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# Science and Culture: How a conference focused on algorithms balances serious math with computational whimsy

In 1998, a few dozen computer scientists and mathematicians gathered at a picturesque seaside resort on the Tuscan island of Elba off the west coast of Italy. They were there to attend a scientific gathering unlike any other.

The 17 presentations suggested peculiar offerings. One explored an algorithmic answer to the question, “What if mathematicians were asked to diffuse bombs?” Using an idea from abstract number theory, the researchers described a generalized solution to a problem posed in the 1995 movie, *Die Hard with a Vengeance.* Another presentation focused on how to help a baker optimize his bagel selection to maximize profits. Still another carefully delineated the rules requisite for a trick, popularized by magician Harry Houdini in the 1920s, that entails folding a piece of paper, making one straight cut with scissors, and producing a recognizable shape.

It was the first meeting of the FUN with Algorithms conference, and every gathering since has strived for the same mix of creativity and rigor. Attendees delight in concocting algorithms, generally defined as mathematical recipes—often translated into code and executed by a computer—that can produce solutions to a problem. Last year’s conference, the ninth, included presentations on the complexity of the 2016 video game *The Witness*, an analysis of “Perversely Awful Randomized Algorithms,” and a discussion of conspiratorial strategies in Secret Santa gift exchanges (1).

Most scientific conferences focus on advances that can push a field forward. FUN with Algorithms instead highlights the creativity and amusement that comes with solving difficult problems, says computer scientist Nicola Santoro at Carleton University in Ottawa, Canada, one of the organizers. “People get quite excited about it,” he says. Although the conference veers mostly toward games, puzzles, challenges, and novelty, its offerings do lead to serendipitous connections among researchers and even, in some cases, surprising applications.

## Serious Games

Papers accepted to FUN with Algorithms have to satisfy two criteria. First, they have to use algorithms to solve a problem that’s computationally interesting. Second, and perhaps more importantly, they have to be motivated by the joy of playing with algorithms. Witty or amusing proposals are often favored. “They need to be interesting in some way other than being useful,” says Erik Demaine, a computer scientist at Massachusetts Institute of Technology (MIT), Cambridge, and a frequent presenter, “but that doesn’t preclude them from being useful.”

The conference began as a tribute to influential Italian computer scientist Fabrizio Luccio at the University of Pisa, Italy. Three of his former advisees wanted to celebrate Luccio’s 60th birthday with a conference, but they insisted that its content align with Luccio’s playful approach to work.

Solving problems with mathematical recipes may be an unusual diversion for most, but Luccio “considers his research an amusing activity,” says computer scientist Linda Pagli at the University of Pisa, who studied under Luccio in the 1970s. Pagli was one of the three original organizers; the other two were Santoro and Elena Lodi, now at the University of Siena, Italy.

FUN with Algorithms was supposed to be a one-time event. But after the inaugural conference, attendees clamored for more, so three years later came the second conference. And, three years after that one, the third. Now, the conference is held every other year. At first, it was called Fun with Algorithms, but Santoro said funding agencies didn’t want to send researchers to a frivolous conference, so they changed the spelling to FUN, in all capital letters, to look like an acronym.

Conference participants acknowledge that not everyone in their fields sees the value of projects like FUN. “I’ve encountered negative reactions to recreational pursuits, sadly,” says Demaine, at MIT. “But I don’t think recreational work ‘takes away’ from the field. It adds to it.” He argues that it’s important to balance “serious” work with recreational work, and adds that recreational pursuits often draw new students to a field by revealing the fun that can be had in research.

As more researchers have become involved, the scope of the conference has grown, says Santoro. It now encompasses three main areas. The first includes people who analyze the computational complexity of games. Past presentations have shown, for example, that both Sudoku and the classic 1980s video game *Super Mario Brothers* can be studied as NP-Hard problems. This means, roughly, that solutions are difficult to find but straightforward to verify. (Computer scientists classify “P” problems as fairly simple and solvable in what’s called “polynomial time,” whereas harder “NP” problems are believed to require an unreasonably long, “nonpolynomial” amount of time to hammer out solutions.)

In *Super Mario Brothers*, the title character has to overcome a barrage of obstacles—carnivorous plants, wicked animated mushrooms, bottomless pits—to reach the game’s end and win. In 2016, researchers presented a paper showing that it’s possible to construct NP-Hard levels in the game. And in 2018, a different group, led by computer scientist Manuel Lafond at the University of Sherbrooke in Quebec, Canada, showed that finding the absolute fastest route to finish the game—which the game signals with an animation of fireworks over the castle—is NP-Hard, or nearly impossible. The most recent conference included analyses of Sudoku, Pachinko (a sort of vertical pinball game that’s popular in Japan), and *Portal*, a first-person, puzzle-based video game. Studying this kind of complexity isn’t merely a trivial pursuit: Finding ways to optimize solutions to NP-Hard problems is at the heart of some efforts to develop algorithms that will run on quantum computers.

Lafond’s work on speed-running games has focused on the optimal strategies—such as route choice or enduring a certain amount of damage—that lead to lower times. “How can we optimize [the winning strategy of] a video game?” he asks. His analysis shows that this question evokes a familiar, tricky optimization challenge called the knapsack problem (2). Given a list of things, as well as their weights and monetary values, how can you pack a backpack to remain under a certain weight while maximizing the value? Lafond noted that in games such as *Castlevania*, a player wants to minimize their playing time without jeopardizing their character’s health and losing the game. That means choosing among many options and weighing time against cost: A player might choose a shorter path but risk more damage to her character, for example, in the same way that a knapsack-packer might choose a heavy but high-valued object.

“I don’t usually work with video games,” says Lafond, whose full-time job entails studying algorithms involved with genes and evolution. But when he learned about the conference, Lafond saw a way to merge his recreational interest in video games with his computer science work.

The second category the conference highlights might loosely be called recreational computer science, which involves finding solutions to puzzles, games, or other challenges for their own sake. The Harry Houdini card trick from the first year falls into this category. So does “The Evolution of Impossible Objects,” a talk given at the 2018 meeting by Japanese mathematician Kokichi Sugihara, at Meiji University in Tokyo, who for four decades has been using mathematics to create three-dimensional illusions. These include a three-dimensionally printed grid that looks square but appears circular in its mirror reflection, and a marble that seems to roll uphill. His work is driven by the ideas of the mathematical field of topology. The secret recipe to his illusions—the algorithm behind his creations—is to use those topological ideas to choose camera angle, shape design, and mirror placement. In his talk, Sugihara demonstrated the illusions and described seven families of illusion that he had discovered.

The third category, Santoro explains, includes more traditional algorithms but with creative applications, or “where the fun part is evident.” In 2018, a group presented a formula to predict how long it takes for social network users to establish a community—that is, a close group of individuals with shared interests—within a given network. (Previous studies suggested that the problem is P-Hard, which means that it takes a reasonable amount of time, but the new work found situations where finding communities can take much longer, exponential time.) The 2018 conference also included a presentation that focused on a warehouse where mobile robots fulfilled and shipped orders. The algorithm offered a way to determine an optimal configuration of recharging stations throughout the warehouse, to make sure no robots ran out of power during the day and service was never interrupted.

## Beyond FUN

Such work hints at practical applications within quantum computing—but other areas could benefit as well. Demaine at MIT coauthored a paper presented at the first FUN conference; this was the one that focused on Houdini’s magic trick, which is well-known among mathematicians as the “fold-and-cut” problem. It probes what shapes can result from folding a piece of paper flat and making a single cut.

One of the earliest mentions of this problem was in a 1721 book of math challenges, published in Japan; Houdini famously described how to do it in a 1922 book. Eventually, researchers took notice. In the early 1990s, physicist and engineer-turned-origami-artist Robert Lang in California laid the groundwork for a new field called “computational origami,” which combined paper-folding with math and computer programming.

The fold-and-cut problem was Demaine’s first major result as a professional computer scientist, and he credits it with propelling him into the field of computational geometry, work that may have implications beyond computer science. Demaine and his collaborators proved, mathematically, that it’s possible to create any shape, if you fold the paper correctly. At the time, it seemed like a curious finding, and little more. “Computational origami was in its infancy,” Demaine says. “Everyone thought it was recreational. Origami was just for fun, but computational origami has become very practical lately.”

Now, there are dozens of software programs that can generate origami patterns for given shapes, and origami ideas have inspired ideas for new materials and technologies, including wearable electronics. The sensors designed by John Rogers at Northwestern University, for example, stick to the body like temporary tattoos but can flex with the natural movement of the skin thanks to their origami-inspired designs (3). The solution could even have implications for the design of car airbags, which must inflate in a split second during a crash.

The three-dimensional airbag has to be folded flat and into a tiny volume to fit into a steering wheel or small compartment. Finding the best way to fold an airbag, Demaine says, essentially becomes a fold-and-cut problem. He hasn’t worked directly on airbag design, but designers have applied and built on origami-based algorithms to find the optimal folds (4).

Santoro says that even though the presentations are flashy and the subject matter is entertaining, the research itself is based on rigorous mathematical proofs, and the conference publishes a volume of articles after every meeting. They’ve already started scouting picturesque Italian islands for the tenth gathering, to be held next year.

Demaine believes the conference’s approach can indeed help lay the groundwork for new advances. “Often, you’re trying to understand something fundamental,” he says, “and the applications come later.”

Published under the PNAS license.

## References

- ↵
- H. Ito,
- S. Leonardo,
- L. Pagli,
- G. Prencipe

- ↵
- M. Lafond

- ↵
- C. Beans

- ↵
- C. Cromvik,
- K. Eriksson

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