All posts tagged: Math

The ‘Lonely Runner’ Problem Only Appears Simple

The ‘Lonely Runner’ Problem Only Appears Simple

Published by skeptic

The original version of this story appeared in Quanta Magazine. Picture a bizarre training exercise: A group of runners starts jogging around a circular track, with each runner maintaining a unique, constant pace. Will every runner end up “lonely,” or relatively far from everyone else, at least once, no matter their speeds? Mathematicians conjecture that the answer is yes. The “lonely runner” problem might seem simple and inconsequential, but it crops up in many guises throughout math. It’s equivalent to questions in number theory, geometry, graph theory, and more—about when it’s possible to get a clear line of sight in a field of obstacles, or where billiard balls might move on a table, or how to organize a network. “It has so many facets. It touches so many different mathematical fields,” said Matthias Beck of San Francisco State University. For just two or three runners, the conjecture’s proof is elementary. Mathematicians proved it for four runners in the 1970s, and by 2007, they’d gotten as far as seven. But for the past two decades, no …

Trying to Pick a Meal Kit Service? These 2 Are the Best Value, According to Our Math

Trying to Pick a Meal Kit Service? These 2 Are the Best Value, According to Our Math

Published by skeptic

Meal kits are about convenience, which means you’ll typically pay more per pound for these recipe bundles than you would if you did the list-making and grocery shopping yourself. Meal kits offer hidden value beyond saving time and energy since there’s often less food waste with meal kits, given they only send you what you need for that night’s meal, and nothing more.  CNET Within the sprawling meal kit categories, you’ll find a number of options priced between $6 and $15 per serving. The premium services offer higher-end cuts of meat and more complex recipes with gourmet ingredients. The budget services keep it simple with recipes that typically include just four or five ingredients.  Among the choices, you may be wondering which meal kit services offer the best overall value in 2026. Well, so were we. To find out, we’ve calculated how meal kit delivery services compare with grocery prices. Here’s what the math says about meal kits and value in 2026. And while these represent the best-value meal kits, we’ve also dug into them to find the absolute …

It’s Not Gambling, It’s ‘Girl Math’

It’s Not Gambling, It’s ‘Girl Math’

Published by José Betancourt

“Come get ready with me for the day,” a young blond woman says over footage of herself making her bed, arranging her pillows, and weighing her clothing choices. The video is just like any other lifestyle content that influencers post to Instagram and TikTok—right up until she whips out her phone and scrolls through the Kalshi app. “I use it to check the weather to help me pick out an outfit for the day,” she says, modeling a black spandex romper for the camera. “Go ahead and check out the app link below.” Recently, my Instagram feed has been haunted by women explaining how much they enjoy betting on elections, the pop-music charts, and Dancing With the Stars. They are advertising prediction markets such as Kalshi and Polymarket, which let users wager on virtually anything. “The boys can do their parlays and use words I’ve never heard of. But the girls can use their pop culture and educated guesses to make decisions and trade on Kalshi,” a woman says in a TikTok on one of …

The Download: a battery company pivots to AI, and a new AI tool seeks to transform math

The Download: a battery company pivots to AI, and a new AI tool seeks to transform math

Published by skeptic

“For years, social media companies have profited from targeting children while concealing their addictive and dangerous design features. Today’s verdict is a referendum—from a jury, to an entire industry.”  —Attorney Rachel Lanier offers her view on yesterday’s fines for Meta and YouTube, the Washington Post reports.   One More Thing  GETTY IMAGES Longevity enthusiasts want to create their own independent state. They’re eyeing Rhode Island.   It’s incredibly difficult and expensive to study innovative ways to slow or reverse aging. In response, longevity enthusiasts have devised an ambitious plan: establish an independent state for life-extension experiments.   They envision a jurisdiction that slashes red tape, encourages self-experimentation with unproven treatments, and eliminates laws that limit how companies develop drugs.   Exactly where their longevity state might emerge is still being worked out—but one appealing location is Rhode Island. Read the full story to learn more about the plans.   —Jessica Hamzelou  We can still have nice things  A place for comfort, fun and distraction to brighten up your day. (Got any ideas? Drop me a line.)  + These gleaming photos of ancient insects in amber are time capsules of the dinosaur age. + Paint with pixels across a world map at this …

This startup wants to change how mathematicians do math

This startup wants to change how mathematicians do math

Published by skeptic

Geordie Williamson, a mathematician at the University of Sydney, who worked on PatternBoost with Charton, has not yet tried Axplorer. But he is curious to see what mathematicians do with it. (Williamson still occasionally collaborates with Charton on academic projects but says he is not otherwise connected to Axiom Math.) Williamson says Axiom Math has made several improvements to PatternBoost that (in theory) make Axplorer applicable to a wider range of mathematical problems. “It remains to be seen how significant these improvements are,” he says. “We are in a strange time at the moment, where lots of companies have tools that they’d like us to use,” Williamson adds. “I would say mathematicians are somewhat overwhelmed by the possibilities. It is unclear to me what impact having another such tool will be.” Hong admits that there are a lot of AI tools being pitched at mathematicians right now. Some also require mathematicians to train their own neural networks. That’s a turnoff, says Hong, who is a mathematician herself. Instead, Axplorer will walk you through what you …

Ancient pottery shows the earliest evidence of humans doing math

Ancient pottery shows the earliest evidence of humans doing math

Published by skeptic

Floral designs on pottery made almost 8,000 years ago may be more than just art. They appear to be the earliest evidence of math-based thinking. The designs appear on pottery made by ancient Halafians. These people lived in Mesopotamia between about 6200 B.C. and 5500 B.C. (Mesopotamia was an ancient region in what is now Iraq. Some of the world’s first civilizations arose there.) The Halafians were known for their skilled ceramics. Many of the floral designs on their pottery show regular numbers of petals. Those patterns hint that these people used math in their art, archaeologists now say. The researchers shared these findings in the December 2025 Journal of World Prehistory. Archaeologists knew that Mesopotamia’s Sumerian people used math. Sumerians are famous for creating the first writing system around 3000 B.C. They did math based on the number 60. That’s the same type of system that gives us 60 seconds per minute and 60 minutes per hour. The new findings suggest Halafians used math thousands of years before the Sumerians. If so, these ancient …

Nvidia’s Nemotron-Cascade 2 wins math and coding gold medals with 3B active parameters — and its post-training recipe is now open-source

Nvidia’s Nemotron-Cascade 2 wins math and coding gold medals with 3B active parameters — and its post-training recipe is now open-source

Published by skeptic

The prevailing assumption in AI development has been straightforward: larger models trained on more data produce better results. Nvidia’s latest release directly challenges that size assumption — and the training recipe behind it may matter more to enterprise AI teams than the model itself. The open-weight model’s Cascade RL post-training pipeline, detailed in Nvidia’s technical report, offers a reproducible blueprint for enterprise teams building domain-specific reasoning systems without training from scratch. Nemotron-Cascade 2 is an open-weight 30B Mixture-of-Experts (MoE) model that activates only 3B parameters at inference time. Despite this compact footprint, it achieved gold medal-level performance on three of the world’s most demanding competitions: the 2025 International Mathematical Olympiad (IMO), the International Olympiad in Informatics (IOI), and the ICPC World Finals. It is the second open model to reach this tier, after DeepSeek-V3.2-Speciale — a model with 20 times more parameters. Why post-training is becoming the real competitive advantage Pre-training a large language model from scratch is enormously expensive — on the order of tens to possibly hundreds of millions of dollars for frontier …

Contributor: The math being used by the wealth-tax crowd is wrong

Contributor: The math being used by the wealth-tax crowd is wrong

Published by Sam Flores

I try to be fair to people I disagree with. Emmanuel Saez — the famous UC Berkeley economist who’s considered an architect of California’s proposed billionaire wealth tax — is someone I read carefully, even when I find his income-inequality work unconvincing. So, when I say that his arguments for the wealth tax are not just biased or misleading, but egregiously wrong, I’m not being careless. I mean it. In a recent debate at Stanford University, Saez offered his central justification (apart from, you know, “billionaires are unfairly rich”): California’s hospitals need it because the federal government cut Medicaid through last year’s One Big Beautiful Bill Act. As Economic Policy Innovation Center researchers have repeatedly documented, under the Biden administration, Medicaid spending expanded by almost 60%, going from roughly $409 billion before the COVID-19 pandemic to $656 billion by 2025. Using the most recent Congressional Budget Office numbers reflecting the One Big Beautiful Bill Act — the supposed instrument of destruction — these researchers now project Medicaid spending to reach $905 billion in 2034. Calling …

I Did the Math: This Meal Kit Service Gives You the Most Bang for Your Buck

I Did the Math: This Meal Kit Service Gives You the Most Bang for Your Buck

Published by skeptic

Meal kits are a convenience product, full stop. While the price gap between meal kits and grocery store prices has shrunk since they first launched, what you’re paying for is premeasured ingredients curated into a single box and delivered to your door ready to be spun into dinner. CNET We’ve calculated how meal kit delivery services stack up against grocery prices, and the findings aren’t surprising, even amid rising food costs nationwide. It’s almost always cheaper to buy groceries at the store, and you prepare meals, especially when you shop in person rather than have them delivered. Read more: I Test Meal Kits for a Living: 7 Mistakes That Cost You Meal kit prices are easy to compare. What’s harder to answer is whether any of them actually deliver value relative to what the same groceries would cost at a supermarket — and whether some services are giving you meaningfully more than others for your money. So I did the math. Considering seven of the most popular traditional-format meal kit delivery services, many of which appear on our Best Meal …

You Can Approximate Pi by Dropping Needles on the Floor

You Can Approximate Pi by Dropping Needles on the Floor

Published by skeptic

Happy Pi Day! March 14 is the date that otherwise rational people celebrate this irrational number, because 3/14 contains the first three digits of pi. And hey, pi deserves a day. By definition, it’s the ratio of the circumference and diameter of a circle, but it shows up in all kinds of places that seem to have nothing to do with circles, from music to quantum mechanics. Pi is an infinitely long decimal number that never repeats. How do we know? Well, humans have calculated it to 314 trillion decimal places and didn’t reach the end. At that point, I’m inclined to accept it. I mean, NASA uses only the first 15 decimal places for navigating spacecraft, and that’s more than enough for earthly applications. The coolest thing, for me, is that there are many ways to approximate that value, which I’ve written about in the past. For instance, you can do it by oscillating a mass on a spring. But maybe the craziest method of all was proven in 1777 by George Louis Leclerc, …