Transcription
Simone: Welcome to "On A Tangent", the podcast where the main characters are the stories behind the mathematics. My name is Simone, and in each episode I will meet a different early career mathematician from Muenster to learn about their stories, their paths towards mathematics, and their hopes for the future. In this episode, I am joined by Alex, a PhD student in General Relativity, 'GR' for short, to learn about eclipses, cosmic censorship, and surgery. I hope you enjoy the episode!
Simone: Hello, Alex and welcome. Thank you for joining us.
Alex: Hello, Simone. It's really nice to be here.
Simone: So you're a PhD student in general relativity. So when you go home and your friends ask you, what do you do? What do you tell them?
Alex: So first, I take a very deep breath. Uh, no, actually, I think that as a mathematician, being in general relativity makes this job of sharing what I do easier, because it's one thing to say, oh, I'm a model theorist, and I study this and that.
Simone: This is a personal attack to myself.
Alex: It is. I mean, it's another thing to mention, say, a black hole, which is much more part of pop culture. And that helps me in some sense. It also saddens me because I realise that I have to be imprecise in order for them to receive the message. But okay, what I typically tell them is that I try to study through math the stability of black hole solutions to Einsteins equations, and this is kind of easy to get through because then people imagine, oh, black holes, there's these things that are described using math and okay, these things are hard, but I can do something with this math. But it creates an idea in their mind typically. Then the next thing they ask me is, so do you make experiments, which I think is something unique to people in my field, I don't think people ask you about experiments.
Simone: No, definitely not.
Alex: Okay, then I have to explain to them that what I do cannot really be experimented, but it's more connected to questioning the consistency of a theory. And I do think that what I do, the message really arrives to say my family, my friends. So I think I feel like I'm in a privileged position.
Simone: I was once reading a message, I think maybe on Twitter by a professor who was saying, you know, everybody learns what a black hole is in high school or what, uh, the DNA is, right. Nobody learns what a manifold is in high school, which might be trickier, but somehow it is a bit easier if you can explain it with the pretty pictures.
Alex: Yeah, and the physical phenomenon maybe is maybe easier to relate to. I think the weird thing is that they don't realise that what I do is still very abstract, and they think of it as being, um, enjoyable in a way that is not really what I go through. Um, there's much more technicality involved, but there's no hope of passing it through, of really creating a picture of this type of technicality. So I just accept that I'm going to mention interstellar and they'll be happy and very excited.
Simone: Having a mainstream reference for it is a very good attack point.
Alex: Yeah. I'm almost as lucky as a physicist, let's say, even if I don't really do what they do. I mean, I don't have the abilities to do what they do.
Simone: So this is you now. Let's take a step back. What is the earliest moment you can remember in your life where maths entered the picture?
Alex: Um, so I'm afraid I might be unrelatable to the general public when I actually answer this question. But I have to be honest, math has always been with me, and that for whatever reason that I couldn't really understand, among all the things that I like, it was my greatest interest and the first memory of it I that I have, which might seem also unrelated, but to me it was a moment of mathematical interest and understanding was when at some point we were waiting for an eclipse to happen. I was home with my mom and dad, and they just told me, the eclipse is going to happen. And I had some trouble understanding what it what it meant, um, because I couldn't picture in my head the kind of the geometric configuration that would allow for the eclipse to happen. And so I asked my dad to explain to me, and we went, you know, over his big bed, and we took some balls, I think an orange and, like, maybe a lemon or something. And my dad, like, put them on the on the bed and said, okay, this is the solar system, this is the moon, this is the Earth. And what we're going to witness today happens because of this geometric configuration. Right? And for me, that was my first approach with math. And I think it also in some sense it is coherent with the sort of interests I've had later, which were more connected to geometry.
Simone: I was going to ask, do you think somehow this is what brought you to a field where maybe geometric intuition or imagining visually what's going on is important?
Alex: I don't know if it brought me. I mean, I don't see it as a cause, rather I see it as a maybe as a symptom of something already there. Maybe I don't have that story of a little kid thinking about numbers, but I was always intrigued by geometry, by a perception of distance, by just configurations of objects in space. And this definitely is something that I also witnessed in the choices I made later during university and uh, and everything that led me to where I am right now.
Simone: So how did you arrive where you are? How did you choose what to do?
Alex: Um, so as I said, I was always drawn to it. It almost felt like, uh, like a choice that was made by someone else. And that for whatever reason, I always felt like, oh, this is actually what I like the most. Then I also liked other things very much. I liked philosophy very much. I really wanted to go into that. I liked ancient languages very much. Part of me wanted to study Latin and Greek.
Simone: Did you study them in school?
Alex: I only studied Latin in school, unfortunately. But I made this choice because I thought, okay, if I want to study math, and it is certainly what I want to know the most before anything else. wI also believe that there is a right time to do it, because I felt like my brain would be better off studying math at an earlier age, and then maybe, uh, other things at a later age, then the opposite. And so this made me confident that what I felt was right for me, which was to study math, was also objectively, in some sense, the most optimal choice\'85 in terms of long term plans, even if it meant sacrificing other interests that I maybe had. And sometimes I wondered, okay, could I try doing something else? And something which may seem unrelated, but that I was very interested in: I've always wanted to be a surgeon, just because how cool is it? Okay, this is going to sound weird, but to actually see the inside of a body.
Simone: It's certainly something, right, you don't see every day. It's a bit of a mysterious thing.
Alex: And also, okay, the idea of having that role where some problems that are very hard to solve, they maybe can be solved through surgery. And somebody that has, you know, studied for years has a special set of skills. They can do that for you. And, um, I try to imagine myself into that career. But then I realised I would have suffered too much the loss of the mathematical knowledge, whereas I could have, you know, accepted the loss of, say, the surgical knowledge, or the knowledge that I've had to sacrifice because of course, there is only one thing you you can reasonably master. I mean, unless you're specially gifted or something.
Simone: Or you have a lot of free time, and somebody at home that takes care of everything. So this is how you came to math. But how did you come to general relativity then? I mean, you told me you've always been geometrically inclined.
Alex: Yeah, but I would say I came to GR because at some point I really took into my own hands my journey. I studied in Italy, where, as you know, we tend to have less freedom than in other countries. Which okay it can be both good and bad. It certainly allowed me to see a lot of different math, which was good. But then I reached a point where I realised that even if I was very much interested in geometric problems and certain type of problems specifically, there was something about GR and black holes because of course, I live in the same world as anybody. And as we said before, GR is much more part of pop culture. And of course this has an effect on me too. And at some point I realised, okay, maybe I like it. This is kind of the base, you know, the bottom line, it's that I like it, but it's also something that it is probably easier to maintain interest in because of course, studying math is hard, right? Sometimes you're like, it's the equivalent of walking into a dark room. Um, and at least for me, I thought it was a good move to pursue an interest in something that, um, I can much more easily, uh, renew my interest for. Because in some sense, it's at least for me much easier to renew my excitement for black holes than it is to renew my excitement for the homology groups of positively curved manifolds.
Simone: And also, how cool is it that you can go and tell people "I work on black holes", right?
Alex: Yes, yes. I mean, let's not hide that. There is, at least for me, an influence in my choices given by the fact that I like to be the person that does this, other than I like to just do it. And of course it is. It is cool. I mean, I like to think of myself as a person that has this interest but at a certain point either you're lucky and the professors and the people around you in the university where you study actually share those interests, or you have to create a path for yourself. And this is what I did. I did it a specific time. I don't think you can do it at all times, like when you're much younger, of course, it's much harder. It certainly would have been too hard for me. But it also was somehow natural because I reached a point where I had a I felt like I had a decent understanding of all the tools needed to pursue this, this interest. And I realised, who are the people that could help me get into this field? And even if they were not in my home university, I looked for ways to get in touch with these people. And I don't know, for whatever reasons, the planets aligned again.
Simone: Like in the eclipse.
Alex: Like an eclipse.
Simone: The orange, the lemon...
Alex: And somehow I've ended up doing something that that I like very much, which was not the only option here, I want to say again, but it's the one on which I bet.
Simone: So you moved to Switzerland first and then here.
Alex: And then I came here, yes. Because there was some previous student of a professor that I had that was somehow between what I was doing before, which was a geometric analysis, and GR, which is what I'm doing right now. And this person was a bridge. But most importantly, moving away from my hometown, which was actually not my hometown, but my home university. It allowed me to meet other people that also made a bridge. And, you know, most of the times, unless you meet the people, you don't even realise that certain areas of research exist. This was my case. I didn't realise that it was possible to study black holes using this set of skills that a mathematician has, which is the set of skills that I have at my disposal. Until I went to Zurich and I met a person that was doing this. So I think overall, other than believing in yourself and kind of for once not doing exactly what you're supposed to do, more than that, you also need to be a bit lucky right, to meet the right person that tells you yes, you can do this. And then you realise, oh, I could do this, and then you do this. Um, so it's a series of factors and. Okay, luck is always a factor.
Simone: So this is the now. This is why you do it. So what is the future ahead of you that you would like to see? What is a theorem that you would like to see proven well by yourself maybe, or others of course, in the next ten, 20, 30 years.
Alex: Among all the things that I initially looked at when I started exploring this mathematical general relativity field, there is something specifically that really caught my attention, and that's something called strong cosmic censorship conjecture.
Simone: Which is a very metal name.
Alex: I mean, it's very cool. It's very easy to sell. And I mean, they sold it to me effectively. Yes. I mean, reasonably, this is something that is probably gonna take on a hundred years, uh, maybe they won't even be enough because also my field is relatively young compared to other fields, but in essence, what I like about it, and I think this is like further proof of how much more easily I can communicate what I do if compared to other people. Basically, this conjecture says that the theory of general relativity is deterministic, and which you would say, oh, why? Why shouldn't it be deterministic? Well, it turns out that this is not something to take for granted because, okay, in very layman terms, there are some black hole solutions to Einstein equations that present something that's called Cauchy horizon, which I won't go into the the reason why it's called like that, but in essence, it's like a geometric locus where the theory at times appears not to be capable of predicting uniquely what happens to an observer or a person or an object passing this horizon. And this conjecture that I mentioned, the strong cosmic censorship conjecture, in essence, it says that although you can, uh, write down solutions of the Einstein's equations which display this behaviour, they are not generic in the sense that if you consider the initial data that give rise to the solution and you perturb them, then once you apply this perturbation, you no longer end up with a spacetime or a solution that that has this feature.
Simone: So somehow the solutions that don't work like we expect, we expect physical theories to work deterministically, right? Yes, we put in the initial data and we know and we predict what's going to happen. Yes. So the solutions that don't behave like this are just an exception. So they just happen. And then but if you move a bit away from that then it works just fine.
Alex: Yeah. Like trying to balance a picture upside down. Right. There is an equilibrium point. Ideally you could balance it and put it up on the wall. But you know the moment you perturb it a little bit, it's just going to go down and eventually it's going to stabilise along the other reasonable equilibrium point that you can use to put a picture up on the wall. And this is the same idea. And also I feel like this is the best representation of what it means to do general relativity. As a mathematician with the skills of a mathematician, I don't have the ability to do what the physicists do. But you know, with our set of skills, we can investigate questions such as this one, which they are really about the consistency of the theory. They are really giving meaning to the words determinism of general relativity. And they're doing it in a very reliable way, because I'm really, you know, taking the equations and rigorously trying to prove that the theory is deterministic.
Simone: And actually predicts our reality as we expect it.
Alex: Yes, yes. Um, so this would be very nice. Um, yeah. I think whoever puts the last brick on this collective effort is certainly going to be a famous man. Uh, but I don't know how long it will take. I would be happy if I gave my contribution. But not necessarily for the glory of it, which, uh, I confess for sure. And for the first years of my journey in math it was part of the motivation. But then I think, certainly once you entered the PhD, what I really want for myself is to, uh, have given some contribution and at the same time have a certain set of skills and of knowledge and of understanding that allows me to sit with my peers and give something to them in conversation, right? What I envy is not, say, the list of awards that, uh, professors have or may have. I mean, in part, we all envy that, right? But what I envy on a daily basis is the fact that they, they can navigate their department and talk to other people, and they have conversations where there's an actual like exchange between them. They don't just have to sit there and take as much as they can, which is what you just have to do at the beginning, right. Somehow it's also a necessary step, I mean, to have these conversations, right? Because nobody will prove the strong cosmic censorship conjecture or any other big conjecture on their own.
Simone: Math is necessarily a collective effort that we all have to do together.
Alex: And then we need to be able to interact and communicate. Yes. I feel like this is in the end, what once you're when you're inside, when you're doing your PhD or doing some research, or maybe if you're just a master's student, you realise that really what gives you the feeling of having owned your spot inside the community? It's really just this, you know, sitting down, having a coffee after lunch and being able to contribute to a conversation. It's not, I don't know, the list of pieces of paper that you've earned. And really it comes from the human interaction, which is something that I only discovered and touched with firsthand once I started doing my PhD. And maybe, maybe this is something that, uh, professors and researchers and everybody in charge should try to pass on to students while they're studying, maybe to boost motivation, because I, I think people think of math as a very lonely career. Unless maybe you're at the top of the top.
Simone: Yes. Because we have these images, right? We see movies or in or in on also the stories we hear. I mean, of Wiles proving Fermat's Last Theorem alone for eight years.
Alex: Yeah, and okay, this can happen. But actually the majority of the work is not like this, right? I mean, it's more about really sitting down, having a coffee, discussing what's going on. Slowly. Brick by brick is anybody would do in their generic work like office work. You have your colleagues, you work together on something and you collaborate. If anything, we're luckier because we are actually working for ourselves. And so yeah, I think that is the best part. That is what I also what reasonably I think keeps us motivated because one does not just blindly pursue this career in hope of one day maybe receiving an incredible piece of recognition. It really is a daily life to daily department life that fuels you and it allows you to move forward.
Simone: Yeah. Also because right, you cannot force maths to work.
Alex: No, sometimes it doesn't work.
Simone: Right. Uh, and so sometimes you, you go and go and go at the same problem for, for infinite time and then you still don't get results because that's how it goes. So yeah, that's true.
Alex: I mean, motivation can hardly come from the success because you cannot control it. You cannot predict it. You have to find a way to make the process, if not enjoyable, because maybe this is aiming too high, but sustainable. So a good balance of positive emotions and negative emotions otherwise I mean you're not going to go anywhere because I feel like it's just against the human nature. And it's weird that the narrative that that people receive from the outside is of people somehow going against the human nature, which is probably the reason why those that are depicted, maybe movies are this very, um, um, this genius people or this very, um, uncommon people in some sense. And I feel like this is what makes them uncommon in the eye of the, of whoever is watching. But really, this is far from the reality of the department, or at least of the departments that I've inhabited and navigated.
Simone: Well, thank you very much for this lovely chat.
Alex: See you soon around the corridor.
