We arrived at Huh’s classroom a few minutes before class was scheduled to begin. Inside, nine students sat in loose rows. One slept with his head down on the table. Huh took a position in a front corner of the room and removed several pages of crumpled notes from his backpack. Then, with no fanfare, he picked up where he’d left off the previous week. Over the next 80 minutes he walked students through a proof of a theorem by the German mathematician David Hilbert that stands as one of the most important breakthroughs in 20th-century mathematics.

Commutative algebra is taught at the undergraduate level at only a few universities, but it is offered routinely at Princeton, which each year enrolls a handful of the most promising young math minds in the world. Even by that standard, Huh says the students in his class that morning were unusually talented. One of them, sitting that morning in the front row, is the only person ever to have won five consecutive gold medals at the International Mathematical Olympiad.

Huh’s math career began with much less acclaim. A bad score on an elementary school test convinced him that he was not very good at math. As a teenager he dreamed of becoming a poet. He didn’t major in math, and when he finally applied to graduate school, he was rejected by every university save one.

Nine years later, at the age of 34, Huh is at the pinnacle of the math world. He is best known for his proof, with the mathematicians Eric Katz and Karim Adiprasito, of a long-standing problem called the Rota conjecture.

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Even more remarkable than the proof itself is the manner in which Huh and his collaborators achieved it — by finding a way to reinterpret ideas from one area of mathematics in another where they didn’t seem to belong. This past spring IAS offered Huh a long-term fellowship, a position that has been extended to only three young mathematicians before. Two of them (Vladimir Voevodsky and Ngô Bảo Châu) went on to win the Fields Medal, the highest honor in mathematics.

That Huh would achieve this status after starting mathematics so late is almost as improbable as if he had picked up a tennis racket at 18 and won Wimbledon at 20. It’s the kind of out-of-nowhere journey that simply doesn’t happen in mathematics today, where it usually takes years of specialized training even to be in a position to make new discoveries. Yet it would be a mistake to see Huh’s breakthroughs as having come in spite of his unorthodox beginning. In many ways they’re a product of his unique history — a direct result of his chance encounter, in his last year of college, with a legendary mathematician who somehow recognized a gift in Huh that Huh had never perceived himself.

Huh was born in 1983 in California, where his parents were attending graduate school. They moved back to Seoul, South Korea, when he was two. There, his father taught statistics and his mother became one of the first professors of Russian literature in South Korea since the onset of the Cold War.

After that bad math test in elementary school, Huh says he adopted a defensive attitude toward the subject: He didn’t think he was good at math, so he decided to regard it as a barren pursuit of one logically necessary statement piled atop another. As a teenager he took to poetry instead, viewing it as a realm of true creative expression. “I knew I was smart, but I couldn’t demonstrate that with my grades, so I started to write poetry,” Huh said.

Huh wrote many poems and a couple of novellas, mostly about his own experiences as a teenager. None were ever published. By the time he enrolled at Seoul National University in 2002, he had concluded that he couldn’t make a living as a poet, so he decided to become a science journalist instead. He majored in astronomy and physics, in perhaps an unconscious nod to his latent analytic abilities.

When Huh was 24 and in his last year of college, the famed Japanese mathematician Heisuke Hironaka came to Seoul National as a visiting professor. Hironaka was in his mid-70s at the time and was a full-fledged celebrity in Japan and South Korea. He’d won the Fields Medal in 1970 and later wrote a best-selling memoir called *The Joy of Learning*, which a generation of Korean and Japanese parents had given their kids in the hope of nurturing the next great mathematician. At Seoul National, he taught a yearlong lecture course in a broad area of mathematics called algebraic geometry. Huh attended, thinking Hironaka might become his first subject as a journalist.

Initially Huh was among more than 100 students, including many math majors, but within a few weeks enrollment had dwindled to a handful. Huh imagines other students quit because they found Hironaka’s lectures incomprehensible. He says he persisted because he had different expectations about what he might get out of the course.

“The math students dropped out because they could not understand anything. Of course, I didn’t understand anything either, but non-math students have a different standard of what it means to understand something,” Huh said. “I did understand some of the simple examples he showed in classes, and that was good enough for me.”

After class Huh would make a point of talking to Hironaka, and the two soon began having lunch together. Hironaka remembers Huh’s initiative. “I didn’t reject students, but I didn’t always look for students, and he was just coming to me,” Hironaka recalled.

Huh tried to use these lunches to ask Hironaka questions about himself, but the conversation kept coming back to math. When it did, Huh tried not to give away how little he knew. “Somehow I was very good at pretending to understand what he was saying,” Huh said. Indeed, Hironaka doesn’t remember ever being aware of his would-be pupil’s lack of formal training. “It’s not anything I have a strong memory of. He was quite impressive to me,” he said.

As the lunchtime conversations continued, their relationship grew. Huh graduated, and Hironaka stayed on at Seoul National for two more years. During that period, Huh began working on a master’s degree in mathematics, mainly under Hironaka’s direction. The two were almost always together. Hironaka would make occasional trips back home to Japan and Huh would go with him, carrying his bag through airports and even staying with Hironaka and his wife in their Kyoto apartment.

“I asked him if he wanted a hotel and he said he’s not a hotel man. That’s what he said. So he stayed in one corner of my apartment,” Hironaka said.

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In Kyoto and Seoul, Hironaka and Huh would go out to eat or take long walks, during which Hironaka would stop to photograph flowers. They became friends. “I liked him and he liked me, so we had that kind of nonmathematical chatting,” Hironaka said.

Meanwhile, Hironaka continued to tutor Huh, working from concrete examples that Huh could understand rather than introducing him directly to general theories that might have been more than Huh could grasp. In particular, Hironaka taught Huh the nuances of singularity theory, the field where Hironaka had achieved his most famous results. Hironaka had also been trying for decades to find a proof of a major open problem — what’s called the resolution of singularities in characteristic *p*. “It was a lifetime project for him, and that was principally what we talked about,” Huh said. “Apparently he wanted me to continue this work.”

In 2009, at Hironaka’s urging, Huh applied to a dozen or so graduate schools in the U.S. His qualifications were slight: He hadn’t majored in math, he’d taken few graduate-level classes, and his performance in those classes had been unspectacular. His case for admission rested largely on a recommendation from Hironaka. Most admissions committees were unimpressed. Huh got rejected at every school but one, the University of Illinois, Urbana-Champaign, where he enrolled in the fall of 2009.

At Illinois, Huh began the work that would ultimately lead him to a proof of the Rota conjecture. That problem was posed 56 years ago by the Italian mathematician Gian-Carlo Rota, and it deals with combinatorial objects — Tinkertoy-like constructions, like graphs, which are “combinations” of points and line segments glued together.

Consider a simple graph: a triangle.

Mathematicians are interested in the following: How many different ways can you color the vertices of the triangle, given some number of colors and adhering to the rule that whenever two vertices are connected by an edge, they can’t be the same color. Let’s say you have *q* colors. Your options are as follows:

*q*options for the first vertex, because when you’re starting out you can use any color.*q*– 1 options for the adjacent vertex, because you can use any color save the color you used to color the first vertex.*q*– 2 options for the third vertex, because you can use any color save the two colors you used to color the first two vertices.

The total number of colorings will be all options multiplied together, or in this case *q *x (*q *– 1) x (*q* – 2) = *q*^{3} – 3*q*^{2} + 2*q*.

That equation is called the chromatic polynomial for this graph, and it has some interesting properties.

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Take the coefficients of each term: 1, –3 and 2. The absolute value of this sequence — 1, 3, 2 — has two properties in particular. The first is that it’s “unimodal,” meaning it only peaks once, and before that peak the sequence only ever rises, and after that peak it only ever falls.

The second property is that the sequence of coefficients is “log concave,” meaning that any three consecutive numbers in the sequence follow this rule: The product of the outside two numbers is less than the square of the middle number. The sequence (1, 3, 5) satisfies this requirement (1 x 5 = 5, which is smaller than 3^{2}), but the sequence (2, 3, 5) does not (2 x 5 = 10, which is greater than 3^{2}).

You can imagine an infinite number of graphs — graphs with more vertices and more edges connected in any number of ways. Every one of these graphs has a unique chromatic polynomial. And in every graph that mathematicians have ever studied, the coefficients of its chromatic polynomial have always been both unimodal and log concave. That this fact always holds is called “Read’s conjecture.” Huh would go on to prove it.

Read’s conjecture is, in a sense, deeply counterintuitive. To understand why, it helps to understand more about how graphs can be taken apart and put back together. Consider a slightly more complicated graph — a rectangle:

The chromatic polynomial of the rectangle is harder to calculate than that of the triangle, but any graph can be broken up into subgraphs, which are easier to work with. Subgraphs are all the graphs you can make by deleting an edge (or edges) from the original graph:

Or by contracting two vertices into one:

The chromatic polynomial of the rectangle is equal to the chromatic polynomial of the rectangle with one edge deleted minus the chromatic polynomial of the triangle. This makes intuitive sense when you recognize that there should be more ways to color the rectangle with the deleted edge than the rectangle itself: The fact that the top two points aren’t connected by an edge gives you more coloring flexibility (you can, for instance, color them the same color, which you’re not allowed to do when they’re connected). Just how much flexibility does it give you? Precisely the number of coloring options for the triangle.

The chromatic polynomial for any graph can be defined in terms of the chromatic polynomials of subgraphs. And the coefficients of all of these chromatic polynomials are always log concave.

Yet when you add or subtract two log concave sequences, the resulting sequence is usually not itself log concave. Because of this, you’d expect log concavity to disappear in the process of combining chromatic polynomials. Yet it doesn’t. Something else is going on. “This is what made people curious of this log concavity phenomenon,” Huh said.

Huh didn’t know any of this when he arrived at Illinois. Most first-year graduate students spend more time in class than on their own research, but following his three-year apprenticeship with Hironaka, Huh had ideas that he wanted to pursue.

Through his first Midwestern winter, Huh developed techniques for applying singularity theory, the focus of his study with Hironaka, to graphs. In doing so, Huh found that when he constructed a singularity from a graph, he was suddenly able to use singularity theory to justify properties of the original graph — to explain, for instance, why the coefficients of a polynomial based on the graph would follow a log concave pattern.

This was interesting to Huh, so he searched the graph theory literature to see if others had previously explained these log concave patterns he was seeing. He discovered that to graph theorists, the patterns were still entirely mysterious.

“I noticed this pattern I’d observed was in fact a well-known conjecture in graph theory, Read’s conjecture. In a sense I solved this problem without knowing the problem,” Huh said.

Huh’s inadvertent proof of Read’s conjecture, and the way he combined singularity theory with graphs, could be seen as a product of his naïve approach to mathematics. He learned the subject mainly on his own and through informal study with Hironaka. People who have observed his rise over the last few years imagine that this experience left him less beholden to conventional wisdom about what kinds of mathematical approaches are worth trying. “If you look at mathematics as a kind of continent divided into countries, I think in June’s case nobody really told him there were all these borders. He’s definitely not constrained by any demarcations,” said Robbert Dijkgraaf, the director of IAS.

Soon after he posted his proof of Read’s conjecture, the University of Michigan invited Huh to give a talk on his result. On December 3, 2010, he addressed a room full of many of the same mathematicians who had rejected his graduate school application a year earlier. By this point Huh’s talent was becoming evident to other mathematicians. Jesse Kass was a postdoctoral fellow in mathematics at Michigan at the time. Just before Huh’s visit, a senior faculty member encouraged Kass to watch the talk because “30 years from now you can tell your grandchildren you saw Huh speak before he got famous,” recalled Kass, who’s now a professor at the University of South Carolina.

Huh’s lecture did not disappoint.

“The talk was somehow very polished and very clear; it just went to the right points. It’s a bit unusual for a beginning graduate student to give such clean talks,” said Mircea Mustaţă, a mathematician at Michigan.

Following his talk, the Michigan faculty invited Huh to transfer, which he did in 2011. By that point he’d learned that Read’s conjecture was a special case of a larger and more significant problem — the Rota conjecture.

The Rota conjecture is very similar to Read’s conjecture, but instead of graphs it addresses more abstract combinatorial objects called “matroids” (a graph can be viewed as a particularly concrete type of matroid) and a different kind of equation that arises from each matroid, called the “characteristic polynomial.” But the underlying point is the same: The Rota conjecture predicts that the coefficients of the characteristic polynomial for any matroid are always log concave.

The statement is simple, and evidence for it is abundant, but proving it — explaining why this log concavity occurs — is difficult. There’s nothing about the matroids themselves that suggests why the log concavity would hold uniformly when you add or subtract the characteristic polynomials of submatroids (just as there’s no obvious reason the log concavity would hold when you add or subtract the chromatic polynomials of graphs). Whenever you observe a pattern with no obvious cause, it’s natural to start digging below the surface — to look for the roots that explain the tree. That’s what Huh did when he and his collaborators began to attack the Rota conjecture.

“Log concavity is easy to observe in concrete examples,” Huh said. “You just compute the sequence you’re interested in and observe [that] it’s there. But for some reason it’s hard to justify why this is happening.”

Initially Huh looked for ways to extend the techniques from singularity theory that he had used for Read’s conjecture, but he quickly found that they didn’t work in the more abstract realm of matroids.

This failure left him looking for some other kind of structure, hidden beneath the surface of matroids, that could explain the way they behaved mathematically.

Some of the biggest leaps in understanding occur when someone extends a well-established theory in one area to seemingly unrelated phenomena in another. Think, for example, about gravitation. People have always understood that objects fall to the ground when released from a height; the heavens became far more intelligible when Newton realized the same dynamic explained the motion of the planets.

In math the same kind of transplantation occurs all the time. In his widely cited 1994 essay “On Proof and Progress in Mathematics,” the influential mathematician William Thurston explained that there are dozens of different ways to think of the concept of the “derivative.” One is the way you learn it in calculus — the derivative as a measure of infinitesimal change in a function. But the derivative appears in other guises: as the slope of a line tangent to the graph of a function, or as the instantaneous speed given by a function at a specific time. “This is a list of different ways of *thinking about* or *conceiving of* the derivative, rather than a list of different *logical definitions*,” Thurston wrote.

Huh’s work on the Rota conjecture involved a reconception of a venerable area of mathematics called Hodge theory. Hodge theory was developed in the 1950s by the Scottish mathematician William Hodge. To call it a “theory” is simply to say that it’s the study of some particular thing, just as you could say that “right triangle theory” is the study of right triangles. In the case of Hodge theory, the objects of interest are called the “cohomology rings of smooth projective algebraic varieties.”

It’s hard to overstate how little Hodge theory would seem to relate to graphs or matroids. The cohomology rings in Hodge theory arise from smooth functions that come packaged with a concept of the infinite. By contrast, combinatorial objects like graphs and matroids are purely discrete objects — assemblages of dots and sticks. To ask what Hodge theory means in the context of matroids is a little like asking how to take the square root of a sphere. The question doesn’t appear to make any sense.

Yet there was good reason to ask. In the more than 60 years since Hodge theory was proposed, mathematicians have found a number of instances of Hodge-type structures appearing in settings far removed from their original algebraic context. It’s as if the Pythagorean relationship, once thought to be the exclusive provenance of right triangles, also turned out to describe the distribution of prime numbers.

“There is some feeling that these structures, whenever they exist, are fundamental. They explain facts about your mathematical structure that are hard to explain by any other means,” Huh said.

Some of these new settings have been combinatorial, which encouraged Huh to wonder whether relationships from Hodge theory might underlie these log concave patterns. Searching for a familiar math concept in a foreign land is not easy, though. In fact, it’s a bit like searching for extraterrestrial life — you might have ideas about signature characteristics of life, hints you might use to guide your hunt, but it’s still hard to anticipate what a new life-form might look like.

In recent years Huh has done much of his most important work with two collaborators — Eric Katz, a mathematician at Ohio State University, and Karim Adiprasito, a mathematician at the Hebrew University of Jerusalem. They make an unusual trio.

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Adiprasito initially wanted to be a chef and spent time backpacking around India before settling down in combinatorics, the area of mathematics that’s home to graph theory and problems like the Rota conjecture. He liked math in high school but turned away from it because “I felt it wasn’t creative enough for me,” he said. Katz has a frenetic mind and obsessively detailed knowledge of indie rock bands, developed in his earlier years as a college radio DJ. Of the three collaborators, he is the closest to having a typical math pedigree, and he views himself as a kind of interpreter between the creative ideas of the would-be poet and the would-be chef.

“Karim has these amazing ideas that come out of nowhere, and June sort of has this beautiful vision of how math should go,” Katz said. “It’s often hard to incorporate Karim’s ideas into June’s vision, and maybe some of what I do is talk to Karim and translate his ideas into something closer to math.”

Katz became aware of Huh’s work in 2011, after Huh proved Read’s conjecture but before he’d made any progress proving the Rota conjecture. Katz read Huh’s proof of Read’s conjecture and observed that if he cut out one particular step in the argument, he could apply the methods from that paper to get a partial proof of the Rota conjecture. He contacted Huh, and over the course of just a few months the two wrote a paper (published in 2012) that explained log concavity for a small class of matroids called “realizable” matroids.

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Yet that paper didn’t solve the hardest part of the Rota conjecture — proving log concavity for “nonrealizable” matroids, which comprise the vast majority of all matroids. Hodge theory, remember, was defined originally in the 1950s on objects called the “cohomology rings of algebraic varieties.” If you want to prove that Hodge-type structures explain phenomena observed in matroids, you need to find a way of explaining how something like a cohomology ring can be distilled out of a matroid. With realizable matroids, there was a very straightforward way to do this, which is why Huh and Katz’s proof for that piece of the Rota conjecture came so quickly. But with nonrealizable matroids, there was no obvious way to instantiate a cohomology ring — they were like a language without a word for that concept.

For four years Huh and Katz tried and failed to find a way to define what a Hodge structure would mean in the context of nonrealizable matroids. During that time they determined that one particular aspect of Hodge theory — known as the Hodge index theorem — would be enough by itself to explain log concavity, but there was a catch: They couldn’t find a way to actually prove that the Hodge index theorem was true for matroids.

That’s when Adiprasito entered the picture. In 2015 he traveled to IAS and visited Huh. Adiprasito realized that while the Hodge index theorem alone would explain log concavity, the way to prove the Hodge index theorem for matroids was to try and prove a larger set of ideas from Hodge theory that includes the Hodge index theorem — what the three collaborators refer to as the “Kähler package.”

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“I told June and Eric there is a way to actually prove this in a purely combinatorial setting,” Adiprasito said. “Then it actually was quick that we came up with a plan. I think they asked the question and I provided the technique.”

This technique provided a full proof of the Rota conjecture. The trio posted their work online in November 2015, and since then it has rippled through the math world. Their work provides a fully combinatorial vision of Hodge theory, which in turn provides a whole new way to approach open problems in combinatorics.

The work has also elevated Huh’s profile. In addition to his new position at IAS, Huh is frequently mentioned as a strong contender for the Fields Medal, which is given every four years to the most accomplished mathematicians under the age of 40. If he doesn’t get it in the 2018 prize cycle, he’s still young enough to qualify in 2022.

Back in 2012, Huh went to Seoul National University to give a talk on his recent proof of Read’s conjecture. Hironaka was in the audience, and he recalls being surprised to learn that singularity theory had applications to graphs. Afterward, he asked Huh if this new work marked a change in his research interests.

“I remember I asked him if he’s completely in graph theory kinds of things and has lost interest in singularities. He said no, he’s still interested in singularities,” Hironaka said.

Huh remembers that conversation, too. It took place at a time when he was indeed setting out in a whole new direction in mathematics. He thinks maybe he just wasn’t ready to say that out loud — especially to the man who changed his life. “That was the point that I was going off the road,” he said. “I think he sensed that and still, I am off the road. Maybe there was some psychological force that made me not want to admit I’d completely left singularity theory behind.”

Huh and Hironaka have not seen each other since. Hironaka is now 86. He’s retired but continues to work toward a proof of the problem in singularity theory that has occupied him for decades. In March he posted a long paper to his old faculty webpage at Harvard University that he says provides a proof. Other mathematicians, including Huh, have taken a preliminary look at the work but have not yet verified that the proof holds. It’s hard for Hironaka to travel, but he wishes it were easier for him to see Huh again. “I only hear about him,” Hironaka said.

Over coffee one afternoon at Huh’s apartment on the IAS campus, I asked him how he feels about not pursuing the research track Hironaka may have hoped for him. He thought for a moment, then said he feels guilty.

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“A lot of the time with Hironaka I sort of had to fake my understanding,” he said. “This lack of mathematical background has prevented me from going on to serious research with him. This has left a sort of long-term homework in me.”

At the same time, Huh regards the distance he has traveled from his mathematical roots as a good and maybe necessary step in the development of his work. As we parted on a street corner in Princeton, he remarked, “I need space to think,” before heading into the quiet confines of IAS. He found his own way into mathematics, and now that he’s there, he’s going to find his own path through it.

]]>The Argentinian-American theorist found a mathematical correspondence between a certain bendy, bounded space-time environment — the universe in the bottle — and a special quantum theory describing particles on the bottle’s rigid surface, which seems to project the dynamic interior like a hologram. Maldacena’s discovery has enabled physicists to probe black holes and quantum gravity inside the imaginary bottled universe by studying corresponding properties of the gravity-free surface. His paper introducing the so-called AdS/CFT correspondence (which links “anti-de Sitter spaces” and “conformal field theories”) has been cited more than 15,000 times, or about twice per day on average over the past two decades, making it the most highly cited paper ever in high-energy physics.

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Maldacena was working alone in his bare office at Harvard’s Jefferson Laboratory when the insight came. While others might find inspiration in features from the actual universe, he thinks best when he can leave just about everything behind. The office “had no decorations,” he said. “For me any quiet place with no visual or auditory distractions would work.”

In 2001, Maldacena moved to the Institute for Advanced Study in Princeton, New Jersey, a pastoral campus free of students and teaching duties where worldly distractions are minimized by design. There, his deep insights have continued to surface. In 2002, he conceived of the ultimate test for cosmic inflation — the modern Big Bang theory — by predicting subtle but theoretically detectable shapes in the sky, which experiments will look for in the coming years.

Maldacena stunned the physics world again in 2013 with a cryptic message first delivered in an email to fellow physics giant Leonard Susskind: “ER = EPR.” It meant that wormholes, hypothetical connections between far-apart black holes also known as Einstein-Rosen bridges (ER), are mathematically equivalent to entangled particles, sometimes called Einstein-Podolsky-Rosen pairs (EPR). Like AdS/CFT, ER = EPR suggests a deep link between the geometry of space-time and quantum connections between particles, and it provides theorists with another clue in their quest for a a theory of quantum gravity.

Maldacena, 48, whom Susskind calls “the master,” is still quietly pondering. “I mostly think in my office,” he said. “But sometimes I can walk by the lake to help clear my mind.”

]]>But new findings published today in *Current Biology* challenge this model, finding that the majority of toxin genes for parasitoid wasp species are instead “moonlighting” from other physiological roles. A further exciting implication is that if this discovery is relevant to compounds other than venoms, it might be a pathway that nature uses to develop other evolutionary solutions rapidly.

“I’ve been working on parasitoid wasps for a very long time,” remarked Jack Werren, a professor of biology at the University of Rochester. His fascination with these animals centers on their specialized venoms, which allow the wasps to be masterful physiological puppeteers. Parasitoid wasps are an enormous group of between 100,000 and 600,000 species that are parasitic when they are larvae, living on or frequently inside a host they eat alive. As free-living adults, they must find and subdue an appropriate creature to play host to their young, which they do with the aid of behavior-altering venoms. The emerald cockroach wasp, for example, transforms its formidable targets — cockroaches many times its size — into complacent meals for the wasps’ hungry offspring by manipulating the animals’ brain chemistry. The *Glyptapanteles* wasp goes even further, turning its caterpillar offerings into zombie bodyguards that protect the young wasps that have just eaten their way out of the caterpillars’ tissues. Another wasp, *Reclinervellus nielseni*, forces its arachnid victims to transform their webs into sturdy nests that will continue to protect the wasp larvae after the spiders expire.

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“The venoms of parasitoids are quite different from those of most of the venomous animals that have been studied because they’ve evolved to manipulate metabolism” rather than to kill outright, Werren explained. He and two postdoctoral fellows in his lab, Ellen O. Martinson and Mrinalini (now at the National University of Singapore), were interested in understanding the diversity of toxins in parasitoid venoms and how those toxins evolve. They and their colleagues started by assembling genomes for several closely related wasp species, and they found something striking: Even close relatives among the wasps shared only about 30 to 40 percent of their venom genes. That surprisingly low number suggested the evolution of new species was accompanied by rapid turnover of the venom genes, with old genes being abandoned and new ones with novel venom functions suddenly arising. “Our next question was, okay, well what happened?” Werren said. “These genes that are being picked up, where are they coming from? And that got us into this broad question of: How do new genes’ functions evolve?”

Based largely on studies of snakes, spiders and other species dangerous to our own, it is thought that most venom genes arise through the mechanism of gene duplication followed by mutation and repurposing (which scientists refer to as neofunctionalization). The process begins when a gene for a molecule with a potentially toxic function, like a protein-chopping enzyme, is accidentally duplicated, typically during the formation of egg cells and sperm. The extra copy, free of the burden of performing the original gene’s biological duties, can accumulate changes through random mutations. Those changes may render the duplicate gene or its protein worthless, and it may disappear. Sometimes, however, those changes alter the protein in such a way that it becomes a useful toxin — and voilà, a venom toxin is born.

But when Martinson, Mrinalini, Werren and their colleagues compared the venom proteins and genes from four closely related species of parasitoid wasps, that’s not what they saw. In stark contrast to studies of other venomous animals, they found that nearly half of the 53 most recently recruited venom genes uncovered through their genetic analyses were single-copy, meaning they were not duplicates of other genes with which evolution had tinkered. In fact, less than 10 percent of the toxin genes clearly arose through duplication and mutation.

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The team then wanted to understand how these single-copy genes went from performing ordinary, nonvenom functions to acting as toxins. And again, the results were surprising. “When we first started doing this, we were actually looking at this all wrong,” Werren said. “We thought that what we were seeing was the rapid specialization of genes as venoms, and loss of their other function.” But when they looked at which tissues in the wasps’ bodies were expressing the genes, “we discovered it wasn’t that.”

Instead, Werren likened the functionality of these single-copy genes to “moonlighting” for extra cash, with the genes taking on a “night job” in the venom gland in addition to their “day job” elsewhere in the body. The genes were routinely expressed to some degree in various tissues during stages of larval or adult development. The venom glands simply expressed the genes much more abundantly and steadily. Consequently, the gene’s protein — which had a benign physiological function elsewhere in the wasp body — reached a concentration with toxic properties in the venom. “That’s why a lot of this is expression evolution,” Werren explained. “The protein isn’t changing much. It’s just its expression pattern that’s changing to make it a venom.”

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The lack of change is also very different from what is expected of venom genes. Implicit in the duplicate-and-mutate model is the assumption that the toxins need to evolve rapidly to be effective because many venomous animals can be locked in an arms race with their toxins’ targets. If the venoms don’t evolve quickly enough, then the predators or prey on which they’re intended to act will evolve a countermeasure and render the toxic advantage moot. And to date, biologists studying other species have seen venom genes evolve at a breakneck pace: The conotoxins employed by cone snails, for example, are known to mutate rapidly.

But the findings suggest that the wasps don’t need mutations in the venom toxin genes to switch from one host to another, or to keep pace with their current hosts. They just need to be able to co-opt and drop genes for use in making venoms quickly.

The results open the possibility that scientists have been overlooking a major pathway for the origins of toxin genes. “These findings raise important questions relating to the processes that other venomous animals may have used to generate their venom toxins,” wrote Nicholas Casewell, senior lecturer and Wellcome Trust research fellow with the Alistair Reid Venom Research Unit at the Liverpool School of Tropical Medicine, in a summary dispatch published alongside the *Current Biology* paper. “While gene duplication and alternative splicing are typically invoked as major mechanisms underpinning protein neofunctionalization, this study suggests that the process of co-option should be re-evaluated as a potentially important method by which genes can acquire novel functions.”

Bryan Fry, head of the Venom Evolution Laboratory at the University of Queensland, generally agreed with that view in comments emailed to *Quanta*. The work by Werren and his team is a “very intriguing paper that reinforces that the more we learn about venom evolution, the more we realise how little we know. Parasitoid wasps were already known to have very weird strategies and this paper reinforces just how uniquely divergent they are.” Whether co-option occurs more widely needs to be determined, he wrote.

“It had not particularly occurred to me as a likely mechanism of venom evolution,” admitted Wolfgang Wüster, a lecturer at Bangor University. He also isn’t convinced that this mechanism of gene evolution is prominent in other venomous groups. “I suspect it will remain unusual,” he said. “As the authors point out, parasitoid venoms act in a much subtler, more fine-tuned manner than the better known predatory or defensive venoms of things like snakes, spiders or cone shells.” That unique ecological role for the wasps’ venom could explain why these animals rely so heavily on a different mechanism for gene evolution than other venomous species. “Extended anaesthesia is much more difficult and requires much more finesse than killing something — ask any surgeon,” Wüster said.

Like Wüster, Werren considers the idea that co-option is rare among venom genes to be “one hypothesis that would have to be explored.” Nevertheless, he thinks it’s likely that this mode of evolution could have been underestimated because other studies have rarely compared evolutionary next of kin. “If you look at species that are very, very divergent from each other, you might find a certain subset of genes are shared and others [are] not, but you don’t really get the fine-scale picture.

“It may be that this process isn’t as important in snakes,” he said, but he noted that “a lot more work has to be done on looking at really closely related snake species before we can say for sure.”

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Werren believes that the role of gene moonlighting might not stop with venoms. Gene moonlighting can occur merely through changes in expression, which may result from as little as a single mutation; it does not require the meandering process of random alteration and selection implied by the duplication and neofunctionalization model. Co-option is therefore likely to be a much faster mechanism for adaptation. “For species that have a very rapidly changing environment, this process of co-option of single genes may be fairly important. It just hasn’t been looked at that much,” he remarked.

“Is this a general function or is that something that only occurs in these specialized organs?” he asked. “I’m looking forward to addressing that question in the next several years, but I think it’s going to be a fairly broad mechanism, particularly when organisms are subject to rapid selection.”

“This paper is another nice illustration of one of the joys of biology,” Wüster said. “Just when you think you have found a generalisation of how animals accomplish something, something else pops up that does it completely differently.”

*Corrections: This article was revised on June 26, 2017, to acknowledge Mrinalini as a co-lead investigator on this project. Also,
the lower limit of the number of parasitoid wasp species, which originally appeared as “100,00,” was corrected to 100,000.*

Kris Pardo, a graduate student working under the astrophysicist David Spergel at Princeton University, assembled a sample of 81 isolated dwarf galaxies. These small galaxies appear to have an especially high concentration of dark matter, and so provide a unique astrophysical laboratory in which to compare various theories. He then measured how quickly those galaxies rotate. The more dark matter that exists in a galaxy — or the stronger the effects of emergent gravity — the faster the galaxy should spin. “Isolated dwarf galaxies are the cleanest test you can get,” Pardo said. “It’s the best we can do right now.”

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Emergent gravity successfully predicts the rotation velocities of the smallest galaxies in the sample. But it predicts velocities far too low for the more massive galaxies, especially the ones full of gas clouds. This discrepancy could pose a serious problem for emergent gravity, since the main success of the theory so far has been predicting the rotation curves of large galaxies.

Physicists who study emergent gravity are taking Pardo’s study seriously. “This is interesting and good work,” Verlinde said. But he cautions that emergent gravity hasn’t been developed to the point where it can make specific predictions about all dwarf galaxies. “I think more work needs to be done on both the observational and the theory side,” he added.

One way Verlinde’s theory might be exonerated is if Pardo’s galaxies are shaped differently than they appear. They look spherical, but if instead they are Frisbee-like, the modified shape would be enough to throw off Pardo’s calculations. To provide a more definitive test, Pardo and colleagues are trying to secure time on the Very Large Array telescopes in New Mexico so they can make high-resolution measurements that map out how fast stars and gas are rotating within the galaxies.

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Other groups of astronomers have been working on complementary tests of emergent gravity. Some are using the theory to predict the warped appearance of galaxies by gravitational lensing. Others are using it to study the motions of galaxy clusters. Emergent gravity also needs to explain the large-scale structure of the universe as well as the cosmic microwave background. In these areas, dark matter does a great job at predicting what astrophysicists observe. But so far, no one has been able to use emergent gravity to work out similarly detailed predictions.

“Verlinde’s collecting puzzle pieces and trying to match them together, but it’s not a complete and coherent picture yet,” said Sabine Hossenfelder, a theoretical physicist at the Frankfurt Institute for Advanced Studies. She recently proposed a modified version of Verlinde’s theory that could better describe the rotational motions of most galaxies. Might it — or something like it — one day replace the theory of dark matter? A definitive answer will take time to emerge.

*Editor’s Note: David Spergel is the director of the **Center for Computational Astrophysics** at the Flatiron Institute, a division of the Simons Foundation. Quanta Magazine is an **editorially independent** division of the foundation. *

Now, new theoretical calculations provide a possible explanation for why naked singularities do not exist — in a particular model universe, at least. The findings indicate that a second, newer conjecture about gravity, if it is true, reinforces Penrose’s cosmic censorship conjecture by preventing naked singularities from forming in this model universe. Some experts say the mutually supportive relationship between the two conjectures increases the chances that both are correct. And while this would mean singularities do stay frustratingly hidden, it would also reveal an important feature of the quantum gravity theory that eludes us.

“It’s pleasing that there’s a connection” between the two conjectures, said John Preskill of the California Institute of Technology, who in 1991 bet Stephen Hawking that the cosmic censorship conjecture would fail (though he actually thinks it’s probably true).

The new work, reported in May in *Physical Review Letters* by Jorge Santos and his student Toby Crisford at the University of Cambridge and relying on a key insight by Cumrun Vafa of Harvard University, unexpectedly ties cosmic censorship to the 2006 weak gravity conjecture, which asserts that gravity must always be the weakest force in any viable universe, as it is in ours. (Gravity is by far the weakest of the four fundamental forces; two electrons electrically repel each other 1 million trillion trillion trillion times more strongly than they gravitationally attract each other.) Santos and Crisford were able to simulate the formation of a naked singularity in a four-dimensional universe with a different space-time geometry than ours. But they found that if another force exists in that universe that affects particles more strongly than gravity, the singularity becomes cloaked in a black hole. In other words, where a perverse pinprick would otherwise form in the space-time fabric, naked for all the world to see, the relative weakness of gravity prevents it.

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Santos and Crisford are running simulations now to test whether cosmic censorship is saved at exactly the limit where gravity becomes the weakest force in the model universe, as initial calculations suggest. Such an alliance with the better-established cosmic censorship conjecture would reflect very well on the weak gravity conjecture. And if weak gravity is right, it points to a deep relationship between gravity and the other quantum forces, potentially lending support to string theory over a rival theory called loop quantum gravity. The “unification” of the forces happens naturally in string theory, where gravity is one vibrational mode of strings and forces like electromagnetism are other modes. But unification is less obvious in loop quantum gravity, where space-time is quantized in tiny volumetric packets that bear no direct connection to the other particles and forces. “If the weak gravity conjecture is right, loop quantum gravity is definitely wrong,” said Nima Arkani-Hamed, a professor at the Institute for Advanced Study who co-discovered the weak gravity conjecture.

The new work “does tell us about quantum gravity,” said Gary Horowitz, a theoretical physicist at the University of California, Santa Barbara.

In 1991, Preskill and Kip Thorne, both theoretical physicists at Caltech, visited Stephen Hawking at Cambridge. Hawking had spent decades exploring the possibilities packed into the Einstein equation, which defines how space-time bends in the presence of matter, giving rise to gravity. Like Penrose and everyone else, he had yet to find a mechanism by which a naked singularity could form in a universe like ours. Always, singularities lay at the centers of black holes — sinkholes in space-time that are so steep that no light can climb out. He told his visitors that he believed in cosmic censorship. Preskill and Thorne, both experts in quantum gravity and black holes (Thorne was one of three physicists who founded the black-hole-detecting LIGO experiment), said they felt it might be possible to detect naked singularities and quantum gravity effects. “There was a long pause,” Preskill recalled. “Then Stephen said, ‘You want to bet?’”

The bet had to be settled on a technicality and renegotiated in 1997, after the first ambiguous exception cropped up. Matt Choptuik, a physicist at the University of British Columbia who uses numerical simulations to study Einstein’s theory, showed that a naked singularity can form in a four-dimensional universe like ours when you perfectly fine-tune its initial conditions. Nudge the initial data by any amount, and you lose it — a black hole forms around the singularity, censoring the scene. This exceptional case doesn’t disprove cosmic censorship as Penrose meant it, because it doesn’t suggest naked singularities might actually form. Nonetheless, Hawking conceded the original bet and paid his debt per the stipulations, “with clothing to cover the winner’s nakedness.” He embarrassed Preskill by making him wear a T-shirt featuring a nearly-naked lady while giving a talk to 1,000 people at Caltech. The clothing was supposed to be “embroidered with a suitable concessionary message,” but Hawking’s read like a challenge: “Nature Abhors a Naked Singularity.”

The physicists posted a new bet online, with language to clarify that only non-exceptional counterexamples to cosmic censorship would count. And this time, they agreed, “The clothing is to be embroidered with a suitable, truly concessionary message.”

The wager still stands 20 years later, but not without coming under threat. In 2010, the physicists Frans Pretorius and Luis Lehner discovered a mechanism for producing naked singularities in hypothetical universes with five or more dimensions. And in their May paper, Santos and Crisford reported a naked singularity in a classical universe with four space-time dimensions, like our own, but with a radically different geometry. This latest one is “in between the ‘technical’ counterexample of the 1990s and a true counterexample,” Horowitz said. Preskill agrees that it doesn’t settle the bet. But it does change the story.

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The new discovery began to unfold in 2014, when Horowitz, Santos and Benson Way found that naked singularities could exist in a pretend 4-D universe called “anti-de Sitter” (AdS) space whose space-time geometry is shaped like a tin can. This universe has a boundary — the can’s side — which makes it a convenient testing ground for ideas about quantum gravity: Physicists can treat bendy space-time in the can’s interior like a hologram that projects off of the can’s surface, where there is no gravity. In universes like our own, which is closer to a “de Sitter” (dS) geometry, the only boundary is the infinite future, essentially the end of time. Timeless infinity doesn’t make a very good surface for projecting a hologram of a living, breathing universe.

Despite their differences, the interiors of both AdS and dS universes obey Einstein’s classical gravity theory — everywhere outside singularities, that is. If cosmic censorship holds in one of the two arenas, some experts say you might expect it to hold up in both.

Horowitz, Santos and Way were studying what happens when an electric field and a gravitational field coexist in an AdS universe. Their calculations suggested that cranking up the energy of the electric field on the surface of the tin can universe will cause space-time to curve more and more sharply around a corresponding point inside, eventually forming a naked singularity. In their recent paper, Santos and Crisford verified the earlier calculations with numerical simulations.

But why would naked singularities exist in 5-D and in 4-D when you change the geometry, but never in a flat 4-D universe like ours? “It’s like, what the heck!” Santos said. “It’s so weird you should work on it, right? There has to be something here.”

In 2015, Horowitz mentioned the evidence for a naked singularity in 4-D AdS space to Cumrun Vafa, a Harvard string theorist and quantum gravity theorist who stopped by Horowitz’s office. Vafa had been working to rule out large swaths of the 10^{500} different possible universes that string theory naively allows. He did this by identifying “swamplands”: failed universes that are too logically inconsistent to exist. By understanding patterns of land and swamp, he hoped to get an overall picture of quantum gravity.

Working with Arkani-Hamed, Luboš Motl and Alberto Nicolis in 2006, Vafa proposed the weak gravity conjecture as a swamplands test. The researchers found that universes only seemed to make sense when particles were affected by gravity less than they were by at least one other force. Dial down the other forces of nature too much, and violations of causality and other problems arise. “Things were going wrong just when you started violating gravity as the weakest force,” Arkani-Hamed said. The weak-gravity requirement drowns huge regions of the quantum gravity landscape in swamplands.

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Weak gravity and cosmic censorship seem to describe different things, but in chatting with Horowitz that day in 2015, Vafa realized that they might be linked. Horowitz had explained Santos and Crisford’s simulated naked singularity: When the researchers cranked up the strength of the electric field on the boundary of their tin-can universe, they assumed that the interior was classical — perfectly smooth, with no particles quantum mechanically fluctuating in and out of existence. But Vafa reasoned that, if such particles existed, and if, in accordance with the weak gravity conjecture, they were more strongly coupled to the electric field than to gravity, then cranking up the electric field on the AdS boundary would cause sufficient numbers of particles to arise in the corresponding region in the interior to gravitationally collapse the region into a black hole, preventing the naked singularity.

Subsequent calculations by Santos and Crisford supported Vafa’s hunch; the simulations they’re running now could verify that naked singularities become cloaked in black holes right at the point where gravity becomes the weakest force. “We don’t know exactly why, but it seems to be true,” Vafa said. “These two reinforce each other.”

The full implications of the new work, and of the two conjectures, will take time to sink in. Cosmic censorship imposes an odd disconnect between quantum gravity at the centers of black holes and classical gravity throughout the rest of the universe. Weak gravity appears to bridge the gap, linking quantum gravity to the other quantum forces that govern particles in the universe, and possibly favoring a stringy approach over a loopy one. Preskill said, “I think it’s something you would put on your list of arguments or reasons for believing in unification of the forces.”

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However, Lee Smolin of the Perimeter Institute, one of the developers of loop quantum gravity, has pushed back, arguing that if weak gravity is true, there might be a loopy reason for it. And he contends that there is a path to unification of the forces within his theory — a path that would need to be pursued all the more vigorously if the weak gravity conjecture holds.

Given the apparent absence of naked singularities in our universe, physicists will take hints about quantum gravity wherever they can find them. They’re as lost now in the endless landscape of possible quantum gravity theories as they were in the 1990s, with no prospects for determining through experiments which underlying theory describes our world. “It is thus paramount to find generic properties that such quantum gravity theories must have in order to be viable,” Santos said, echoing the swamplands philosophy.

Weak gravity might be one such property — a necessary condition for quantum gravity’s consistency that spills out and affects the world beyond black holes. These may be some of the only clues available to help researchers feel their way into the darkness.

*This article was reprinted on Wired.com.*