The Case for the Brambles


In  a month, I’ll be returning to Heidelberg, Germany. I’ll interview young researchers, ask a few questions of Fields Medalists, and save my deepest inquiries for the German chocolate cake. It’s the kind of absurd opportunity I had no reason to believe my career would afford when I began teaching math in 2009.

This has me thinking about a brief conversation I had last year with John Hopcroft, one of the honored laureates in Heidelberg.

You could be forgiven for thinking that John Hopcroft’s impressive career has followed a preordained trajectory. Bachelor’s, PhD, professorship. Stanford, Princeton, Cornell. Textbook author; National Science Board appointee; Turing Award winner. A well-groomed C.V. born from strategic calculations, right?


“A sequence of strange events that happened,” summarizes Hopcroft.


Hopcroft describes his career in terms of chance encounters and curiosities pursued. “I’ve never really planned things,” he says. “I’ve just been lucky.”

But “luck” doesn’t mean Hopcroft views his story as some anomaly, or a fluke to be dismissed. Rather, Hopcroft’s experiences mirror his values. He believes in helping to create a world where researchers can be open to chance, and chase curiosity wherever it leads.

To Hopcroft’s mind, progress isn’t found by following the well-worn garden path. It’s somewhere off in the brambles.


By way of explanation, Hopcroft cites a historical distinction between two types of research: basic and applied.

“It has nothing to do with the quality,” Hopcroft says. “It’s the question of why you’re doing it. Applied research is being done because there’s a national need… Basic research is to produce the next generation of talent.”

I’ve always heard a slightly different definition: where applied research seeks to solve practical problems, basic research pursues truth for its own sake. But Hopcroft gives a compelling alternative: basic research is not truth for its own sake, but truth for the sake of the researcher’s growth.


“If you got an NSF [National Science Foundation] grant—at least when I was coming up—you didn’t have to do the research you specified you were going to do,” Hopcroft recalls. “If you found something else that was more exciting, do that.”

The government wasn’t funding specific projects. It was investing in the curiosity and potential of the young scholars themselves.

Hopcroft knows this idealism—and lack of direct accountability—may sound dubious to 21st-century ears. (“We didn’t even have to write final reports,” he admits; NSF recipients these days certainly do.) But he is certain that the open-ended approach helped to foster the American research community as we know it today.

“The US made some fundamental decisions which were right,” he says. “I just can’t believe someone was bright enough.”


Hopcroft’s own stumbling path began in his hometown of Seattle.

“I went to a small Jesuit university,” he remembers. “I was going to stay in Seattle and go to the University of Washington to get a PhD. So I went over and talked to a faculty member.” But, for whatever reason, the professor rebuffed him. “He said, ‘Look, you can’t be admitted to our PhD program because you went to an un-accredited engineering program.”

Hopcroft was befuddled. “I went back to my department chair, and he said, ‘Why are you applying to the University of Washington? Why don’t you go to Stanford?’”

So Hopcroft wound up at one of country’s most prestigious universities, right at the birth of computer science—all because someone had (incorrectly, it turned out) sent him away. “It was just that stupid thing that person said,” Hopcroft smiles. “That had a major impact.”


After his PhD, Hopcroft planned to return to Seattle. Then, one day, “I happened to walk past my advisor’s office, and he said, ‘Come on in,’ and he handed me the phone.” Hopcroft’s advisor had just received a call from the chair of the Electrical Engineering department at Princeton. They were looking to hire.

It could easily have been one of the advisor’s other students instead of Hopcroft. But once again, Hopcroft happened to be at the right place at the right time.

He finds the academic environment today less conducive to these moments of serendipity. His home institution of Cornell, for example, “has become a lot more administrative. When I was [first] there, basically the faculty told the administration what to do. Now, the administration has all kinds of rules.”

Hopcroft doesn’t necessarily blame individuals; to him, it’s a systemic failure. “Everybody adds something which is good to do,” he says of new requirements and regulations, “and nobody ever drops anything.”

Thus researchers and teachers find themselves slowly surrounded by layers of fencing, until they are virtually immobilized.


“People also want objective measures of quality,” says Hopcroft. He understands the impulse, but laments it. “Take our No Child Left Behind Act,” he says. “Teachers are now teaching to tests.”

For each of the last several years, Hopcroft has spent several months teaching in China. He also advises the Premier of China on how to improve the country’s sprawling university system. In China, Hopcroft sees America’s current problems pushed the extreme, with an awful added twist: junior faculty work for senior faculty.

“Instead of picking their own problem,” Hopcroft explains, “they work on something that the senior faculty wants them to do. And that’s not how you do creative work.”


Now, you could write all of this off as the nostalgia and griping of a late-career academic. A professor who thinks that professors need more autonomy and freedom? A researcher who thinks researchers should be paid to do whatever they feel like, no questions asked? If you want to read wishful self-indulgence into Hopcroft’s vision, it’s not hard to do.

As for me—although I’m not a professor, a researcher, or a late-career anything—I find Hopcroft’s account compelling. And Hopcroft’s own career furnishes more evidence for the value of serendipity and chance.

In his first job at Princeton, he says, “the chair of the department understood that computers were going to be important. So he said, ‘We ought to create a computer science theory course.’ That’s what my first assignment was.”

Hopcroft created the course and wrote a textbook for it. Before long, “It turned out that everyone around the world used that book, because it was the only one.”

The first book led to more: algorithms, then discrete math. He planned none of it, just followed the currents.


“The fact that my department chair asked me to teach this computer science course made me one of the world’s first computer scientists,” Hopcroft says. “Later, whenever our government was looking for a senior computer scientist, although I wasn’t very old, I was on the short list.”

Eventually, President George H.W. Bush appointed him to the National Science Board. “I was only in my forties,” Hopcroft says, “but there wasn’t anybody older than me.”

How, then did Hopcroft find himself as one of the elder statesmen of the discipline that’s reshaping modern life? By following his curiosity. By remaining open to new directions. By chasing interesting thoughts off into the brambles.

Born in 1939, Hopcroft has watched his discipline evolve before his eyes. Now, in 2016, he thinks we’re in a moment of transition.

“The last 40 years, we were involved in making computers useful,” Hopcroft says. “Now we’re starting to ask, ‘What are they being used for?’”


When he gives advice to young researchers on how to navigate this shifting landscape, it’s simple: “Do the research that you want to do.”

Hopcroft knows the risks of wandering into the brambles. He doesn’t promise that everyone will wind up tenured at Cornell. Even so, he sees pursuing your curiosity as a matter of principle. “If you are going to do really fundamental research,” says Hopcroft, “it’d better be something you’re excited about.”

Before we parted ways, I asked him to draw a cartoon. Ever willing to indulge a wild goose chase, he grabbed a blue marker and sketched the following:


On the left: the safe and uninspiring way to do research. The junior researchers huddle like obedient children around the desk of the senior researcher, who tells them, “Here is the research you should work on today.”

Meanwhile, on the right: the ambitious, Hopcroft-ian way to do research. “Another junior” sets out—with an intrepid gait, I’d like to note—saying, “I am going to work that excites me.”

Off into the brambles.

[edited 8/26/2017, with thanks to commenters below]

16 thoughts on “The Case for the Brambles

  1. I shared this with my children, who thought they were going one way, then decided one day to go a completely different way. Thanks, Ben!

  2. As someone who has enjoyed working in the brambles, I fully support what Hopcroft has said. All of my best research was on topics different from those written in NSF or ONR proposals. I did my best research when I got excited about solving a problem, and then devoted lots of energy and thought to solving it.

    I’m glad and proud that all of my children enjoy brambles.

    1. Thanks, Dad!

      I get why grant proposals work the way they do, but it seems really hard for a researcher to anticipate what will capture their thoughts and engage their interest in the coming months/years.

  3. Loved this. My life has been a series of being in the right place at the right time, and occasionally I have to stop and ask myself how I have gotten where I am today. Having great people around and a sense of gratefulness, as well as a healthy curiosity, certainly helps. Doing something you life and are interested in, as you mention is the icing on the cake. Great blog, I enjoy it very much.

    1. Thanks for reading! I think you’re right on all those forces, both the few in our control (curiosity and gratitude) and the many that are not.

  4. Having read a number of success stories like this one, and as someone who is currently deep in brambles, I feel it is important to point out that you can work hard, pursue your dreams, and still *not* be as successful as Prof. Hopcroft here. It’s easy to get discouraged when you read a lot of stories where things just “fell into place” for other scientists, when they don’t seem to magically fall into place for you…no offense intended of course, but success stories like yours and his may be the exception, rather than the rule.

    1. You’re completely right – thanks for commenting.

      Reading your thoughts and others’, I’m reflecting that the best interpretation of Hopcroft’s advice is not “Go wander in the brambles, everybody! You’ll come out fine like me!” but rather “We should design our research system to create opportunities for people to wander into the brambles, rather than punishing people who stray from the path.” I might try to edit the post to bring out that distinction a bit more.

  5. I learned yesterday from mathematician Emily Riehl’s twitter @emilyriehl about University of Washington algebraic topologist Steve Mitchell, who just passed away. Mitchell’s website has a wonderful “autobiography” describing how he became to be a mathematician, and it was certainly not the the standard path. Brambles abound.

    “I’m a 3-time college dropout. In fact, I don’t even have an undergrad degree. It’s a long story, most of which has nothing to do with math…”

    1. Looks fascinating! I’ll look forward to digging in. And I just followed Emily on Twitter – I could always use more algebraists in my feed.

  6. Hopcroft happened to be at the right place at the right time.

    And brilliant. And very learned. And the sort of person who can cope with the disorientation that doing wildly new things brings. It’s hardly a common combination.

    I’ve seen loads of students leave school and wander into the brambles. To end up drug users, drop-outs in some cases, and without a job they enjoy for decades in others because they went the wrong way. It’s a dangerous path if you are unprepared.

    I was lucky and ended up as a Maths teacher, which I love, after a winding path, with lots of job changes and overseas travel. I could do it only because when I was at university I had enough discipline to do difficult topics like 3rd year Maths well, even though it was not required for my degree (Chemistry).

    So, by all means wander off piste. But not if you haven’t the required mental and emotional mind for it, and not if you haven’t prepared well before-hand so that you can take advantage of opportunities when they arise.

    I tell all my students to work hard at school and university because it allows you to take opportunities, and you cannot foresee those opportunities. I also tell them that wandering around hoping things will work out is a loser strategy.

    As for the “wrong” way to do research, well, opinions differ. I suspect that a mix of both sorts is required, and that in order for it to pay — and companies aren’t going to fund research for fun — its researchers who are told what to research that make more discoveries. A few very brilliant people might work better when freed to do what they want, but most people would just get nowhere without a specific goal. But, hey, that’s a way less sexy story bro.

    1. That’s all very fair – I think you and standingoutinmyfield above have highlighted for me the possible pitfalls of highlighting a story like Hopcroft’s (especially in the sloppy way that I have, which conflates a few distinct issues).

      When it comes to research, there’s obviously a balance to be struck between pursuing knowledge for its own sake and pursuing useful applications. Hopcroft seemed to feel that things had tilted too far one way; I don’t think he was arguing for the abolition of usefulness! He was also talking more about the academic setting than the corporate one; there’s a natural specialization of the former in “basic” research and the latter in “applied.” (That said, it’s worth noting that corporations like Google and Facebook seem eager to carve out small long-term strategic research groups that function much more like universities.)

Leave a Reply