In this conversation, Semon Rezchikov and I talk about what other disciplines can learn from mathematics, creating and cultivating collaborations, working at different levels of abstraction, and a lot more!

Semon is currently a postdoc in mathematics at Harvard where he specializes in symplectic geometry. He has an amazing ability to go up and down the ladder of abstraction — doing extremely hardcore math while at the same time paying attention to *how* he's doing that work and the broader institutional structures that it fits into. Semon is worth listening to both because he has great ideas and also because in many ways, academic mathematics feels like it stands apart from other disciplines. Not just because of the subject matter, but because it has managed to buck many of the trend that other fields experienced over the course of the 20th century.  

Links

Semon's Website

Transcript

[00:00:35 ] 

Welcome back to idea machines. Before we get started, I'm going to do two quick pieces of housekeeping. I realized that my updates have been a little bit erratic. My excuse is that I've been working on my own idea machine. That being said, I've gotten enough feedback that people do get something out of the podcast and I have enough fun doing it that I am going to try to commit to a once a month cadence probably releasing on the pressure second [00:01:35 ] day of.

Second thing is that I want to start doing more experiments with the podcast. I don't hear enough experiments in podcasting and I'm in this sort of unique position where I don't really care about revenue or listener numbers. I don't actually look at them. And, and I don't make any revenue. So with that in mind, I, I want to try some stuff.

The podcast will continue to be a long form conversation that that won't change. But I do want to figure out if there are ways to. Maybe something like fake commercials for lesser known scientific concepts, micro interviews. If you have ideas, send them to me in an email or on Twitter. So that's, that's the housekeeping.

This conversation, Simon Rezchikov and I talk about what other disciplines can learn from mathematics, creating and cultivating collaborations, working at different levels of abstraction. is currently a post-doc in mathematics at Harvard, where he specializes in symplectic geometry. He has an amazing ability to go up, go up and down the ladder of [00:02:35 ] 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.

He's worth listening to both because he has great ideas. And also because in many ways, academic mathematics feels like it stands apart from other disciplines, not just because of the subject matter, but because it has managed to buck many of the trends that other fields experience of the course of the 20th century.

So it's worth sort of poking at why that happened and perhaps. How other fields might be able to replicate some of the healthier parts of mathematics. So without further ado, here's our conversation.

[00:03:16 ] Ben: 

I want to start with the notion that I think most people have that the way that mathematicians go about a working on things and be thinking about how to work on things like what to work on is that you like go in a room and you maybe read some papers and you think really hard, and then [00:03:35 ] you find some problem.

And then. You like spend some number of years on a Blackboard and then you come up with a solution. But apparently that's not that that's not how it actually works. 

[00:03:49 ] 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.

Vary between disciplines I think yeah, within mathematics. So I think, but also on the other hand, it's also hard to define what is a single project. As you know, a single, there might be kind of a single intellectual art through which several papers are produced, where you don't even quite know the end of the project when you start.

But, and so, you know, two, a two years on a single project is probably kind of a significant project for many people. Because that's just a lot of time, but it's true that, you know, even a graduate student might spend several years working on at least a single kind of larger set of ideas because the community does have enough [00:04:35 ] sort of stability to allow for that.

But it's not entirely true that people work alone. I think these days mathematics is pretty collaborative people. Yeah. If you're mad, you know, in the end, you're kind of, you probably are making a lot of stuff up and sort of doing self consistency checks through this sort of formal algebra or this sort of, kind of technique of proof.

It makes you make sure helps you stay sane. But when other people kind of can think about the same objects from a different perspective, usually things go faster and at the very least it helps you kind of decide which parts of the mathematical ideas are really. So often, you know, people work with collaborators or there might be a community of people who were kind of talking about some set of ideas and they may be, there may be misunderstanding one another, a little bit.

And then they're kind of biting off pieces of a sort of, kind of collective and collectively imagined [00:05:35 ] mathematical construct to kind of make real on their own or with smaller groups of people. So all of those 

[00:05:40 ] Ben: happen. And how did these collaborations. Like come about and 

[00:05:44 ] Semon: how do you structure them? That's great.

That's a great question. So I think this is probably several different models. I can tell you some that I've run across. So during, so sometimes there are conferences and then people might start. So recently I was at a conference and I went out to dinner with a few people, and then after dinner, we were.

We were talking about like some of our recent work and trying to understand like where it might go up. And somebody, you know, I was like, oh, you know, I didn't get to ask you any questions. You know, here's something I've always wanted to know from you. And they were like, oh yes, this is how this should work.

But here's something I don't know. And then somehow we realized that you know, there was some reasonable kind of very reasonable guests as to what the answer is. Something that needed to be known would be so I guess now we're writing a paper together, [00:06:35 ] hopefully that guess works. So that's one way to start a collaboration.

You go out to a fancy dinner and afterwards you're like, Hey, I guess we maybe solved the problem. There is other ways sometimes people just to two people might realize they're confused about the same thing. So. Collaboration like that kind of from somewhat different types of technical backgrounds, we both realized we're confused about a related set of ideas.

We were like, okay, well I guess maybe we can try to get unconfused together. 

[00:07:00 ] 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?

Well, 

[00:07:28 ] Semon: you probably have to understand a little bit about the other person's work and you probably have to in some [00:07:35 ] 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.

So that's actually a crucial thing. It's like the personal aspect of it. Then you know it because maybe you'll you kind of like this person's work and maybe you like the way they go about it. That's interesting to you. Then you can try to, you know, talk about what you've recently been thinking about.

And then, you know, the same mathematical object might pop up. And then that, that sort of, that might be you know, I'm not any kind of truly any mathematical object worth studying, usually has incarnations and different formal languages, which are related to one another through kind of highly non-obvious transformation.

So for example, everyone knows about a circle