Physics or Math, and some other questions

[RandomAllTime]

Hello everyone. I came to gather some advice from all the experienced people here. I'm 16 and going to be a 10th grader in high school this coming year. I have taken Algebra 2 while doing Algebra 1, and they are letting me into AP Calculus this year early. I personally love math and physics, but lately have just been studying pure mathematics. At the moment I can't decide whether or not I should go into Theoretical Physics, Astrophysics, or Math as a career. So far I have been teaching myself Differential and integral Calculus and have gone on to explore a bit of partial derivatives and differential equations. I am also somewhat versed in Set theory and more abstract maths, I currently am studying Abstract Algebra among other things. I also really enjoy modern Physics, but I feel as if I lack the mathematical training to truly get into Quantum mechanics at the moment. I have considered becoming a mathematician and eventually getting a Phd in it. However, all the info I've gathered on the internet is super discouraging. As if no one can do it. I am a dedicated student, and I have no problem striving to whatever ends I must go to to suceed, but my god, these people make it sound like a soul destroying activity that ruins lives. Is it that horrible? This is really sad and dissapointing to hear. I feel as if my heart is truly set on the theoretical side of math, but it seems that I would have to become an applied mathematician to get a job other than professor. Can I become an applied mathematician and still contribute to developing and contributing to more theoretical areas of math? This is my dream. I would also like being a theoretical physicist or astrophysicist. I have considered going into one of these two fields and doing mathematics on the side as a hobby, could I contribute to pure mathematics if I follow that path? Also, I wish to ask all of you mathematicians out there of what sort of materials you would recommend for someone like me trying to self teach themselves pure mathematics. I spend most of my mental time thinking about mathematical ideas, and it is my dream to contribute to the field, even as a different profession. Thank you very much for reading.

 

[micromass]

I am a dedicated student, and I have no problem striving to whatever ends I must go to to suceed, but my god, these people make it sound like a soul destroying activity that ruins lives. Is it that horrible?

No, it's not. Sure, it's not easy at all. But it's neither impossible nor soul crushing. In fact, a lot of people enjoy their PhD since it gives them a very great liberty to do research. Other people hate their research, and they typically drop out soon. So it's all about whether you enjoy this or not, and that is something that you can't know at this stage.

This is really sad and dissapointing to hear. I feel as if my heart is truly set on the theoretical side of math, but it seems that I would have to become an applied mathematician to get a job other than professor.

Theoretical mathematicians do get jobs, but (aside from professor) they don't typically deal with pure math. They are more likely to deal with programming or financial stuff.

Can I become an applied mathematician and still contribute to developing and contributing to more theoretical areas of math? This is my dream.

It's not impossible, but it's also not very likely. A research mathematician has a very specific training and works on very specific problems. He typically has little idea what is going on in other fields. To be able to contribute to math, you need to know what the major unsolved problems are in a specific field, and what the important results are. If you are trained as an applied mathematician and have no help from pure mathematicians, it doesn't seem that you will know these things

 

[axmls]

Could you contribute to pure mathematics as a hobbyist? Not likely. Possible, yes, but you can probably count on one hand the number of hobbyist mathematicians that have made appreciable contributions to pure math. (Hobbyist meaning someone who does not have a Ph.D)

The unemployment rate for math Ph.D holders is like 1% right now. And that doesn't even take people in between jobs into consideration. Sure, they're not all professors, but they're not starving.

 

[RandomAllTime]

I see. Thank you.

 

[jtbell]

At the moment I can't decide whether or not I should go into Theoretical Physics, Astrophysics, or Math as a career.

Don't stress out trying to make up your mind now. You don't have to commit yourself to a major until (usually) the end of your second year in college / university which is almost four years from now. Until then you can take both math and physics courses in parallel.

 

[RandomAllTime]

Don't stress out trying to make up your mind now. You don't have to commit yourself to a major until (usually) the end of your second year in college / university which is almost four years from now. Until then you can take both math and physics courses in parallel.

Youre right. Thank you.

 

[homeomorphic]

No, it's not. Sure, it's not easy at all. But it's neither impossible nor soul crushing.

It's simply counterfactual to claim that it's not for everyone. The reality of it is that it CAN very well be soul-crushing for some people. My soul was pretty much crushed by doing a PhD in math, and I know quite a number of other people who had similar experiences. Not everyone feels this way, but it's certainly a risk. Dropping out is not a simple matter that is that easy to do when you realize, 2 years into your research and 4 or 5 years into your PhD program that it's not for you. I don't think it's very predictable who will enjoy or not enjoy it, even 2 years into grad school, which is part of why I just make the blanket statement that just not doing it is generally a good idea, unless you are completely dead set on it and REALLY know what you're getting into, which is very hard to do beforehand. It's not that it's certain to not be worth it, but there is a risk of it not being worth it, and furthermore, a risk that is hard to assess at that. Also, the opportunity cost incurred by doing something that takes so much work for such little pay in grad school is tremendous.

The unemployment rate for math Ph.D holders is like 1% right now. And that doesn't even take people in between jobs into consideration. Sure, they're not all professors, but they're not starving.

Well, I may be an outlier, but it took me over a year to get a job after my PhD, and I have heard of people in worse situations. The main thing here is to be VERY, VERY prepared BEFORE you graduate (difficult to do while trying to finish that soul-crushing PhD), especially if you are like me and are not a social super-star who can just breeze through stuff like networking and getting through job interviews. If you really take the job search serious, maybe even as early as the beginning of grad school, then you'd probably be okay, but it's better to think of the job search as a big, mean bully who is going to come and beat you up and take your lunch money that you have to be very afraid of and prepared for, rather than something that is just going to work itself out. Don't count on anything.

 

[DeldotB]

To be honest,
I wouldn't search on the Internet for answers to questions like these. If you want something, go out and get it. There is too much negativity out there probably from people who had dreams like yourself but were shot down somewhere along the way to their goals and decided they couldn't do it. I am studying physics and mathematics at Berkeley and I'm going to be going onto my phD in physics. Its my dream to become a theoretical physicist - but I do not DARE read the " should I become a physicist/ mathematician " type posts. It's easy for people who are out there on the Internet working in some job that they probably didn't want to shoot down those who had similar dreams. They don't care if they shoot you down as long as they remain faceless. Above I read " you probably just shouldn't pursue it" - that frustrates the hell out of me! Who is some random person on the internet to tell you you probably just " shouldn't pursue it"? If you want inspiration read the works of Poincare, Hardy, Gauss, Maxwell, Newton, Euler and so on, those are the mathematicians you should be listening to. Sorry in advance to the onslaught of people who won't agree with this.

 

[vela]

My god, these people make it sound like a soul destroying activity that ruins lives. Is it that horrible?

That's grad school for ya. ;) I kid, I kid. You should keep in mind that people like to complain, so you're getting a skewed impression of what graduate school is like.

A lot of people go to grad school and end up not finishing because they come to realize it's not what they want to do. There's no shame in that, and at least, they gave it a shot. Whether it's soul crushing depends on the individual. If you have unrealistic hopes or expectations, having reality slap you down hard can be quite traumatic.

 

[radium]

People used to think number theory was useless. There's a book called A mathematician's apology and the author G.H. Hardy once said "The Theory of Numbers has always been regarded as one of the most obviously useless branches of Pure Mathematics." I believe he also said it was one of the only things that was completely harmless for that reason. He obviously did not anticipate the birth of cryptography and eventually the RSA algorithm. So I am always careful about calling something useless. The thing is, you never know. Sometimes these ideas are way ahead of their times and applications don't come until much later.

Also, when I hear people say things similar to the comments above, I always take it with a grain of salt. Doing a PhD is definitely not for everyone. Same with medicine, law, and any other demanding career. But don't go telling everyone it's worthless just because you happened to be miserable. Just because you felt it was a mistake doesn't mean that other people didn't know what they were getting into. Before I started my PhD in theoretical physics I talked to a ton of grad students and professors. So far I feel like I knew pretty well what I was getting into. That doesn't mean that it isn't difficult and you won't become discouraged, but you power through and become stronger.

Another thing is that if you want to do a PhD, you need to lose the ego fast. If you always feel the need to be the smartest one in the room you won't be happy. There will always be someone that's smarter. The key is to learn from them.

Another thing that people seem to have forgotten about medicine is how emotionally draining a lot of it can be.

 

[radium]

The problem isn't with your opinion, it's with how you present it.

 

[IGU]

I like my job way better than doing math (software development)

Congratulations! You discovered that you are a programmer, not a mathematician. It would have possibly been better had you discovered that as an undergrad, but so it goes. It's way better than never figuring it out. And luckily for you it's a very lucrative job, and easy for people who are good at it.

But the proper conclusion to be drawn is not that math sucks, or isn't what it's portrayed to be. Neither is programming. Nor anything else. The proper conclusion is that it's important to figure out what you like. Yes, it's tricky. Internships are good because you can watch the people around you. Job shadowing is good. Observing as a second party is not as good as being the first party, but it's better than third party (being told what it's like by an observer). But the primary rule is know thyself. And the second rule is to talk to people, especially people who hold the job you think you might like. Find out what they like best and what they can't stand about it, and see if you can apply that to yourself.

 

[atyy]

@homeomorphic, congrats on the job! Especially after more than a year of searching.

 

[RandomAllTime]

To be honest,
I wouldn't search on the Internet for answers to questions like these. If you want something, go out and get it. There is too much negativity out there probably from people who had dreams like yourself but were shot down somewhere along the way to their goals and decided they couldn't do it. I am studying physics and mathematics at Berkeley and I'm going to be going onto my phD in physics. Its my dream to become a theoretical physicist - but I do not DARE read the " should I become a physicist/ mathematician " type posts. It's easy for people who are out there on the Internet working in some job that they probably didn't want to shoot down those who had similar dreams. They don't care if they shoot you down as long as they remain faceless. Above I read " you probably just shouldn't pursue it" - that frustrates the hell out of me! Who is some random person on the internet to tell you you probably just " shouldn't pursue it"? If you want inspiration read the works of Poincare, Hardy, Gauss, Maxwell, Newton, Euler and so on, those are the mathematicians you should be listening to. Sorry in advance to the onslaught of people who won't agree with this.

Thanks, I appreciate that.

 

[RandomAllTime]

That's grad school for ya. ;) I kid, I kid. You should keep in mind that people like to complain, so you're getting a skewed impression of what graduate school is like.

A lot of people go to grad school and end up not finishing because they come to realize it's not what they want to do. There's no shame in that, and at least, they gave it a shot. Whether it's soul crushing depends on the individual. If you have unrealistic hopes or expectations, having reality slap you down hard can be quite traumatic.

Lol I see. Thanks.

 

[RandomAllTime]

homeomorphic, as you stated above, you are essentially telling the OP not to pursue a PhD in math. Then the obvious question would be -- what would you suggest to the OP instead? What can he/she do that would be fulfilling for him/her?

Thank you both for showing interest and elaborating on your viewpoints. It helps me gain a wider perspective.

 

[RandomAllTime]

You say it because it's true based on your experiences and perceptions, which by its definition is skewed. I don't discount your experience, and it is a cautionary tale, but it would be a mistake to draw any larger inference on it.

I have known many people who have pursued graduate studies in mathematics (both pure and applied) and their experiences do not correspond to your own. Now are these people "crazy"? I don't think they are, but what do I know? What I can say is that the road to completing their PhD was intense (according to their testimony) but very fulfilling to them, and all were successful, whether in academia or outside.

I see. I feel as if a love for a subject will drive you through whatever it takes. Perhaps I am unexperienced, though.

 

[radium]

Well for one, I think saying a PhD is soul crushing is very dramatic. Saying that it made you depressed, stressed or feel stupid is one thing. Some people are better at dealing with that than others. I question myself almost everyday. However, rather than allowing it to get to me, I use it as motivation to learn more on my own and from other people, including classmates

However, to me, soul crushing describes a very traumatic event like getting into a bad accident or a loved one suddenly dying.

Also, calling people who enjoyed their math PhDs crazy is pretty insulting. Just because you didn't like it doesn't mean that people who do are crazy. I know a lot of people in math/theoretical physics who are very happy. They also realize you need to have a life outside academics to stay sane and be the most productive they can be. The string theorists and quantum gravity students are for the most part very friendly, happy, and energetic. According to what you are saying this would be a huge anomaly since most people think string theory is useless. I personally don't think it is because the math they help develop has been useful in other fields. In fact some of the methods they use to study entanglement may be related to neuroscience. There is also a lot of very fancy, beautiful math that is useful. in computer science.

So what I am trying to say is a PhD is not for everyone, and that is perfectly okay. A lot of people will go on to apply their skills to something they are truly passionate about. Math and physics give you the skills to do that. In my department l, we get emails all the time about all kinds of job prospects.