Collaboration (in Cartoons)

a dispatch from the fourth annual Heidelberg Laureate Forum

Mathematics is lonely work. Or so the romantic stereotype has it: the lone genius in an empty library. The sage on the mountaintop. Andrew Wiles in the attic.

But most mathematical work is profoundly collaborative.

I caught four young researchers between events, and gave them the prompt: On one piece of paper, show me the essence of good collaboration.

Their drawings? Four different flavors of brilliant.

First, from Ana Djurdjevac, born in Serbia and now studying partial differential equations:


In pursuing PDEs, Ana perhaps missed her other calling: as a painter specializing in stark symbolism.

“First, you need different types of people,” she explained. “Men and women. Standing and sitting.”

“Gray and purple,” I added.

“They all share the same space,” she said, pointing to the stage-like center of her drawing.

“Their own Eden,” I said.

“The sun and the moon represent day and night,” Ana said.

“So they work hard?”

“Yes, and each person plays a different role,” she said. Then Ana pointed to her stick figures, from left to right. “He is listening. She is teaching. He is asking a question. And she is angry.”

“Angry?” I asked. “Is that important for collaboration?”

“Oh yes!” Ana said. “Someone must bring the anger.”

Second, from Lashi Bandara, from Australia and now studying harmonic analysis:


Lashi is effusively social, with a fondness for vulgar humor—I had to warn him to keep it PG-rated.

He was disappointed, but resilient. “Can I at least draw a beer?” he asked.

Lashi produced three playful sketches showing the three pillars of good collaboration, Bandara-style.

First, communication: sharing a blackboard, and sharing thoughts.

Second, socializing—although Lashi mused that his handwriting looks more like “socialism.” “That also works,” he said.

Thirdly, diversity—for which Lashi drew two topologically distinct objects, representing topologically distinct people. “So that torus-person cannot be smoothly deformed into a sphere-person?” I said.

“And that’s the essence of diversity!” Lashi agreed.

Third, from Chenhao Tan, born in China and now studying social networks:


As befits his academic interests, Tan laid out two different graph theoretic models of collaboration: efficient and inefficient.

In an efficient collaboration, everyone is connected, offering compliments and constructive discussion.

But in an inefficient one, the hierarchy is strict. (Graph theorists would call it a tree.) Authoritarianism reigns, and there is no goodwill between collaborators.

Personally, if I ran an MBA program, I would totally build Tan’s illuminating charts into the coursework.

And finally, from Helena Andre Terre, born in Spain and now studying computational biology:


Helena’s cartoon is equal parts cynicism and inspiration.

“So the guy with the roller skates is just coasting, isn’t he?” I asked.

“No,” she insisted. “You need him. The collaboration needs someone providing the carrot.”

“So the carrot is like the question being asked?” I said.

“It could be,” Helena replied. “It’s whatever drives the project forward, gives it a goal.”

“And which one are you?” I asked.

Helena, still working on her PhD at Cambridge University, pointed to the one on the bike. Then she smiled. “But, someday…” she said, and her finger moved towards the other figure.

12 thoughts on “Collaboration (in Cartoons)

  1. It reminds me of what the commencement speaker at my graduation said.

    When you get n people together it doesn’t increase you brain power n-fold it increases it by 2^n. But then that would imply that one mathematician working alone has 2 times the normal brainpower, doesn’t it.

  2. 🙂 super ideas 🙂 especially about the anger – I need to think about that one.

    Weird (but probably should have been obvious) that what they’re studying has such an influence on their drawings

  3. I loved this idea so much I just used it as an activity in my 9th grade Conceptual Physics class. Their responses are funny and very insightful. I had one group draw a group of three working on a fighter jet: “One guy has duct tape, because duct tape fixes everything. The second guy is holding a hammer, because he doesn’t know what to do, and the third guy is just standing there because it seemed like the place to be.” I think that is the essence of group work in 9th grade. Ha!

    Another group drew a group of bank robbers, because “if you don’t work together, you’ll go to jail.”

    Can’t wait to try this with my next two classes!

  4. Socializing works. Socialism …

    Socialism is a beautiful and engaging theory that scales from family-sized groups to groups of enterprise, municipality, and nation-sized groups exceptionally poorly. It is a theory that illustrates the aphorism that in theory, theory and practice are the same; in practice, they are not. Socialism uniquely attempts to allocate scare resources more fairly by introducing a new and even-more-scarce-resource into the process: a perfectly informed and impartial volunteer allocator. If an allocator happens to mis-distribute resources due to ignorance, or partiality towards his or her own class or gender or political supporters, or by cutting off a slice of the resources under consideration for his or her own use rather than the use of the original competitors, then the theory fails. Again, socialism may sometimes work when an self-abnegating allocator named “Mom” or “Dad” decides on how to fairly allocate the family’s budget or even divide up the estate among the potential heirs. Among groups or societies with membership larger than some number “N”, (where “N” experimentally appears to be a single digit integer) socialism fails.

    Among nations, socialism NEVER works.

    There have been several “natural” experiments (North and South Korea, East and West Germany, independent India before and after 1990) illustrating how the same resources distributed among the same tribal and ethnic groups in the same locations produce completely NOT-the-same — nearly orthogonal — outcomes under socialism and alternative allocation algorithms.

    For the statement “socialism works” to be true, I would expect a novel and unanticipated definition of the term “works” to be introduced. Perhaps someone here would be kind enough to define this notion of “works” for me.

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