Contemplating a career change to physics fear of the grim possibilites

[jorgearce321]

Hello everyone! I am a 20 year old student from a country in Latin America. Right now I am studying pure mathematics, you could say, and I am finishing my third year.

Let me start by stating that I am really dissatisfied by the path my major has been steering towards during this last year. Groups and rings, analysis, functional analysis (I took this course on advance)... I don't know what to say. These topics have pure beauty within them, and solving problems and really understanding the theory and implications behind them is just thrilling for me. But at the end of the day, I am left with many personal questions, such as: "what the hell is this actually good for?" "Will I ever find this useful in my future professional life?" "I fear I am wasting my time"... and so on. Pure mathematicians don't have much going on for them apart from academia. I don't really know when did I fall in this place. But I know how, let me explain.

My background is actually more from physics. I took some university courses in high school: physics I to III, calculus I, chemistry I to II. I was really really good at physics, and I enjoyed it deeply. I even managed to participate and win in international competitions.

Then I got into college. I have been dealing with some psychological issues during this time, but before that my low self esteem made me think I had to be good in everything in order to suceed. In order to be a good physicist, I thought I needed to also be a mathematician and an engineer! So I tried to triple major. I finished the first two years of physics and only took a couple of courses from EE. Inertia made me follow the mathematical path, since I was really good at it and the first courses are WAY more challenging and entertaining than the physics ones. But that eventually comes to an end. You need to think in your future career, and also the maths get unboundedly harder and harder. I could go on as a mathematician with lots of effort and a conscious commitment to study and growth in this area. But I don't see the point anymore in a career with so much effort investment yet so marginal options.

My head is now in a place to take a better decision. I will probably switch to applied mathematics in order to take advantage of what I have done so far and finish a degree. I will dearly miss the mathematical beauty, I must admit. But it is a really, really unhealthy relationship, haha. I find myself dreading it more for all the reasons exposed than loving it and feeling secure in it. It is a little bit frustrating that when I think of leaving it, I get this feeling of remorse, but I need to think of what is best to me.

But that is not what I really want. What I want is to get back into the physical sciences and exploit the biggest talent I have. This could be done in either physics or engineering. My real dream is to study applied physics and work researching and developing something really cool, that has a measurable impact over the world. A career that may benefit from the upcoming technological revolution (nanotechnology, quantum computing, artificial intelligence...), but that may also benefit humanity.

In all of this, I feel huge anxiety and fear. Fear that I get stuck in a PhD without a job I love and without a good income. Fear that I will never be able to develop something good. Fear that I waste so much time studying this and that the market for physics majors becomes SO bad (as many people seem to point). Fear that my only option will be to struggle in academia to get a poorly paid job.

As an engineer, I would fear not having the education needed to understand some of the complex phenomenons that will govern our future life (such as quantum mechanics), and that I will be stuck in a monotone job, even if good paying. I fear I will regret not going into a more theoretical field, with all of its "beauty". I fear I could be selling myself out to a more common and secure career path... all because of fear!

I needed to vent a little bit, but this doesn't seem to stop the confusion, actually. I think I need some advice. Do you think as a physics major (who later goes on to grad school) it is plausible to go into applied physics and have a social mobility similar to an engineer, yet the capability to work in more interesting problems, even more theoretical in the future?

I am feeling really confused right now. Any kind of help would be greatly appreciated. Thank you very much!

 

[homeomorphic]

Let me start by stating that I am really dissatisfied by the path my major has been steering towards during this last year. Groups and rings, analysis, functional analysis (I took this course on advance)... I don't know what to say. These topics have pure beauty within them, and solving problems and really understanding the theory and implications behind them is just thrilling for me. But at the end of the day, I am left with many personal questions, such as: "what the hell is this actually good for?" "Will I ever find this useful in my future professional life?" "I fear I am wasting my time"... and so on. Pure mathematicians don't have much going on for them apart from academia. I don't really know when did I fall in this place.

Well, I guess you were smarter than me. I was only 1-2 years away from getting a topology PhD before I figured that out. Actually, I think that some of that stuff is good for something. My problem is that so few people seem to address that question. When you first start studying math, it can really suck you in because it's like a game. At the beginning, it can be simple and fun, and you can blissfully forget about a lot of those other issues you are talking about. But once you reach a certain threshold of complexity, you can start questioning the value of what you are doing. You start to realize the emperor has no clothes. It caused me a lot of frustration that no one even seems to even dare to ask the question of what the hell is this actually good for. If it's only hypothetically good for something, then fine, but in the mathematical culture that I found myself in, it almost seemed like very few people even considered that something that they should even be concerned with. I also had severe problems with the way things were often presented sort of dogmatically, without motivation. Functional analysis actually grew out of stuff like studying the wave equation and Dirichlet's problem. But the way everyone presents it is as if someone just found the theorems written in the sky and copied them down. It was and still is quite infuriating. If you make a definition, I don't accept it, unless you tell me why I should care (or if I can figure it out on my own). The fact that other mathematicians all too often don't have that attitude is what has made such a mess of things today. You have to dig so hard to find the answers because not enough people cared. They just cared about getting to the frontier and cranking out papers, rather than understanding the basics and putting it in order.

There are quite a few applications of deep math, like coding theory, for example. http://plus.maths.org/content/coding-theory-first-50-years

You can find a lot more stuff like that, but unfortunately, it can often be very difficult and time consuming to understand the applications in detail in a satisfying way. You'd think mathematicians would be parading these achievements through the streets, as a triumph of math, but we don't see that happening. They could well mention it in an algebra class as an application of finite fields. Stuff like that would make it a lot less disillusioning. I'm also starting to become a fan of the idea that mathematicians should make more use of computers and programming because a computer gives you a physical realization of the math when it computes and gives you its output on the screen. Not to mention it would make them much more marketable outside their math bubble, so far away from reality and anything that anyone else cares about. In the past, it was possible to be a pure mathematician, yet remain within a reasonable distance from reality, but with the current level of complexity in the theories, that has changed. Of course, I wouldn't want people to be forcing their math into applications that is not really suited for.

It's true that mathematical discoveries sometimes have unexpected applications, many years after the fact, that no one intended or foresaw, as in the case of number theory in cryptography. There's a quote from von Neumann where he points that out, but there's another quote from him that it can be dangerous when math gets too far removed from its roots in applications. So, to me the question of whether mathematicians need to worry about applications is not just one with a yes or no answer. For example, you can ask what would happen if we increased the number of students studying applied math by 20% and decreased the number studying pure math by 20%. Would that be good or bad? Not so clear. I think it would actually be a very good thing, but I'm not going to go to extremes and say no one should study pure math, and it's far from obvious what the right balance is. If some people get their kicks from it and are not bothered by lack of applications, maybe they'll come up with something useful. I guess I wish more of them would at least do something interesting, if it's not going to be useful. One of my fellow topology students said that everything people are studying these days is ugly--and not without reason.

I don't know why you'd miss the beauty of math. It's always there for you, if you have time for it. You don't need to do it for a living. If you do do it for a living, from what you are saying, it seems quite possible to me that you wouldn't actually find it that beautiful once you got to the modern research-level stuff. I found it to be nowhere near as compelling as classical math, partly because of the dogmatic way that it is presented, often stripped of its motivations, as I pointed out with functional analysis. Engineering is the safest bet, I would say.

As a counter point, here are a couple of videos to somewhat restore your faith in math to some extent:

 

[StatGuy2000]

homeomorphic, the key thing about your gripes regarding pure mathematics is that so much of it is so far removed from applications. But I would argue that that is precisely the point: pure mathematics is a field that exists precisely because it does not rely upon the existence of other sciences, and is a study intended to be studied primarily for its own sake. Pure mathematicians engage in their research field with that mindset. That's not to suggest that there aren't applications that could be found eventually, but it's not their primary motivation.

A common attitude among pure mathematicians with respect to applications is the view held by British mathematician G. H. Hardy, who in his Apology stated that:

"I have never done anything 'useful'. No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world."

(Ironically, many areas of mathematics that he has developed has been applied to a number of different sciences, including the Hardy-Weinberg principle of population genetics and his work on integer partitions with Ramanujan have been applied widely applied in physics to find quantum partition functions of atomic nuclei)

 

[homeomorphic]

As Gowers says, most mathematicians fall somewhere in between Hardy and someone who is only interested in applications.

The view that pure math exists for its own sake is not really tenable, if it really is the case that applications are eventually found. Once there is an application of something, that opens the door for someone who is interested in math partly for the sake of application. In my case, I was interested in applications to physics. There are people who don't view it as just a game. Also, I found a lot of the math that I encountered to be very over-complicated and ugly and unmotivated, and that is a big part of my gripes, too, apart from being removed from applications. I like understanding things, and I found that people are doing a lot of building on top of things that they don't understand. So, I didn't see that there was any pleasure in that that would be worth pursuing for its own sake, anyway. Originally, I wanted to mainly focus on transferring things from math into the physics world, but I imagined myself doing some stuff for its own sake. But that was when I thought it was just going to be a more sophisticated version of what I was doing in my classes. It wasn't like that. Even if you are a pure mathematician, there's nothing preventing you from doing stuff like talking about coding theory in your abstract algebra class. That is relatively independent of whether you care about applications in your research.

 

[homeomorphic]

Some people may say that math should be driven by curiosity, rather than by applications. The problem with that is that a lot of people's curiosity is driven by applications. I find things much more interesting if they have some relevance to the real world. Even if it has no application, if it is somehow tied in with reality, to me that makes it way more interesting. Not everyone has the same taste and that's fine. But I think someone like me should be able to pursue what they find interesting and not go along with what the herd is doing.