Should physics/maths graduates be worried about maths/physics graduates?

Theoretical physics is such a great field because people from lots of different academic backgrounds can transition into it! Fields that might seem far removed like computer science, engineering and even biology can often lead into theoretical physics. The main two sources of theorists are maths and physics graduates, this can sometimes be a source of worry for both cohorts, I know maths graduates have worried me in the past and still do! 

Lets talk about the concerns these two groups might have about how each other could have an advantage over them. After that I hope to at least reduce your worries, whether you are a physics or maths undergraduate. I'll also offer some advice to those of you who are approaching theoretical physics from a subject a bit further away than maths or physics.

Concerns of Physicists:

Lets start with something I know well, fear of mathematicians! I think a lot of the fear physicists have of mathematicians comes from the Cambridge Part III and the number of successful theorists that have come from that maths course. The study of high abstract topics like string theory, super-gravity, super-symmetry and similar topics is seen as being more akin to pure mathematics than physics sometimes. They deal with very generalised situations and use a language not featured in a large proportion of undergraduate physics topics (if any). 

Mathematicians often receive in depth training in subjects like topology and differential/algebraic geometry to a high level. These are linked heavily with subjects like string theory and general relativity, so such training is often seen by physics graduates as being a point of weakness on their part.

Furthermore, mathematicians spend a lot of time studying proofs and the art of proof, something physics students definitely DO NOT spend much time on it if any. The impression given is that theorists spend a lot of time proving things and as such physics students get nervous about their lack of experience with proving in a mathematical context.

There can also be a general atmosphere that mathematics is a trickier and purer subject than physics. I have had the idea that maths is superior to physics impressed upon me more than once, it does certainly get you down. Feelings of academic inferiority don't help the previous matters.

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Concerns of Mathematicians:

Now not being a mathematician, this is not personal experience I'm drawing on but comments from academics, students from both disciplines and some general logic and know how about maths courses.

Mathematicians are not always trained in advanced classical mechanics. This can appear quite the weakness when compared to physicists who are often trained quite well in the Hamiltonian and Lagrangian formalism by the time they finish their degree! This can be perceived as a weakness when beginning the study of field theory but in reality it is something a mathematician will pick up very quickly.

Physicists have often studied very specific (and highly relevant topics) like particle physics and electromagnetism. Mathematicians might be concerned that they haven't covered the standard model in qualitative detail or Maxwell's equations in depth. Special relativity also comes up, like electromagnetism this is not something necessarily covered in a maths course and a highly relevant topic to many areas of theory.

A more general skill physicists utilise is the contextualisation of mathematical results in a physical setting. Mathematics often does not focus on this, it maintains a more abstract setting (which itself can be perceived as a strength of maths students vs physics students) so mathematicians may fear that lacking experience of this leaves them at a disadvantage.

Like physicists, there can also be a feeling of academic inferiority though for my money I think this affects mathematicians much less. But it does happen, some mathematicians talk about theoretical physicists like they are scary people!

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Addressing concerns...

Firstly... you might notice that each side has plenty of perceived issues. So even if my proceeding comments don't offer you some peace about your perceived disadvantage, know that the 'other side' (for want of a better term) probably have a similar number of completely different deficits to your skill sets. I touched on this when talking about going to a 'non-perfect' uni, everyone, no matter their route, has advantages and disadvantages.

Furthermore, the primary skill you learn in a degree is to, well, LEARN. You can learn skills from maths and physics whichever camp you are approaching theory from. The subjects are not miles apart in the grand scheme of things either, mathematicians and physicists have the closest of languages in comparison to other academic fields. It is not hard for mathematicians to get acquainted with the physical context and interpretation commonly associated with skills acquired through studying physics. Likewise as a physicists you use maths all the time, it isn't hard to pick up a book on topology and starting learning it and the more generalised, proof driven structure of mathematics.

As this cross-over becomes more and more prominent, courses inevitably react as well! Mathematics courses these days often offer modules in quantum mechanics, physics courses also have more advanced maths modules. These supplement perceived weaknesses and can help prepare you for a career in theoretical physics.

I myself took a 'Further Mathematical Methods' module in my 3rd year. It involved studying complex analysis, linear algebra and basic group theory. After this I felt much better equipped to begin venturing into the world of mathematics for theoretical physics.

From my perspective the best thing you can do if you are in the midst of your degree is to (as always) take relevant options to your career path. If you're doing a maths degree take quantum mechanics options, if you're doing physics then take some higher level maths options. Asides from that, don't worry! Both sides have initial weaknesses but these disappear with further study.

With regards to feelings of inferiority, maybe comparison is just a silly idea. Both fields have their own methods and goals, own strength and weaknesses just as their students have. 

From my own experience, the criticism levelled at mathematicians by physicists is that their work is too abstract and inapplicable. Any physicist who says this is doing their own field a disservice, development of the language and techniques that physicists (and all scientists) work with on a daily basis is a purely positive thing. No group theory... no standard model, no crystal structure study, no cryptography etc.

Physicists can sometimes get the vibe from mathematicians that their work is not a 'pure' as theirs. This notion of purity and beauty is (sorry to be such a scientist here but) not as yet a measurable quantity. The 'pureness' of a subject is nothing to be concerned about. 'Yes but you haven't proven it in a self contained manner' (to para-phrase), its an irrelevant statement. It's not what physics is about, in the same way that pure mathematicians rarely spend time on applying their work to real world problems, and both of those aspects are ok. And lets not forget that sometimes physicists end up developing serious developments in mathematics (string theory cough cough). 

Theorists and mathematicians especially are very close in reality these days so its best not to be comparing ourselves to each other. We should worry more about defending ourselves to the sciences that are do immediate good for the world and explaining why we are still needed!

(Sorry for that rant...)

What if you studied theory and want to go into maths?

This is possible, though I think it's harder than transitioning to theory from maths. If you have covered sufficient mathematical content then it certainly can happen! What I mean by this is by studying GR you can gain experience in differential geometry for example. If you've focused on more numerical topics you might find applied maths fits well and if you've focused on the abstract purer mathematics will probably appeal to you more. Again maths and theoretical physics can be almost indistinguishable at certain boundaries, as a result transitioning from physics to mathematics is not unheard of. But as someone interested in this myself it's not easy to demonstrate you have the pre-requisites to do a PhD in geometry for example. This is only fair though, it's very unlikely that a maths grad would get on an applied particle theory PhD, that's a very real career option for someone like myself.

What if I'm further away from physics than that?

I'm not going to push an illusion here, you would be in a very exclusive (potentially entirely exclusive) group if you managed to do a degree in biology and then end up doing a PhD in say string theory. But for a lot of subjects that might seem a bit further away from theoretical physics, you might be surprised at the areas available to you. Mathematical biology and biophysics are two areas that come to mind when considering moving from traditional biology to a more physics-y direction. Did your degree in geology? Try geophysics. Computer science? Have a look at quantum information and the sub-branches of that. There are a large number of fields like atmospheric physics, physical chemistry and nuclear engineering that can definitely take a theoretical physics perspective. Not all theoretical physics is string theory, in fact most of it isn't!

So whilst I make no promise that anyone/everyone can get a slice of particle theory, I think there are plenty of opportunities for you to get a piece of the theoretical physics pie if you are coming from a different area of science. Sorry English students... I don't think you'll be able to re-specialise this drastically unless you're the next Witten. The key thing is to like (and ideally be good with) maths. Programming is always useful as well.


There you have it, my reasoning for not being afraid of your academic counterparts in other fields within the realms of theory. Ultimately its best to focus on acquiring knowledge and skills and then mastering them. This will put you ahead of your competition, not the nuances of the field you studied.

Is theory worth the odds?

Whilst it might not be pleasant to think about, the fact is there aren't many theoretical physicists in the world. Even worse is the comparison of the number of physics undergrads to the number of theoretical physics academics (a more useful comparison). Unfortunately I can't quote a specific number, but needless to say it will be very very small.

So is it worth it? That is, will the repeated applications, potentially to Masters, then PhD, then postdoc, then trying to work your way up the academic food chain till you gain a (reasonably) permanent position be worth a job in theory? Fighting for funding all the while, almost certainly having to teach in one way or another (good thing for me, but might not be your cup of tea) and compromising on your salary potential. Is it worth it?

I preface this with a warning, the whole post might seem like me listing off a load of reasons not to pursue theory but that is really not my intention. I would encourage anyone and everyone to go for a career in theoretical physics academia! But it's important to know the difficulties of getting there, I've tried to offer advice when I think there's something useful to be said, but this is more about what you'll be getting yourself into if you want to become a theorist...

PhD application odds:

It's no secret that PhDs in theory are not readily available. This statement can be much more relevant to you depending on what area of theory you're looking at, more on this later. Due to the lack of places you're likely to encounter the following problems.

High entry requirements: Just because the advertised entrance is 2:1, for many universities the chances are successful applicants will have a 1st. This not to say that if you don't get a 1st you can't do a PhD, not at all. It just means that you will be more limited and ultimately sport a less competitive application. For many people this seems unfair, but you have to bare in mind that for theory the skills they need you to have are difficult to measure without exams in the current system. Check my article on how to set yourself apart when studying theory for some things you can do outside of exams that might help you.

Now the most obvious but hardest answer to this problem is do as well in your exams as you can. If you can get a 1st, that would be ideal. But there are always complications in exam season, so what if you get a 2:1? Well there are plenty of PhD programmes that will take 2:1s, you might have to fight a bit (by which I mean write a kick-ass application and try and add some extra stuff on your CV like placements an such) but a good number of people get into theory PhDs with a 2:1. 

If you get a 2:2, in my personal opinion its unlikely that you would get onto a theoretical physics PhD. Please give it a go if you want to, but I wouldn't want to give an illusion of inflated odds. But that doesn't mean you can't do a PhD in a related field, to some this might sound like a cop out, but I think its a perfectly valid route and one that can be very rewarding.

Funding problems: You might get a PhD place... but is it funded? As an example, Imperial has funding for maybe 4 theory doctorates a year (at most). That's tiny. Some of you may be aware that the government has introduced a doctoral loan, but I would advise you not to use this in place of funding. Asides from that fact that the numbers don't really add up, I would strongly advise you to only do a PhD if it funded. There are many reasons why I believe this is the case but I won't discuss those here. One exception I can think of is if you gain a substantial graduate scholarship (like the ones offered at Oxford). 

You should also be aware that funding is often for 3.5 years, it is not unheard of for theorists to take considerably longer than that to complete their thesis. This would inevitably cause financial concerns if you aren't on track to complete within the funding window.

So what can you do about this? The main thing is to apply for full funded PhDs on topics that you are suited to. This insures financial security and if you are suited to the topic you would (hopefully) be more likely to complete the PhD on time. Funding is a difficulty all members of the theoretical physics academic system face, I don't see this changing anytime soon...

Getting the right PhD: When you apply your specific interests as a filter to the small puddle of theory PhDs you will probably be left with a droplet! You simply cannot avoid this as its absolutely essential you find a PhD that interests you. If you have broad interests, that's great. If you're like me and you only want mathematical physics and don't like phenomenology then things can become really quite tricky...

Some comments: So in essence the problem is that getting on a funded theoretical physics PhD that is on a topic you enjoy is not going to be a piece of cake. That's no reason not to give it a go. There's no denying that applying for PhDs can be incredibly stressful, but the pay-off can be amazing. The best thing you can do is try and do well in your exams and don't pick one you don't like or an unfunded one.

Scarcity of postdoctoral positions:

So even if you get on a theory PhD, the number of postdoc positions awaiting the years PhD cohort isn't large enough for everyone to get a job! This is a fact theorists especially have had to face of late. It's also a reason why you should only take a funded PhD, chances are if your PhD wasn't funded you won't have a shot at a postdoc position.

There are implications of this narrowing of the funnel...

Where you do your PhD matters: I wish I could say otherwise, but on balance of probabilities if you did your PhD at Surrey and you're up against someone who did theirs at Oxford you would be at a disadvantage. I'm not having a go at Surrey as a uni (it has a really good physics department) but relaying my assessment of the state of the perceived academic hierarchy at present. There are several reasons for this bias. 

Inevitably there is some bias of academics towards universities of higher repute, whether you see this as valid or not is besides the point, it is there. Somewhere like Oxford also has more funding and more pull within the scientific community, this has several implications. Your PhD research is more likely to reach further if you go to a better known institution, this is certainly beneficial when applying for postdoc. Also previous members of universities like Oxford/Cambridge dominate theoretical physics departments across the UK. They maintain links with Oxbridge and some of them have a preference for Oxbridge graduates, even over those who complete PhDs within their own department.

When I have spoken to theorists about career prospects they always said that what mattered most was the institution I did my PhD at. I'm not saying if you don't do your PhD at Oxbridge you've got no chance, but I'm under the impression it could help a lot...

What you do your PhD on matters: A little preface here, a lecturer of mine told me last year that trying to predict what topics would be 'in' by the time you finish your PhD was an absolute waste of time. I stand by that completely so take what I'm saying with a pinch of salt.

The most important part of this is that have to LOVE the topic you are going to research in your PhD. This gives you the best chance of producing good research that will be noticed by the scientific community because you will have maximum motivation to keep working hard. It also means that if you can't get on the postdoc ladder, you won't see your PhD as a waste of time. If you have a very specific idea of what you want to do, go with it. If you are a bit more open, you might want to consider the following...

If you are 50:50 stuck between string theory and particle phenomenology, you really like both, you might want to consider which one gives you better career prospects. In that case you would go for phenomenology, it has much more funding available and string theory is currently under stress. If you wanted to research formal string theory later in your career, this wouldn't be a hard transition and you'd be much more likely to get a postdoc in phenomenology than string theory. This is only for those who don't have a specific idea of what they want, I wish I liked phenomenology (who knows, maybe I'll change my mind over the next few months, it would make my life a lot easier) but I know its not right for me so I won't try and spend 3-4 years researching it! This can get even more specific so try and get a good idea of where the field is heading.

Some comments: It is key to realise that getting on a PhD does nothing to guarantee you a career as an academic. The best thing you can do is to pick a PhD that you love and then if you don't get into academia afterwards you'll still have loved the time you spent in research. It is also important to be aware of time scales, you may not immediately move from PhD to postdoc, you might have to work in industry for 6 months for example. Also bare in mind the reputation of the institutions you're applying for, they matter more than they ever have before. 

Difficulties in getting a permanent position:

This is a really important one to be aware of if you are seriously thinking about academic theory. Most academic positions these days are temporary, at least the kind of positions you'd be looking at for the first 5-10 years of your career after PhD. Some star theorists land professorships in that time frame, but that is certainly not the norm! Most departments work on 2 year contracts, forcing you to either fight to renew your contract, move up to a higher role in the same department or find a position at another university. 

This uncertainty and movement is something that will work for some and not others. What may not work for anyone is the potential to be left without a salary and no redundancy package to support you after that contract ends. It is a risk you should be well aware of when considering this career path. The path does lead to permanent positions but how long this takes is not set. Your progress is very dependent on your research and ultimately there is no way of predicting the quality and amount of research you'll produce in what time frame throughout your career. 

Dependence on funding:

Alongside the temporary nature of positions, academics have a continuous battle for funding. This involves a heap load of applications, presenting to panels and more in the continued fight for your academic livelihood! This is another level of uncertainty that would affect you in a number of ways.

Perhaps the most important is that your research capabilities may be directly impacted by your funding. This means you'll be fighting for resources that would enable you to carry out the research you're so passionate about. This is very different from say industry where often scientific researchers are provided with any resource they need! 

This has further impact, if there is a lack of funding, your research quality may decrease and subsequently you may be denied funding again. And so a vicious cycle may begin...

Furthermore, you may be fighting for group or departmental funding, this places the funding of colleagues under your responsibility and your success or lack of would not just impact you but potentially many others. That is a serious responsibility that could land in your lap if you take on a more senior academic role, you should be aware that this could be something you face one day. As mentioned above lack of funding can have serious long term consequences...

Teaching responsibilities:

There are no theoretical physics research institutes in the UK, so you would have to take up a research post at a university. For almost all of these you will be required to teach in some form. This could be lab supervision, lecturing, PhD supervision etc.

For some the prospect of teaching is enjoyable and a key part of being a scientist, for others they see it as getting in the way of their research. I'd advise you to convert to the former if you are currently in the latter. Some academics don't have teaching responsibilities but that is a small group and is especially true in theory.

The lure of other jobs and the question of money:

Having any level of qualification in theoretical physics from degree to PhD gives you serious (and I mean serious) career prospects outside of academia. Finance, defence, consultation, energy, data science, software engineering... in fairness not all of them considered savoury professions.

These are often (in comparison to academia) easier to get into than to carry on the path of theory. They also have more set career paths and perhaps most alluringly, more money...

Money vs your real passion is not a new question. Its especially relevant for theorists because they can earn A LOT of money outside of their real passion. Those who don't make the transition from PhD to postdoc often end up in very well paid jobs (this is another good reason to do a PhD regardless of your postdoc chances). You simply have to ask which matters more to you, but if you go into academia you should feel safe in the knowledge that well paid work awaits you outside academic research.

Choice of field:

Its important to know that some fields within theory are significantly more competitive than others. For example condensed matter theory PhDs often have a 2:1 entrance whereas particle theory PhDs often (basically always) have a 1st class entrance requirement. There are also far more postdoc opportunities for condensed matter theorists than particle theorists. This is something to be aware of if you undecided as to which direction to go in, there are certainly easier routes than others. Bare this in mind if you don't have a particular direction in theory you're passionate about.

Closing comments:

I hope that hasn't put anyone off pursuing theory, my intention was to make people aware of the difficulties associated with the career path and to offer some relevant advice. These challenges do perhaps ensure that you are truly committed to the career path, you absolutely have to be if you want to succeed in this business.