Jibes from fellow students who have taken a more experimental route suggesting theorists don't really do science. Mathematicians saying that theorists never prove anything and aren't thorough enough, suggesting maths is a more 'intellectually superior' route. Those from other scientific disciplines can also be very harsh. I had a chemistry teacher once say that theoretical physicists just turned up to conferences with their "pony-tails" to talk about nothing (I have long hair now so I find this even more offensive...). More rightly come questions from the public as to how theorists can benefit them.
Perhaps this is a bit of karma though, it is not unheard of for theoretical physicists to be associated with a superiority complex. Now that a lot of the work of popularised particle theory (like string theory and super-symmetry) is under stress due to the exploration of higher energy scales at the LHC, perhaps all those who felt bullied by theory now have the ammunition they need to exact vengeance!
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This is absolutely not about starting arguments but giving you confidence that theory is useful! Both historically and at present. I'll throw in a few examples to counter specific critics as well though... (just for fun). Here's a few reasons why theory is important!
Theory develops new mathematics! (one for the mathematicians)
Most of the time theorists are busy trying to apply mathematics to develop new methods for physics, but sometimes theorists end up solving problems in mathematics or even developing entire new ideas in mathematics! Dr Robert Dijkgraaf (a mathematical physicist) gave a lecture at the Perimeter Institute titled 'The Unreasonable Effect of Quantum Physics in Modern Mathematics' in 2014 (find it on YouTube and watch it). He explains how a problem in algebraic geometry was solved by string theorists working with Calabi-Yau manifolds.
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The problem was to find the number of solutions to the so called 'quintic equation' (not a degree five polynomial, you can prove this to be unsolvable using Galois theory), specific to a given degree of curve. In other words to find the number of linear, quadratic, cubic etc. solutions to the quintic equation. Mathematicians worked out the numbers for linear and quadratic solutions analytically, but when it came to cubics they ended up turning to computational methods. Turns out that string theorists had not only the number of cubics but knew the number of every degree of solution analytically! Dijkgraaf adds much more detail and tells the story very well so go watch the lecture, but the point is sometimes theorists beat mathematicians to it (if not very often).
Historically theorists have made good predictions
Concerns regarding string theory and super-symmetry draw current theorists predictions into doubt but historical theory has done very well. Paul Dirac correctly predicted the existence of anti-matter (specifically the positron), Peter Higgs did the same for the Higgs boson. Glashow, Salam and Weinberg formulated electroweak theory which was validated by the discovery of the W and Z bosons. And all these just in particle theory (there are many others in particle theory)! BSC theory has been immeasurably successful in predicting super-conductor phenomena for condensed matter physics. Outside of specific fields of theory, quantum mechanics (specifically QED) has been shown to be ridiculously precise.
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I think a lot of the present distrust of theory is due to the public nature of string theory and super-symmetry. It's not 'in' publicly to be improving cross-section calculation methods for the LHC or researching condensed matter, but these are two areas that come to my mind when I think of areas of theory that are being very productive at present. So whilst theory might be perceived to be going through a rough patch, that might not be entirely the case and it certainly hasn't been previously.
Knowledge moves down the chain
Lets address my chemistry teacher's attitude. Modern chemistry is dependent on the foundations quantum mechanics laid nearly a century ago. Quantum information science is moving into computer science, biology is utilising statistical mechanics. My point is that there is a progression of techniques and knowledge moving from science to science. Physics (well all sciences) use mathematics as a tool, new tools are developed by mathematicians and these (usually slowly) find a use in science. Physics studies fundamental (arguably simple) situations and knowledge/methods of/for these move into sciences that study more complex situations, chemistry, biology, neuroscience, psychology and these all feed in to each other. That's science!
What people often don't think about is that the feedback for these fields takes different amounts of time. Physics may often be the first science to utilise new mathematics (along with computer science) but that doesn't happen quickly. Pure maths is often said to be a hundred years ahead of application, for theoretical physics there can also be a reasonable gap. Experiments take time to build and after validation of methods other fields take time to accept and utilise techniques developed in theory.
Failure is a key part of science
When theory gets it wrong, that's part of science and its not a bad thing. In fact getting it wrong is REALLY important. Theory is crucial because it provides research with a direction and despite some people opinions... theory is not plucked out of the air, not good theory anyway. Good theory is focused on trying to solve problems where we are at now and with minimal new assumptions, or at least making those assumptions testable. Theory can also be about testing the water with new tools that are still in development.
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Particle phenomenology is about predicting new particles to solve current problems in particle physics, like dark matter candidates for example. These are testable and candidate particles are based on knowledge of current particle physics and therefore the best idea of what could exist that hasn't been found yet. Often these models are phased out as experiments explore the energy scales and processes which should feature these particles. In the current climate, this often results in theorists having to adjust their predictions and that's ok!
Often the problem comes from (string theory cough cough) theorists extending their predictions to far or making assumptions/jumps that are simply too big. In fairness this has often led to serious progress in mathematics but often criticism from the scientific community. Some of these culprit areas have since reigned things in, but over the last forty years some ridiculous statements have been made along the lines of theory not needing to be testable. Theory is not a one way street there are lots of directions theorists take and they all have their strengths and weaknesses. But just because their predictions aren't fore-filled doesn't necessarily mean they're doing a bad job, sometimes it turns out to be really useful!
Theory leads to new technology
Most modern electronics can be traced back to quantum electrodynamics, a theory that started development in the 1920s. So it's not unreasonable to argue that modern technologies like I don't know... the internet, personal computers, satellite navigation, I could go on, would simply be impossible if it wasn't for the endeavour of the theorists who laid the ground work for QED. GPS wouldn't work without relativity either, you might know that from A-level! All stages of science are crucial to the development of technologies that benefit human kind. Theoretical physics works quietly in the background, laying the foundations often decades before tangible effects are seen. But that doesn't mean theorists are any less important!
So if you're feeling a bit insecure about studying/pursuing theory because of the mentioned pressures, have a real think about where those opinions come from and whether they actually make sense!
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