben: So, no, I like it also because it's, again, it's, it's sort of this extreme example of some kind of continuum where it's like, everybody knows that math is really important, but then everybody also knows that it's not a
Chapter 106 32 sec
Semon: applicable. Yeah. And there's this question of, how do you kind of make the navigation that continuum smoother and that has you know, that's like a cultural issue and like an institutional issue to some degree, you know, it's probably true that new managers do know lots of stuff, empirically they get hired and then they get, they like, their lives are fine
Chapter 107 59 sec
people to explore. There is a lot of resistance in the pure mathematics community for people to try to like try random stuff and collaborate with people
Chapter 108 6 sec
issues are things that I guess anyone has a saying, and I, I'm kind of very curious how they will evolve in the coming 50 years
Chapter 109 13 sec
Ben: To, to change the subject just a bit again the, can you, can you dig into how. Do you call them retreats? Like when, when the, the thing where you get a bunch of mathematicians and you get them to all live in a place
Chapter 110 38 sec
Semon: for like, so there's this interesting well that's, there are things with a couple CS there
Chapter 111 59 sec
funding has changed the structure of mathematics. Cause like the Institute of advanced study is basically one of these things. Yes. This Institute at Princeton where like basically a few old people, I mean, I'm kind of joking, but you know, there's a few kind of totemic people like people who have gone there because they sort of did something famous and they sit there
Chapter 112 49 sec
kind of contemporary research and then they like rent out a giant house and then they have, I don't know, 20 people live in this house and maybe cook together and stuff. And then, you know, everyone there's like every learning center is like a week long learning seminar where there's some people who are like real experts in the area, a bunch of people who don't know that much, but would like to learn
Chapter 113 9 sec
Ben: like, I don't know if I'm misremembering this, but I remember you telling me a story where like, there were, there were two people who like needed
Chapter 114 9 sec
to figure something out together and like they never would have done it except for the fact that they just were like sitting at dinner together every night for, for some number of nights
Chapter 115 49 sec
Semon: I. I mean, there are definitely apocryphal stories of that kind where eventually people realize that they're talking about the same thing. I can't think of an example, right? I think I told you, you asked me, you know, is there an example of like a research program where it's clear that some major advance happened because two people were in the same area
Chapter 116 14 sec
people didn't quite realize like how far this would go. So that's kinda, I just gave you that as an example and that happens on a regular basis. That's maybe the reason why people have these programs and conferences, but it's hard to predict because so, you know, I don't really, like, I wish I could measure a rate
Chapter 117 42 sec
Ben: You just need that marination. It's actually like, okay. Oh, a weird thought that just occurred to me. Yeah. That this sort of like just getting people to hang out and talk is unique in mathematics because you do not need to do cause like you can actually do real work by talking and writing on a whiteboard
Chapter 118 1 sec
Semon: subject is. That would
Chapter 119 29 sec
be ideal, but that would be hard because experiments are slow
Chapter 120 5 sec
Ben: And is it, how, how does mathematics not fall into that trap?
Chapter 121 23 sec
Semon: That is a great question. In part there is. So I'm part, there are somewhat strong norms against that, like, because the community is small enough. If it's everyone finds out like, oh yeah, well this person just like scooped kind of, yeah
Chapter 122 40 sec
could do this and somebody does the thing and it's because it was that it's sort of not really scooping. Sure. But if you, if there is really You know, word gets around, like who kind of had which ideas and when people behave in a way that seems particularly adversarial that has consequences for them
Chapter 123 7 sec
Ben: it's like small enough that everybody can have a specialization such that there are people like you, you can always do something that someone else can't
Chapter 124 10 sec
Semon: Often there are people, I mean, that, that might depend on who you are
Chapter 125 59 sec
can develop some intuition about some area where yeah. Other people might be able to kind of prove what you're proving, but you might be much better at it than them. So people will be like, yeah, why don't you do it?
Chapter 126 2 sec
or committees of scientists
Chapter 127 2 sec
Ben: I mean, you could argue about that, right? Because
Chapter 128
Semon: don't
Chapter 129 19 sec
Ben: is it, is it like, I mean, yes, but then like, those committees are sort of mandated by the structure of the funding agencies. Right. And so is it which, and there's of course a feedback loop and they've been so intertwined for decades that I'm clear which way that causality runs
Chapter 130 32 sec
Semon: Yeah. So I remember those are my two guesses for how it's like one, there's just like a very strong norm against this. And you don't, you just don't, you know, if you're the person with the idea. And then you put the other person on the paper because they like were helpful. You don't lose that much. So it's just, you're not that disincentivized from doing it
Chapter 131 2 sec
Ben: It seems like a lot of this does is depend on, on
Chapter 132 44 sec
Semon: scale. Yeah. It's very scale because you can actually find out. Right. And that's a trade-off right
Chapter 133 4 sec
Ben: Do you want to say anything about choosing the right level of Metta newness?
Chapter 134 6 sec
Semon: Yeah. You're thinking about, I guess this is a, this is like a question
Chapter 135 59 sec
for, this is like a personal question for everyone almost. I mean, everyone who has some freedom over what they work on, which is actually not that many people you know, You in any problem domain, whether that's like science, like science research or whether that's like career or whatnot, or even, you know, in a company there's this kind of the, the bird frog dichotomy is replicated
Chapter 136 59 sec
really likes doing kind of like explicit work on something, being down to the ground as a faculty, she would have to do more coordination based work. But that, like, let's see, you kind of have more scope. And also in many cases you are so in many areas, but not in all doing the
Chapter 137 18 sec
system. A B there's just no structural reason why the system would be compensating people appropriately, unless like, there are specific people who are really trying to arrange for that to be the case. And that's you know, that's very hard
Chapter 138 40 sec
Ben: I think, I think that's, yeah. I liked that idea that the. Unless sort of by default, both like status and compensation will flow to the more Metta people. But then that ultimately will be disastrous if, if, if taken to its logical conclusion
Chapter 139
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