Tag Archives: grad school

Grad Students Don’t Have Majors

A pet peeve of mine:

Suppose you’re writing a story, and one of your characters is studying for a PhD in linguistics. You could call them a grad student or a PhD student, a linguistics student or even just a linguist. But one thing you absolutely shouldn’t call them is a linguistics major.

Graduate degrees, from the PhD to medical doctors to masters degrees, don’t have majors. Majors are a very specific concept, from a very specific system: one that only applies to undergraduate degrees, and even there is uncommon to unheard of in most of the world.

You can think of “major” as short for “major area of study”. In many universities in the US, bachelor’s degree students enter not as students of a particular topic, but as “undecided” students. They then have some amount of time to choose a major. Majors define some of your courses, but not all of them. You can also have “minors”, minor areas of study where you take a few courses from another department, and you typically have to take some number of general courses from other departments as well. Overall, the US system for bachelor’s students is quite flexible. The idea is that students can choose from a wide range of courses offered by different departments at a university, focusing on one department’s program but sampling from many. The major is your major focus, but not your only focus.

Basically no other degree works this way.

In Europe, bachelor’s degree students sign up as students of a specific department. By default, all of their courses will be from that department. If you have to learn more math, or writing skills, then normally your department will have its own math or writing course, focused on the needs of their degree. It can be possible to take courses from other departments, but it’s not common and it’s often not easy, sometimes requiring special permission. You’re supposed to have done your general education as a high school student, and be ready to focus on a particular area.

Graduate degrees in the US also don’t work this way. A student in medical school or law school isn’t a medicine major or a law major, they’re a med student or a law student. They typically don’t take courses from the rest of the university at that point, just from the med school or the law school. A student studying for an MBA (Master’s in Business Administration) is similarly a business student, not the business major they might have been during their bachelor’s studies. And a student studying for a PhD is a PhD student, a student of a specific department. They might still have the option of taking classes outside of that department (for example, I took classes in science communication). But these are special exceptions. A linguistics PhD student will take almost all of their classes from the linguistics department, a physics PhD student will take almost all of their classes from the physics department. They don’t have majors.

So the next time you write a story with people with advanced degrees, keep this in mind. Majors are a thing for US bachelor’s degrees, and a few similar systems. Anything else, don’t call it a major!

Musing on Application Fees

A loose rule of thumb: PhD candidates in the US are treated like students. In Europe, they’re treated like employees.

This does exaggerate things a bit. In both Europe and the US, PhD candidates get paid a salary (at least in STEM). In both places, PhD candidates count as university employees, if sometimes officially part-time ones, with at least some of the benefits that entails.

On the other hand, PhD candidates in both places take classes (albeit more classes in the US). Universities charge both for tuition, which is in turn almost always paid by their supervisor’s grants or department, not by them. Both aim for a degree, capped off with a thesis defense.

But there is a difference. And it’s at its most obvious in how applications work.

In Europe, PhD applications are like job applications. You apply to a particular advisor, advertising a particular kind of project. You submit things like a CV, cover letter, and publication list, as well as copies of your previous degrees.

In the US, PhD applications are like applications to a school. You apply to the school, perhaps mentioning an advisor or topic you are interested in. You submit things like essays, test scores, and transcripts. And typically, you have to pay an application fee.

I don’t think I quite appreciated, back when I applied for PhD programs, just how much those fees add up to. With each school charging a fee in the $100 range, and students commonly advised to apply to ten or so schools, applying to PhD programs in the US can quickly get unaffordable for many. Schools do offer fee waivers under certain conditions, but the standards vary from school to school. Most don’t seem to apply to non-Americans, so if you’re considering a US PhD from abroad be aware that just applying can be an expensive thing to do.

Why the fee? I don’t really know. The existence of application fees, by itself, isn’t a US thing. If you want to get a Master’s degree from the University of Copenhagen and you’re coming from outside Europe, you have to pay an application fee of roughly the same size that US schools charge.

Based on that, I’d guess part of the difference is funding. It costs something for a university to process an application, and governments might be willing to cover it for locals (in the case of the Master’s in Copenhagen) or more specifically for locals in need (in the US PhD case). I don’t know whether it makes sense for that cost to be around $100, though.

It’s also an incentive, presumably. Schools don’t want too many applicants, so they attach a fee so only the most dedicated people apply.

Jobs don’t typically have an application fee, and I think it would piss a lot of people off if they did. Some jobs get a lot of applicants, enough that bigger and more well-known companies in some places use AI to filter applications. I have to wonder if US PhD schools are better off in this respect. Does charging a fee mean they have a reasonable number of applications to deal with? Or do they still have to filter through a huge pile, with nothing besides raw numbers to pare things down? (At least, because of the “school model” with test scores, they have some raw numbers to use.)

Overall, coming at this with a “theoretical physicist mentality”, I have to wonder if any of this is necessary. Surely there’s a way to make it easy for students to apply, and just filter them down to the few you want to accept? But the world is of course rarely that simple.

The Impact of Jim Simons

The obituaries have been weirdly relevant lately.

First, a couple weeks back, Daniel Dennett died. Dennett was someone who could have had a huge impact on my life. Growing up combatively atheist in the early 2000’s, Dennett seemed to be exploring every question that mattered: how the semblance of consciousness could come from non-conscious matter, how evolution gives rise to complexity, how to raise a new generation to grow beyond religion and think seriously about the world around them. I went to Tufts to get my bachelor’s degree based on a glowing description he wrote in the acknowledgements of one of his books, and after getting there, I asked him to be my advisor.

(One of three, because the US education system, like all good games, can be min-maxed.)

I then proceeded to be far too intimidated to have a conversation with him more meaningful than “can you please sign my registration form?”

I heard a few good stories about Dennett while I was there, and I saw him debate once. I went into physics for my PhD, not philosophy.

Jim Simons died on May 10. I never spoke to him at all, not even to ask him to sign something. But he had a much bigger impact on my life.

I began my PhD at SUNY Stony Brook with a small scholarship from the Simons Foundation. The university’s Simons Center for Geometry and Physics had just opened, a shining edifice of modern glass next to the concrete blocks of the physics and math departments.

For a student aspiring to theoretical physics, the Simons Center virtually shouted a message. It taught me that physics, and especially theoretical physics, was something prestigious, something special. That if I kept going down that path I could stay in that world of shiny new buildings and daily cookie breaks with the occasional fancy jar-based desserts, of talks by artists and a café with twenty-dollar lunches (half-price once a week for students, the only time we could afford it, and still about twice what we paid elsewhere on campus). There would be garden parties with sushi buffets and late conference dinners with cauliflower steaks and watermelon salads. If I was smart enough (and I longed to be smart enough), that would be my future.

Simons and his foundation clearly wanted to say something along those lines, if not quite as filtered by the stars in a student’s eyes. He thought that theoretical physics, and research more broadly, should be something prestigious. That his favored scholars deserved more, and should demand more.

This did have weird consequences sometimes. One year, the university charged us an extra “academic excellence fee”. The story we heard was that Simons had demanded Stony Brook increase its tuition in order to accept his donations, so that it would charge more similarly to more prestigious places. As a state university, Stony Brook couldn’t do that…but it could add an extra fee. And since PhD students got their tuition, but not fees, paid by the department, we were left with an extra dent in our budgets.

The Simons Foundation created Quanta Magazine. If the Simons Center used food to tell me physics mattered, Quanta delivered the same message to professors through journalism. Suddenly, someone was writing about us, not just copying press releases but with the research and care of an investigative reporter. And they wrote about everything: not just sci-fi stories and cancer cures but abstract mathematics and the space of quantum field theories. Professors who had spent their lives straining to capture the public’s interest suddenly were shown an audience that actually wanted the real story.

In practice, the Simons Foundation made its decisions through the usual experts and grant committees. But the way we thought about it, the decisions always had a Jim Simons flavor. When others in my field applied for funding from the Foundation, they debated what Simons would want: would he support research on predictions for the LHC and LIGO? Or would he favor links to pure mathematics, or hints towards quantum gravity? Simons Collaboration Grants have an enormous impact on theoretical physics, dwarfing many other sources of funding. A grant funds an army of postdocs across the US, shifting the priorities of the field for years at a time.

Denmark has big foundations that have an outsize impact on science. Carlsberg, Villum, and the bigger-than-Denmark’s GDP Novo Nordisk have foundations with a major influence on scientific priorities. But Denmark is a country of six million. It’s much harder to have that influence on a country of three hundred million. Despite that, Simons came surprisingly close.

While we did like to think of the Foundation’s priorities as Simons’, I suspect that it will continue largely on the same track without him. Quanta Magazine is editorially independent, and clearly puts its trust in the journalists that made it what it is today.

I didn’t know Simons, I don’t think I even ever smelled one of his famous cigars. Usually, that would be enough to keep me from writing a post like this. But, through the Foundation, and now through Quanta, he’s been there with me the last fourteen years. That’s worth a reflection, at the very least.

Learning for a Living

It’s a question I’ve now heard several times, in different forms. People hear that I’ll be hired as a researcher at an institute of theoretical physics, and they ask, “what, exactly, are they paying you to research?”

The answer, with some caveats: “Whatever I want.”

When a company hires a researcher, they want to accomplish specific things: to improve their products, to make new ones, to cut down on fraud or out-think the competition. Some government labs are the same: if you work for NIST, for example, your work should contribute in some way to achieving more precise measurements and better standards for technology.

Other government labs, and universities, are different. They pursue basic research, research not on any specific application but on the general principles that govern the world. Researchers doing basic research are given a lot of freedom, and that freedom increases as their careers go on.

As a PhD student, a researcher is a kind of apprentice, working for their advisor. Even then, they have some independence: an advisor may suggest projects, but PhD students usually need to decide how to execute them on their own. In some fields, there can be even more freedom: in theoretical physics, it’s not unusual for the more independent students to collaborate with other people than just their advisor.

Postdocs, in turn, have even more freedom. In some fields they get hired to work on a specific project, but they tend to have more freedom as to how to execute it than a PhD student would. Other fields give them more or less free rein: in theoretical physics, a postdoc will have some guidance, but often will be free to work on whatever they find interesting.

Professors, and other long-term researchers, have the most freedom of all. Over the climb from PhD to postdoc to professor, researchers build judgement, demonstrating a track record for tackling worthwhile scientific problems. Universities, and institutes of basic research, trust that judgement. They hire for that judgement. They give their long-term researchers free reign to investigate whatever questions they think are valuable.

In practice, there are some restrictions. Usually, you’re supposed to research in a particular field: at an institute for theoretical physics, I should probably research theoretical physics. (But that can mean many things: one of my future colleagues studies the science of cities.) Further pressure comes from grant funding, money you need to hire other researchers or buy equipment that can come with restrictions attached. When you apply for a grant, you have to describe what you plan to do. (In practice, grant agencies are more flexible about this than you might expect, allowing all sorts of changes if you have a good reason…but you still can’t completely reinvent yourself.) Your colleagues themselves also have an impact: it’s much easier to work on something when you can walk down the hall and ask an expert when you get stuck. It’s why we seek out colleagues who care about the same big questions as we do.

Overall, though, research is one of the free-est professions there is. If you can get a job learning for a living, and do it well enough, then people will trust your judgement. They’ll set you free to ask your own questions, and seek your own answers.

The Many Varieties of Journal Club

Across disciplines, one tradition seems to unite all academics: the journal club. In a journal club, we gather together to discuss papers in academic journals. Typically, one person reads the paper in depth in advance, and comes prepared with a short presentation, then everyone else asks questions. Everywhere I’ve worked has either had, or aspired to have, a journal club, and every academic I’ve talked to recognizes the concept.

Beyond that universal skeleton, though, are a lot of variable details. Each place seems to interpret journal clubs just a bit differently. Sometimes a lot differently.

For example, who participates in journal clubs? In some places, journal clubs are a student thing, organized by PhD or Master’s students to get more experience with their new field. Some even have journal clubs as formal courses, for credit and everything. In other places, journal clubs are for everyone, from students up through the older professors.

What kind of papers? Some read old classic papers, knowing that without an excuse we’d never take the time to read them and would miss valuable insights. Some instead focus on the latest results, as a way to keep up with progress in the field.

Some variation is less intentional. Academics are busy, so it can be hard to find a volunteer to prepare a presentation on a paper every week. This leads journal clubs to cut corners, in once again a variety of ways. A journal club focused on the latest papers can sometimes only find volunteers interested in presenting their own work (which we usually already have a presentation prepared for). Sometimes this goes a step further, and the journal club becomes a kind of weekly seminar: a venue for younger visitors to talk about their work that’s less formal than a normal talk. Sometimes, instead of topic, the corner cut is preparation: people still discuss new papers, but instead of preparing a presentation they just come and discuss on the fly. This gets dangerous, because after a certain point people may stop reading the papers altogether, hoping that someone else will come having read it to explain it!

Journal clubs are tricky. Academics are curious, but we’re also busy and lazy. We know it would be good for us to discuss, to keep up with new papers or read the old classics… but actually getting organized, that’s another matter!

When Your Research Is a Cool Toy

Merry Newtonmas, everyone!

In the US, PhD students start without an advisor. As they finish their courses, different research groups make their pitch, trying to get them to join. Some promise interesting puzzles and engaging mysteries, others talk about the importance of their work, how it can help society or understand the universe.

Thinking back to my PhD, there is one pitch I remember to this day. The pitch was from the computational astrophysics group, and the message was a simple one: “we blow up stars”.

Obviously, these guys didn’t literally blow up stars: they simulated supernovas. They weren’t trying to make some weird metaphysical argument, they didn’t believe their simulation was somehow the real thing. The point they were making, instead, was emotional: blowing up stars feels cool.

Scientists can be motivated by curiosity, fame, or altruism, and these are familiar things. But an equally important motivation is a sense of play. If your job is to build tiny cars for rats, some of your motivation has to be the sheer joy of building tiny cars for rats. If you simulate supernovas, then part of your motivation can be the same as my nephew hurling stuffed animals down the stairs: that joyful moment when you yell “kaboom!”

Probably, your motivation shouldn’t just be to play with a cool toy. You need some of those “serious” scientific motivations as well. But for those of you blessed with a job where you get to say “kaboom”, you have that extra powerful reason to get up in the morning. And for those of you just starting a scientific career, may you have some cool toys under your Newtonmas tree!

No, PhD Students Are Not Just Cheap Labor

Here’s a back-of-the-envelope calculation:

In 2019, there were 83,050 unionized graduate students in the US. Let’s assume these are mostly PhD students, since other graduate students are not usually university employees. I can’t find an estimate of the total number of PhD students in the US, but in 2019, 55,614 of them graduated. In 2020, the average US doctorate took 7.5 years to complete. That implies that 83,050/(55,614 x 7.5) = about one-fifth of PhD students in the US are part of a union.

That makes PhD student unions common, but not the majority. It means they’re not unheard of and strange, but a typical university still isn’t unionized. It’s the sweet spot for controversy. It leads to a lot of dumb tweets.

I saw one such dumb tweet recently, from a professor arguing that PhD students shouldn’t unionize. The argument was that if PhD students were paid more, then professors would prefer to hire postdocs, researchers who already have a doctoral degree.

(I won’t link to the tweet, in part because this person is probably being harassed enough already.)

I don’t know how things work in this professor’s field. But the implication, that professors primarily take on PhD students because they’re cheaper, not only doesn’t match my experience: it also just doesn’t make very much sense.

Imagine a neighborhood where the children form a union. They decide to demand a higher allowance, and to persuade any new children in the neighborhood to follow their lead.

Now imagine a couple in that neighborhood, deciding whether to have a child. Do you think that they might look at the fees the “children’s union” charges, and decide to hire an adult to do their chores instead?

Maybe there’s a price where they’d do that. If neighborhood children demanded thousands of dollars in allowance, maybe the young couple would decide that it’s too expensive to have a child. But a small shift is unlikely to change things very much: people have kids for many reasons, and those reasons don’t usually include cheap labor.

The reasons professors take on PhD students are similar to the reasons parents decide to have children. Some people have children because they want a legacy, something of theirs that survives to the next generation. For professors, PhD students are our legacy, our chance to raise someone on our ideas and see how they build on them. Some people have children because they love the act of child-raising: helping someone grow and learn about the world. The professors who take on students like taking on students: teaching is fun, after all.

That doesn’t mean there won’t be cases “on the margin”, where a professor finds they can’t afford a student they previously could. (And to be fair to the tweet I’m criticizing, they did even use the word “marginal”.) But they would have to be in a very tight funding situation, with very little flexibility.

And even for situations like that, long-term, I’m not sure anything would change.

I did my PhD in the US. I was part of a union, and in part because of that (though mostly because I was in a physics department), I was paid relatively decently for a PhD student. Relatively decently is still not that great, though. This was the US, where universities still maintain the fiction that PhD students only work 20 hours a week and pay proportionate to that, and where salaries in a university can change dramatically from student to postdoc to professor.

One thing I learned during my PhD is that despite our low-ish salaries, we cost our professors about as much as postdocs did. The reason why is tuition: PhD students don’t pay their own tuition, but that tuition still exists, and is paid by the professors who hire those students out of their grants. A PhD salary plus a PhD tuition ended up roughly equal to a postdoc salary.

Now, I’m working in a very different system. In a Danish university, wages are very flat. As a postdoc, a nice EU grant put me at almost the same salary as the professors. As a professor, my salary is pretty close to that of one of the better-paying schoolteacher jobs.

At the same time, tuition is much less relevant. Undergraduates don’t pay tuition at all, so PhD tuition isn’t based on theirs. Instead, it’s meant to cover costs of the PhD program as a whole.

I’ve filled out grants here in Denmark, so I know how much PhD students cost, and how much postdocs cost. And since the situation is so different, you might expect a difference here too.

There isn’t one. Hiring a PhD student, salary plus tuition, costs about as much as hiring a postdoc.

Two very different systems, with what seem to be very different rules, end up with the same equation. PhD students and postdocs cost about as much as each other, even if every assumption that you think would affect the outcome turns out completely different.

This is why I expect that, even if PhD students get paid substantially more, they still won’t end up that out of whack with postdocs. There appears to be an iron law of academic administration keeping these two numbers in line, one that holds across nations and cultures and systems. The proportion of unionized PhD students in the US will keep working its way upwards, and I don’t expect it to have any effect on whether professors take on PhDs.

From Journal to Classroom

As part of the pedagogy course I’ve been taking, I’m doing a few guest lectures in various courses. I’ve got one coming up in a classical mechanics course (“intermediate”-level, so not Newton’s laws, but stuff the general public doesn’t know much about like Hamiltonians). They’ve been speeding through the core content, so I got to cover a “fun” topic, and after thinking back to my grad school days I chose a topic I think they’ll have a lot of fun with: Chaos theory.

Getting the obligatory Warhammer reference out of the way now

Chaos is one of those things everyone has a vague idea about. People have heard stories where a butterfly flaps its wings and causes a hurricane. Maybe they’ve heard of the rough concept, determinism with strong dependence on the initial conditions, so a tiny change (like that butterfly) can have huge consequences. Maybe they’ve seen pictures of fractals, and got the idea these are somehow related.

Its role in physics is a bit more detailed. It’s one of those concepts that “intermediate classical mechanics” is good for, one that can be much better understood once you’ve been introduced to some of the nineteenth century’s mathematical tools. It felt like a good way to show this class that the things they’ve learned aren’t just useful for dusty old problems, but for understanding something the public thinks is sexy and mysterious.

As luck would have it, the venerable textbook the students are using includes a (2000’s era) chapter on chaos. I read through it, and it struck me that it’s a very different chapter from most of the others. This hit me particularly when I noticed a section describing a famous early study of chaos, and I realized that all the illustrations were based on the actual original journal article.

I had surprisingly mixed feelings about this.

On the one hand, there’s a big fashion right now for something called research-based teaching. That doesn’t mean “using teaching methods that are justified by research” (though you’re supposed to do that too), but rather, “tying your teaching to current scientific research”. This is a fashion that makes sense, because learning about cutting-edge research in an undergraduate classroom feels pretty cool. It lets students feel more connected with the scientific community, it inspires them to get involved, and it gets them more used to what “real research” looks like.

On the other hand, structuring your textbook based on the original research papers feels kind of lazy. There’s a reason we don’t teach Newtonian mechanics the way Newton would have. Pedagogy is supposed to be something we improve at over time: we come up with better examples and better notation, more focused explanations that teach what we want students to learn. If we just summarize a paper, we’re not really providing “added value”: we should hope, at this point, that we can do better.

Thinking about this, I think the distinction boils down to why you’re teaching the material in the first place.

With a lot of research-based teaching, the goal is to show the students how to interact with current literature. You want to show them journal papers, not because the papers are the best way to teach a concept or skill, but because reading those papers is one of the skills you want to teach.

That makes sense for very current topics, but it seems a bit weird for the example I’ve been looking at, an early study of chaos from the 60’s. It’s great if students can read current papers, but they don’t necessarily need to read older ones. (At least, not yet.)

What then, is the textbook trying to teach? Here things get a bit messy. For a relatively old topic, you’d ideally want to teach not just a vague impression of what was discovered, but concrete skills. Here though, those skills are just a bit beyond the students’ reach: chaos is more approachable than you’d think, but still not 100% something the students can work with. Instead they’re learning to appreciate concepts. This can be quite valuable, but it doesn’t give the kind of structure that a concrete skill does. In particular, it makes it hard to know what to emphasize, beyond just summarizing the original article.

In this case, I’ve come up with my own way forward. There are actually concrete skills I’d like to teach. They’re skills that link up with what the textbook is teaching, skills grounded in the concepts it’s trying to convey, and that makes me think I can convey them. It will give some structure to the lesson, a focus on not merely what I’d like the students to think but what I’d like them to do.

I won’t go into too much detail: I suspect some of the students may be reading this, and I don’t want to spoil the surprise! But I’m looking forward to class, and to getting to try another pedagogical experiment.

Cabinet of Curiosities: The Coaction

I had two more papers out this week, continuing my cabinet of curiosities. I’ll talk about one of them today, and the other in (probably) two weeks.

This week, I’m talking about a paper I wrote with an excellent Master’s student, Andreas Forum. Andreas came to me looking for a project on the mathematical side. I had a rather nice idea for his project at first, to explain a proof in an old math paper so it could be used by physicists.

Unfortunately, the proof I sent him off to explain didn’t actually exist. Fortunately, by the time we figured this out Andreas had learned quite a bit of math, so he was ready for his next project: a coaction for Calabi-Yau Feynman diagrams.

We chose to focus on one particular diagram, called a sunrise diagram for its resemblance to a sun rising over the sea:

This diagram

Feynman diagrams depict paths traveled by particles. The paths are a metaphor, or organizing tool, for more complicated calculations: computations of the chances fundamental particles behave in different ways. Each diagram encodes a complicated integral. This one shows one particle splitting into many, then those many particles reuniting into one.

Do the integrals in Feynman diagrams, and you get a variety of different mathematical functions. Many of them integrate to functions called polylogarithms, and we’ve gotten really really good at working with them. We can integrate them up, simplify them, and sometimes we can guess them so well we don’t have to do the integrals at all! We can do all of that because we know how to break polylogarithm functions apart, with a mathematical operation called a coaction. The coaction chops polylogarithms up to simpler parts, parts that are easier to work with.

More complicated Feynman diagrams give more complicated functions, though. Some of them give what are called elliptic functions. You can think of these functions as involving a geometrical shape, in this case a torus.

Other functions involve more complicated geometrical shapes, in some cases very complicated. For example, some involve the Calabi-Yau manifolds studied by string theorists. These sunrise diagrams are some of the simplest to involve such complicated geometry.

Other researchers had proposed a coaction for elliptic functions back in 2018. When they derived it, though, they left a recipe for something more general. Follow the instructions in the paper, and you could in principle find a coaction for other diagrams, even the Calabi-Yau ones, if you set it up right.

I had an idea for how to set it up right, and in the grand tradition of supervisors everywhere I got Andreas to do the dirty work of applying it. Despite the delay of our false start and despite the fact that this was probably in retrospect too big a project for a normal Master’s thesis, Andreas made it work!

Our result, though, is a bit weird. The coaction is a powerful tool for polylogarithms because it chops them up finely: keep chopping, and you get down to very simple functions. Our coaction isn’t quite so fine: we don’t chop our functions into as many parts, and the parts are more mysterious, more difficult to handle.

We think these are temporary problems though. The recipe we applied turns out to be a recipe with a lot of choices to make, less like Julia Child and more like one of those books where you mix-and-match recipes. We believe the community can play with the parameters of this recipe, finding new version of the coaction for new uses.

This is one of the shiniest of the curiosities in my cabinet this year, I hope it gets put to good use.

Types of Undergrad Projects

I saw a discussion on twitter recently, about PhD programs in the US. Apparently universities are putting more and more weight whether prospective students published a paper during their Bachelor’s degree. For some, it’s even an informal requirement. Some of those in the discussion were skeptical that the students were really contributing to these papers much, and thought that most of the work must have been done by the papers’ other authors. If so, this would mean universities are relying more and more on a metric that depends on whether students can charm their professors enough to be “included” in this way, rather than their own abilities.

I won’t say all that much about the admissions situation in the US. (Except to say that if you find yourself making up new criteria to carefully sift out a few from a group of already qualified-enough candidates, maybe you should consider not doing that.) What I did want to say a bit about is what undergraduates can typically actually do, when it comes to research in my field.

First, I should clarify that I’m talking about students in the US system here. Undergraduate degrees in Europe follow a different path. Students typically take three years to get a Bachelor’s degree, often with a project at the end, followed by a two-year Master’s degree capped with a Master’s thesis. A European Master’s thesis doesn’t have to result in a paper, but is often at least on that level, while a European Bachelor project typically isn’t. US Bachelor’s degrees are four years, so one might expect a Bachelor’s thesis to be in between a European Bachelor’s project and Master’s thesis. In practice, it’s a bit different: courses for Master’s students in Europe will generally cover material taught to PhD students in the US, so a typical US Bachelor’s student won’t have had some courses that have a big role in research in my field, like Quantum Field Theory. On the other hand, the US system is generally much more flexible, with students choosing more of their courses and having more opportunities to advance ahead of the default path. So while US Bachelor’s students don’t typically take Quantum Field Theory, the more advanced students can and do.

Because of that, how advanced a given US Bachelor’s student is varies. A small number are almost already PhD students, and do research to match. Most aren’t, though. Despite that, it’s still possible for such a student to complete a real research project in theoretical physics, one that results in a real paper. What does that look like?

Sometimes, it’s because the student is working with a toy model. The problems we care about in theoretical physics can be big and messy, involving a lot of details that only an experienced researcher will know. If we’re lucky, we can make a simpler version of the problem, one that’s easier to work with. Toy models like this are often self-contained, the kind of thing a student can learn without all of the background we expect. The models may be simpler than the real world, but they can still be interesting, suggesting new behavior that hadn’t been considered before. As such, with a good choice of toy model an undergraduate can write something that’s worthy of a real physics paper.

Other times, the student is doing something concrete in a bigger collaboration. This isn’t quite the same as the “real scientists” doing all the work, because the student has a real task to do, just one that is limited in scope. Maybe there is particular computer code they need to get working, or a particular numerical calculation they need to do. The calculation may be comparatively straightforward, but in combination with other results it can still merit a paper. My first project as a PhD student was a little like that, tackling one part of a larger calculation. Once again, the task can be quite self-contained, the kind of thing you can teach a student over a summer project.

Undergraduate projects in the US won’t always result in a paper, and I don’t think anyone should expect, or demand, that they do. But a nontrivial number do, and not because the student is “cheating”. With luck, a good toy model or a well-defined sub-problem can lead a Bachelor’s student to make a real contribution to physics, and get a paper in the bargain.