Mathematicians Solve Multidimensional Shape-Slicing Dilemma
Bourgain's slicing problem asks whether every convex shape in n dimensions has a 'slice' such that the cross section is bigger than some fixed value. For three-dimensional objects, this is like asking whether an avocado of a given size, no matter the exact shape, can always be split into two halves with each side revealing at least some sizable slice. Bourgain, a titan of mathematics, is said to have spent more time on this problem than any other; although it may seem deceptively easy to resolve in the physical world's two or three dimensions, it quickly balloons in difficulty when we consider four or five. This added complexity makes determining anything in n-dimensional space seem impossible. 'If you believe in this so-called curse of dimensionality, you might just give up,' Klartag says. Fortunately, he adds, he and Lehec 'belong to a different school of thought.'
The pair's breakthrough builds on recent progress by mathematician Qingyang Guan of the Chinese Academy of Sciences, who approached the problem with a technique based on physics rather than geometry. Specifically, Guan showed that modeling how heat diffuses out of a convex shape can reveal hidden geometric structures. Researchers could calculate filling any convex shape with warm gas and carefully observe the heat's dissipation according to physical laws. Guan's key insight—a precise limit on how rapidly the rate of dissipation changes during this heating process—proved to be just what Klartag and Lehec needed. 'Guan's bound tied together all the other key facts' known for the problem, says mathematician Beatrice-Helen Vritsiou of the University of Alberta.
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The result let Klartag and Lehec resolve the problem in only a few days. Klartag notes that 'it was lucky because we knew [Guan's result] was exactly one of the things we needed' to connect several seemingly disparate approaches to the puzzle. With this final piece in place, the geometry of convex bodies in high dimensions is now a little less mysterious—although, as always in mathematics, each new slice reveals more questions to explore.
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Scientific American
3 days ago
- Scientific American
Recommended Books to the Beach This Summer
Rachel Feltman: For Scientific American 's Science Quickly, I'm Rachel Feltman. You might not know this, but Scientific American is a great place to go for book recommendations—and not just for nonfiction science titles either. Our team is packed with voracious readers, and we publish lists of our favorites at the end of each year. You can also get book recommendations every Friday in our daily newsletter, Today in Science. Now that summer is in full swing, we thought it would be fun to chat about some of our favorite beach reads. Today I'm joined by Bri Kane, Scientific American's resident reader, to go through some of her top picks for summer reading across a range of genres. On supporting science journalism If you're enjoying this article, consider supporting our award-winning journalism by subscribing. By purchasing a subscription you are helping to ensure the future of impactful stories about the discoveries and ideas shaping our world today. Bri, thanks so much for coming on to chat with us. Would you start by just telling our listeners a little bit about what you do at SciAm and, of course, how it involves books? Bri Kane: Well, my day job is helping our contractors, writers and illustrators with their contracts and their invoices, but as everyone in the office knows, I'm constantly bullying people into reading more books and shoving books in their hand. Feltman: [Laughs] Yes, and we love it. We love that you do that [laughs]. Some of our listeners who read Scientific American might already know that you can get awesome book recommendations from there—and not just nonfiction science books: we also talk about science fiction and just our favorite books of the year—so we thought we would have Bri on to talk about some exciting summer reads as a way to give you some stuff to read this summer but also introduce you to the concept of getting book recommendations from Scientific American, because our editors and reporters read a lot [laughs]. Our expertise is: we're nerds [laughs]! Kane: Yeah, I mean, Scientific American has been reviewing books for over 100 years. I've been spending a lot of time in our archive this summer in anticipation of our 180th anniversary this August, and we've had some really spicy takes on books over the years, and I'm really excited to offer listeners my own spicy takes on books now. Feltman: Amazing, so why don't we start with the more obvious Scientific American book recommendations, the low-hanging fruit: those, like, nonfiction science books that we just have to read this summer. What do you have to recommend to us in that department? Kane: So the first one is Clamor by Chris Berdik. It's a really interesting deep dive into sound and hearing in a whole new way, beyond just the decibel count: how loud our human nature is and how loud we are making nature. It's a really interesting way to think about your own hearing, and as someone who is spending a lot of time on the New York City subway and trying to go to shows with my friends on the weekend, I've never been more aware of my long-term hearing health. Feltman: Yeah, that sounds great. And I think if listeners wanna get a little bit more information before they read it, I believe you recently reviewed this one, right? Where can folks find that? Kane: Oh, yeah, I'm reviewing books every Friday in our Today in Science newsletter. Feltman: So what else do you have for us today? Kane: The next one is Empire of AI by Karen Hao. It's a really buzzy book this year, but it's really good. It's an investigative reporter's deep dive into how AI and the companies that have built it have sprung up so fast and are making millions of dollars. I need to catch up on what's going on with AI in Silicon Valley, but this is a great one. Feltman: Yeah, I love when a book comes along that allows me to rectify the fact that I have been willfully trying to know as little about a subject [laughs] as possible. AI, I haven't quite been able to do that because it, it is too involved in my life and my job and this industry, but there are definitely things in the tech world where I'm like, 'Nope.' Everything I've learned about NFTs has been against my will. So when an incredibly talented science and technology reporter comes along and is like, 'Here, this is everything you need to know about this,' I'm like, 'Okay, great. Thank you.' [Laughs] Kane: I've never been to Silicon Valley, but I still wanna know what they're up to. Feltman: [Laughs] So what other recommendations do you have? Kane: I also wanted to recommend Waste Wars by Alexander Clapp. He spent two years living out of a backpack, traveling to the smelliest places of the most beautiful countries in the world, with hidden dump sites in jungles and millions of dollars being exchanged in black market economies just to move our garbage all around the world. Feltman: Wow, that sounds great. Do you have any fiction to recommend? Kane: There's a lot of really exciting fiction coming out this year, but one I wanted to talk to you [about], Rachel, is Lucky Day by Chuck Tingle. I know we're both big fans. Feltman: I love Chuck [laughs]. Kane: Lucky Day, coming out in August, is shockingly funny, and it's really scary. It's very existential: What is the meaning of life, and if there's no meaning in life, what's my meaning, and where am I going? It's really funny and really heartfelt in a way that Chuck Tingle can really handle: making you laugh and asking those big, existential questions. Feltman: Yeah, I haven't read that one yet. I know there are, like, ARCs floating around, and I'm, like, saving it, but I, I can't wait. I love all of his other books, so really excited. Kane: Yeah, another really weird and exciting fiction book out this year is Harriet Tubman: Live in Concert by Bob the Drag Queen. Feltman: Yeah, that one sounds really interesting. Kane: This one no one saw coming, but it's such a great take on historical fiction. I don't really read a lot of historical fiction, but I love the idea of taking a historical figure and bringing them to our modern world and [letting] the plot go from there. There's a lot of real history in this book, but Harriet Tubman has really been put on a pedestal for so long, and she's treated as a real person, with an incredible history and a searing, intense personality. It was so fun. This one is a great, really fast read—perfect for a beach day. Feltman: That sounds great. Kane: Another more interesting take on classic sci-fi is Metallic Realms by Lincoln Michel. It's a really funny and cringey story about someone who desperately loves their best friend and just wants to join their really cool science-fiction writing group—except he can't 'cause he's not really a writer and he's really annoying and weird. It's so funny to be stuck in this protagonist's head who just doesn't understand why they are being the cringey one, but they love science fiction, and it's a really creative version of the story within the story. Feltman: Yeah, that one sounds really interesting. Kane: And then for my own summer reading this year, I'm working on Octavia Butler's Lilith's Brood series. My book club made me read the first one, Dawn, and I absolutely fell in love. It's a really brilliant and disturbing first-contact story. I've never really seen one that handles not only who am I when I interact with an alien, but what is humanity, and where does the line between human and alien blur once we start—copulating, I'll say? Feltman: Yeah, that series has been on my list for a long time. Over the last couple of years I finally picked up Parable of the Sower, also by Octavia Butler, and I was like, wow, I always knew this was a good book; everybody says it—it's a great book, and I believed them, but it's also so prescient, you know? Her speculative-fiction writing was just brilliant and forward-looking, so I'm also looking forward to reading more of her this summer, and you have inspired me. Kane: Yeah, I mean, Octavia Butler is awesome. The hype is real. Like, if you haven't checked her out yet, I really recommend checking out the backlist, and if you're more of a straight science-fiction reader, I highly recommend Dawn and the Lilith's Brood series; it's really unique science fiction. Feltman: Amazing, well, Bri, thank you so much for coming on and giving us these amazing recommendations. Would you remind our listeners where else they can find info on SciAm 's book lovers and the amazing stuff we do [laughs]? Kane: Yeah, I'll be reviewing books every Friday in our daily newsletter Today in Science. And keep an eye out later this year for our three end-of-year books lists: our staff favorites as usual, but we also have some best-of coming out. Feltman: And I am also participating in making that list, so—I'm constantly behind on my reading assignments for Bri, but I [laughs], but I'm working on it. And if listeners do wanna sign up for Today in Science, which they absolutely should, we'll have a link in our show notes today. Bri, thank you so much for coming on today. Kane: Thanks for having me, Rachel. I can't wait to see what you end up reading this summer. Feltman: That's all for today's episode. Don't forget to subscribe to Today in Science so you can get more of Bri's recommendations. Science Quickly is produced by me, Rachel Feltman, along with Fonda Mwangi, Kelso Harper and Jeff DelViscio. This episode was edited by Alex Sugiura. Shayna Posses and Aaron Shattuck fact-check our show. Our theme music was composed by Dominic Smith. Subscribe to Scientific American for more up-to-date and in-depth science news.
Yahoo
5 days ago
- Yahoo
1906 shipwreck is filled with rare oysters to boost marine species
A cargo ship lying at the bottom of the sea off the Belgian coast has been fitted with a new treasure chest: a stash of rare flat oysters. Molluscs have mostly disappeared from the North Sea due to human activity, including overfishing. Now, a Belgian project is trying to reintroduce it in a move scientists believe will help boost other marine species. "We have to bring them back because they are essential elements in our marine ecosystems," Vicky Stratigaki, an engineer working on the restoration project, told AFP. In mid-July, a load of 200,000 oyster larvae attached to biodegradable materials was deposited about 100 feet under the sea in the ship's hull. The environmental project, named Belreefs, aims to turn the wreckage into a biodiversity sanctuary. Flat oysters form reefs that purify water and that other sea animals, from fish to algae, use as breeding and feeding grounds, explained Stratigaki. "There is a lot of predation in the sea, it's a wild environment," she said, with about 30,000 of the oyster larvae expected to survive their first year at sea. "Then they will start reproducing, extending the reef and also supporting the biodiversity of the reef." The laying of the oyster stash is the culmination of two years' work for the Belgian government project, which is supported by European Union funding. "Until around the 1850s, the North Sea and the European waters were full of these oyster reefs," Stratigaki explained. Then overfishing, the spreading of an imported parasite called Bonamia and "climatic adverse effects" caused them to disappear, she said. The 1906 wreckage, located about 20 miles off the coastal city of Ostend, was selected to house the pilot as fishing and other disruptive activities are banned around it. "In Belgium every wreck that is for more than one hundred years on the sea bottom gets protected automatically as cultural heritage, because it's nice for divers to go there," said Merel Oeyen, a marine environment expert at the Belgian ministry of health. "It's also a hot spot for biodiversity." A 2023 paper published in BioScience found that shipwrecks provide important ecological resources for a wide variety of organisms, from tiny microbes to large marine creatures. "Small fish and mobile crustaceans often find shelter in the crevices of the sunken material, and larger baitfish and predators use shipwrecks as feeding grounds and rest stops as they swim from one place to another," according to NOAA, which helped conduct the study. However, scientists also warned shipwreck can also cause damage to existing marine life in the area, or carry harmful cargo, such as oil. Still, the study's author, Avery Paxton, said shipwrecks can have "second lives" as homes to a variety of marine life. "A ship's transformation from an in-service vessel into a thriving metropolis for marine life has a fairy-tale quality to it," Paxton said in an article published by the Washington Post after the study was released. What shocked "Matlock" star Kathy Bates? A new you: The science of redesigning your personality "Somebody Somewhere" star Bridget Everett Solve the daily Crossword
Yahoo
19-07-2025
- Yahoo
Can U.S. Math Research Survive NSF Funding Cuts?
A 72 percent reduction in federal funding is devastating to math research. The American Mathematical Society is offering $1 million in backstop grants—but it's likely not enough. Mathematics research typically requires few materials. To explore the secrets of prime numbers, investigate unimaginable shapes or elucidate other fundamental mysteries of our universe, mathematicians don't usually need special labs and equipment or to pay participants in clinical trials. Instead funding for mathematicians goes toward meetings of the mind—conferences, workshops and institutes where they gather for intensive sessions to work out math's knottiest problems. Funding also supports the stipends of research fellows, postdoctoral scholars and promising early-career mathematicians. But under the Trump administration's National Science Foundation, much of this funding is being revoked or cut—which, according to experts, could be catastrophic for the present and future of the field. In one recent example, the NSF canceled funding for the Association for Women in Mathematics' research symposium in Wisconsin just four business days before the event was set to begin in May. The threat to this event catalyzed the American Mathematical Society to offer $1 million in backstop grants to support programs whose federal funding has been cut or remains in limbo. These grants are meant to provide a financial safety net that will temporarily allow math programs, researchers and departments to continue operating—but it's not a permanent solution. (Disclosure: The author of this article currently has a AAAS Mass Media Fellowship at Scientific American that is sponsored by the American Mathematical Society.) 'The funding cut is severe, and all of mathematics will be impacted,' says Raegan Higgins, president of the Association for Women in Mathematics and a mathematician at Texas Tech University. [Sign up for Today in Science, a free daily newsletter] Movies and television shows often portray mathematicians scribbling on chalkboards in seclusion, but that picture is often far from accurate. 'None of us work in isolation,' Higgins says. In fact, mathematicians rely heavily on their ability to gather and discuss ideas with their peers—perhaps even more than researchers in other fields do. For mathematicians, conferences, workshops and research talks are not just opportunities to share research and network but also crucial moments to work out tough problems together with colleagues, pose field-propelling questions and generate new ideas. 'It's a thinking science, [and] it's a communication science, so we rely on being together to share ideas and to move the needle forward,' says Darla Kremer, executive director of the Association for Women in Mathematics. According to John Meier, CEO of the American Mathematical Society, 'the ability of mathematicians to gather and talk with each other is absolutely central to the vitality of the field.' Federal dollars, largely through the NSF, are responsible for a significant portion of math funding. But a lot of that funding is disappearing under the Trump administration. In April NSF staff members were instructed to 'stop awarding all funding actions until further notice.' Over the past 10 years, on average, the NSF has awarded $113 million in grants to mathematics by May 21 of each year. This year the NSF has awarded only $32 million, representing a 72 percent reduction. By this metric, mathematics is one of the most deeply affected subjects, second only to physics, which has seen an 85 percent reduction. The administration is also canceling and freezing funding that it had previously promised to researchers. More than $14 million of funding already promised to mathematics programs was revoked earlier this year, according to an analysis by Scientific American. In response to a request for comment, the National Science Foundation told Scientific American that 'the agency has determined that termination of certain awards is necessary because they are not in alignment with current NSF priorities and/or programmatic goals.' This withdrawal of grants is eroding trust and seeding uncertainty, experts say, and it comes with long-term consequences. Even if funding gets renewed again later, it can be very difficult for halted programs to recover. 'If you have to shut down a lab and mothball it, that actually takes time and effort,' Meier says. 'You can't just walk in two weeks later, flip a switch and have everything running again. You've got to rebuild it.' Even in mathematics, that process of rebuilding is time-intensive and not always possible if the space has been reallocated or the people have moved on. American Mathematical Society leadership fears these cuts will hurt young mathematicians the most. Like in the sciences, the funding cuts are eliminating research experiences and supportive programming for undergraduates, fellowships for graduate students and positions for postdoctoral researchers. Travel funding for conferences is also disappearing, which leaves young researchers to choose between shelling out for airfare and lodging they can't really afford and forgoing major career and research building opportunities. As these opportunities disappear, young mathematicians are beginning to look elsewhere—either to more lucrative jobs in the private sector or to more supportive countries. 'We worry about diminishing opportunities in the United States and people early in their career deciding that maybe there's a more profitable venue for them to pursue mathematics in another country,' Meier says. 'We love good mathematics wherever it arises, but we'd really like to see a lot of it arising in the United States. We think that's very, very important.' The $1 million in backstop grants can't fill the hole left by the more than $14 million in promised funding that has been denied or the more than $80 million in reduced funding so far this year. But it might be enough to keep many projects afloat simply by offering guaranteed access to funds in a turbulent time. 'I think one of the great difficulties that we're dealing with right now is the high level of uncertainty,' Meier says. Some mathematicians, for example, simply don't know whether their projects are still being funded or not. In some applications for the backstop grants, researchers 'basically talk about being ghosted,' Meier explains. 'They say, 'I can't actually verify that we no longer have funding. I can only tell you my program officer [at the NSF] isn't replying to my request for information.'' Meier hopes the grants can provide some backup for programs that aren't sure where they stand with the NSF. Without it, researchers, universities and independent organizations may find themselves facing impossible situations. Do they pay their research assistants, run their conferences and continue to fund travel out of pocket, assuming all the financial risk themselves and hoping the grants come through? Or do they halt their projects, losing valuable momentum and perhaps leaving important stakeholders unpaid for their work? Still, the backstop grants are a one-time offering—not a sustainable source of funding for an imperiled field. 'I really view them as trying to take a little bit of the sharp edges off of the sudden loss of funding, as opposed to anything that could sustain the field long-term,' Meier explains. The effects of the Trump administration's cuts to mathematics research—unlike research on, say, Alzheimer's disease, vaccines or climate change—may not be the most immediately concerning to human health and safety. But experts like Meier say that ignoring the role mathematics plays in that development is shortsighted. As a spokesperson of the NSF itself put it in response to an inquiry about the organization's changing priorities (and as the agency has said on its website), 'Mathematical sciences are crucial to everyday society and play an essential role in the innovation engine that drives the U.S. economy, strengthens national security and enhances quality of life.' And the search for the answers to math's biggest mysteries also seeds development in physics, earth science, biology, technology, and more. Any progress we make on these questions in the future, Meier says, is 'based entirely [on what] we are doing in research mathematics right now.' Solve the daily Crossword
