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New Knot Theory Discovery Overturns Long-Held Mathematical Assumption

Scanning the crowd at a fancy soiree may reveal a wide array of neckties, each fastened with a highly complex mathematical object masquerading as fashion. An entire field of mathematics is devoted to understanding mathematical knots, which one can obtain from any traditional knot by gluing the loose ends together. Mathematicians long believed that if you attach cut ends of two different knots to each other, the new knot will be just as complex as the sum of the individual knots’ complexity. But

The worst possible antitrust outcome

Today's links The worst possible antitrust outcome (permalink) Well, fuck. Last year, Google lost an antitrust case to Biden's DoJ. The DoJ lawyers beat Google like a drum, proving beyond a shadow of a doubt that Google had deliberately sought to create and maintain a monopoly over search, and that they'd used that monopoly to make search materially worse, while locking competitors out of the market. In other words, the company that controls 90% of search attained that control by ill

This Apple Intelligence tool saved me from paying a hefty subscription

Nina Raemont/ZDNET Follow ZDNET: Add us as a preferred source on Google. ZDNET's key takeaways Apple Intelligence can transcribe your voice memos for free. The transcriptions are easy to access and fairly accurate. The Otter.ai alternative is $17 per month. When you hear of AI features on smartphones, you often think of the flashiest, agentic AI features that could carry out tasks for you without you having to lift a finger. However, I am a firm believer that the litmus test as to whethe

Finally, an AirTag alternative that fits my wallet and works well with Android phones

LuLuLook AirCard Pro ZDNET's key takeaways The LuLuLook AirCard Pro is thin, lightweight, and fits seamlessly into wallets. The built-in rechargeable battery lasts for 4 to 5 months between top-ups. Handy slot cut to allow the finder to be attached to luggage. $24.69 at Amazon Follow ZDNET: Add us as a preferred source on Google. My grandfather had a saying -- a place for everything, and everything in its place. It turns out that I'm not as tidy as he was, and I have a tendency to… misplace

My iPhone 15 Pro Max battery life went from great to awful in less than two years - what happened?

Adrian Kingsley-Hughes/ZDNET Follow ZDNET: Add us as a preferred source on Google. ZDNET's key takeaways My iPhone is less than 18 months old. It now cannot make it through a day without a recharge. Nothing appears abnormal in the settings, so what gives? Rather than do my usual and upgrade my iPhone again last year with only about a year on the clock, I decided to try what most people end up having to do -- keep it going for a few years. Apple says that the battery is designed to retain

Topics: 80 battery day ios iphone

Nuclear: Desktop music player focused on streaming from free sources

Desktop music player focused on streaming from free sources Links Official website Downloads Documentation Mastodon Twitter Support channel (Matrix): #nuclear:matrix.org Discord chat: https://discord.gg/JqPjKxE Suggest and vote on new features here: https://nuclear.featureupvote.com/ Readme translations: What is this? nuclear is a free music streaming program that pulls content from free sources all over the internet. If you know mps-youtube, this is a similar music player but with

Audi design finds its minimalist groove again with Concept C

Fans of the TT rejoice—there's a new Audi two-seater on the way. The German automaker just unveiled Concept C, a stylish and minimalist sports car that marks the start of a new styling philosophy and, hopefully, a return to the bold designs that brought it so much success. There are design cues and links back through Audi's history, but this is no pastiche of a retro design as we might have seen from J Mays. Rather, Audi's design team under Chief Creative Officer Massimo Frascella says that the

They know where you are: Cybersecurity and the shadow world of geolocation

Tony Soprano knew. When one of his follow poker players in season 5, episode 4 of The Sopranos asks Tony how he likes his new Cadillac Escalade, the fictional mobster responds, “I love it. After I pulled out that global positioning [system].” OK, his language was a little more spicy than “system,” but the point is that Tony knew the dangers of being trackable. The rest of us might not have the same concerns Tony had about being findable just about anywhere, but we should all realize how danger

I used my iPhone 15 Pro Max for over a year: Here's how the battery life has changed

Adrian Kingsley-Hughes/ZDNET Follow ZDNET: Add us as a preferred source on Google. ZDNET's key takeaways My iPhone is less than 18 months old. It now cannot make it through a day without a recharge. Nothing appears abnormal in the settings, so what gives? Rather than do my usual and upgrade my iPhone again last year with only about a year on the clock, I decided to try what most people end up having to do -- keep it going for a few years. Apple says that the battery is designed to retain

Topics: 80 battery day ios iphone

Great, Now I Need a Next-Gen, Cassette Tape-Playing Boombox

If you’re super nostalgic for the days of analog, modern Bluetooth devices probably aren’t cutting it. You can’t pick Bluetooth up; you can’t see it; you can’t… forget to rewind it and then have to wait to start your favorite album over again. Luckily, IFA 2025 is here, and the sky is the limit, which means we now have a modern boombox that can play honest-to-God cassettes while still leaving room for the convenience of wireless music streaming and hi-fi audio. We Are Rewind’s GB-001 is billed

Own a Samsung phone? Changing these 10 settings gave mine a big performance boost

Kerry Wan/ZDNET Follow ZDNET: Add us as a preferred source on Google. I've been fairly vocal recently that Samsung's One UI 7 is my favorite Android skin. It is fast, responsive, and intuitive. But nothing comes fine-tuned to your experience straight out of the box. You need to personalize your smartphone to make it more appealing. I change almost a dozen settings on every Samsung Galaxy phone to best suit my needs, and I believe these will elevate your user experience, too. Also: The best S

As an Android user, this is the closest thing to AirTags for my wallet (and better in some ways)

LuLuLook AirCard Pro ZDNET's key takeaways The LuLuLook AirCard Pro is thin, lightweight, and fits seamlessly into wallets. The built-in rechargeable battery lasts for 4 to 5 months between top-ups. Handy slot cut to allow the finder to be attached to luggage. View now at Amazon Follow ZDNET: Add us as a preferred source on Google. My grandfather had a saying -- a place for everything, and everything in its place. It turns out that I'm not as tidy as he was, and I have a tendency to… misplac

Acer Chromebook Plus Spin 514 review: The new ChromeOS sweet spot

In the last few years, I’ve felt like Chromebooks have hit a plateau. ChromeOS is a quirky but mature platform at this point, and Google has continued to add smart and useful features on a regular basis. But the hardware has felt pretty stagnant, with a few exceptions. Most Chromebooks at this point are utilitarian devices that get the job done but inspire little excitement, and I’ve found most Intel-based Chromebooks don’t get me through a day of work before the battery dies. But earlier this

Puffy Cloud Mattress Review: Soft but Supportive

I will admit that, once upon a time, I was not the Puffy Cloud’s biggest supporter. I’ve tested this memory foam mattress multiple times over my five-year mattress testing career and believed it simply wasn’t for me—too soft, not enough spinal support. Well, times change, don’t they? Granted, during my previous tests, I didn’t spend a whole week sleeping on the Cloud in my own bedroom, as I did this time. I now also consider myself a side sleeper, which has a whole other set of requirements than

Acer’s 16-inch Air weighs even less than a 13-inch MacBook Air

is a reviewer covering laptops and the occasional gadget. He spent over 15 years in the photography industry before joining The Verge as a deals writer in 2021. Posts from this author will be added to your daily email digest and your homepage feed. Acer is announcing a new Swift Air 16 at IFA 2025, and it’s an absolute featherweight of a 16-inch laptop. Weighing in at 2.18 pounds / 0.99kg with an IPS display or 2.43 pounds / 1.1kg with its optional OLED, the Swift Air is lighter than even a 13

Battery sizes on flagship phones are about to explode

Paul Jones / Android Authority TL;DR A leaker has claimed that three upcoming Pro flagship phones will see notable battery capacity upgrades. It looks like the tipster is referring to the Xiaomi 16 Pro, vivo X300 Pro, and OPPO Find X9 Pro. The OPPO Find X9 Pro in particular could offer a 7,550mAh battery. Many smartphone brands have embraced silicon-carbon batteries in the past year or two, resulting in some flagship Android phones with huge batteries. They’re not stopping here, though, as i

Finnish City Inaugurates 1 MW/100 MWh Sand Battery

Support CleanTechnica's work through a Substack subscription or on Stripe There are more ways to store energy than just using batteries. Some are using fire bricks, particularly for process heat for industries that rely on high heat in manufacturing. Others propose an arrangement of massive concrete blocks that move up and down like the weights of a giant grandfather clock, converting kinetic energy to potential energy and back again. In Finland, two intrepid engineers began experimenting with

Salesforce CEO confirms 4,000 layoffs ‘because I need less heads' with AI

Salesforce CEO Marc Benioff participates in an interview at the World Economic Forum in Davos, Switzerland, on Jan. 22, 2025. Salesforce has cut 4,000 of its customer support roles, CEO Marc Benioff recently said while discussing how artificial intelligence has helped reduce the company headcount. Benioff revealed the layoffs during an interview published Friday on The Logan Bartlett Show podcast. "I've reduced it from 9,000 heads to about 5,000, because I need less heads," Benioff said while

Cloudflare stops new world's largest DDoS attack over Labor Day weekend

Hollie Adams/Bloomberg via Getty Images Follow ZDNET: Add us as a preferred source on Google. ZDNET's key takeaways The biggest, baddest DDoS attack to date was just fended off. The attack used the trivial, but nasty, UDP flood attack. You must protect yourself against DDoS attacks. Over the Labor Day weekend, Cloudflare says it successfully stopped a record-breaking distributed denial-of-service (DDoS) attack that peaked at 11.5 terabits per second (Tbps). This came only a few months afte

In under 18 months, my iPhone's battery life has gone from great to terrible

Adrian Kingsley-Hughes/ZDNET Follow ZDNET: Add us as a preferred source on Google. ZDNET's key takeaways My iPhone is less than 18 months old. It now cannot make it through a day without a recharge. Nothing appears abnormal in the settings. Rather than do my usual and upgrade my iPhone again last year with only about a year on the clock, I decided to try what most people end up having to do -- keep it going for a few years. Apple says that the battery is designed to retain 80% of its orig

Topics: 80 battery day ios iphone

Waymo starts testing in Denver, Seattle in bid to expand robotaxi service across U.S.

Alphabet's Waymo unit will begin test drives of its robotaxis in Denver and Seattle this week, with humans behind the wheel, the company said Tuesday. "We will begin driving manually before validating our technology and operations for fully autonomous services in the future," a company spokesperson said in an email. Waymo announced the tests in blog posts. The autonomous vehicle venture aims to expand its driverless, ride-hailing service across the U.S. after already launching commercial opera

Finally, a Samsung phone that I'd put my S25 Ultra away for (especially at this price)

Samsung Galaxy S25 Edge ZDNET's key takeaways The Samsung Galaxy S25 Edge currently sells for $699 for the 12GB of RAM and 256GB of storage configuration. With its sleek profile and solid hardware, this phone sets a new standards for mobile devices. You'll have to settle with subpar battery life and the absence of a telephoto lens due to the limited size. View now at Amazon View now at Best Buy View now at Samsung more buying choices Follow ZDNET: Add us as a preferred source on Google. The

My Blink Outdoor Camera Battery Lasted Nearly Two Years. Now It's 50% Off for This Last-Minute Labor Day Deal

Labor Day deal: The Blink Outdoor 4 security camera typically costs $100. Right now, you can get a two-pack of them for $90, a discount of more than 50%. The deal is part of a limited-time Labor Day sale, so we recommend buying it before it's gone for good. CNET's key takeaways The Blink's Outdoor 4 security camera comes with lithium AA batteries that lasted me well over a year, unlike competitor cameras that need frequent recharging as often as every month. The Blink Outdoor 4 is one of the

Waymo expands to Denver and Seattle with its Zeekr-made vans

Waymo announced Tuesday that it’s going to bring both of its vehicles — the Jaguar I-Pace SUV and the Zeekr van — to Denver and Seattle starting this week, the latest move in a continued expansion across the United States. The vehicles will be manually driven to start, before the company starts testing its autonomous tech in both cities. Waymo told TechCrunch that it hopes to start offering robotaxi trips in Denver next year and the Seattle metropolitan area “as soon as we’re permitted to do so

This Common Heart Attack Drug May Actually Be Worthless for Most People

A common treatment given after heart attacks may not be worthwhile for a large segment of the population. New trial data finds that most people who suffer a heart attack do not benefit from taking beta-blockers afterward. A large international team of researchers conducted the trial, which compared the outcomes of nearly 10,000 heart attack patients who were either given beta-blocker therapy or not. “This trial will reshape all international clinical guidelines.’ On average, people with prese

‘It: Welcome to Derry’ Will Arrive Just in Time for Halloween

We knew It: Welcome to Derry was arriving in October, but now we know exactly when to start looking for red balloons in the sky and paper boats in the sewer: October 26. Andy Muschietti, Barbara Muschietti, and Jason Fuchs’ expansion of Stephen King’s haunted Maine town as seen in the recent It movies announced the news today with a suitably festive social media post: Everyone’s dying to see IT. #ITWelcomeToDerry premieres October 26 on HBO Max.pic.twitter.com/9HqODk9P1Q — IT: Welcome to Derry

Cloudflare blocks largest recorded DDoS attack peaking at 11.5 Tbps

Internet infrastructure company Cloudflare said it recently blocked the largest recorded volumetric distributed denial-of-service (DDoS) attack, which peaked at 11.5 terabits per second (Tbps). In volumetric DDoS attacks, attackers overwhelm the target with massive amounts of data, consuming the bandwidth or exhausting system resources, leaving legitimate users with no access to the targeted servers and services. "Cloudflare's defenses have been working overtime. Over the past few weeks, we've

I found an AirTag wallet alternative that works with Android (and is cheaper)

LuLuLook AirCard Pro ZDNET's key takeaways The LuLuLook AirCard Pro is thin, lightweight, and fits seamlessly into wallets. The built-in rechargeable battery lasts for 4 to 5 months between top-ups. Handy slot cut to allow the finder to be attached to luggage. $24.69 at Amazon Follow ZDNET: Add us as a preferred source on Google. My grandfather had a saying -- a place for everything, and everything in its place. It turns out that I'm not as tidy as he was, and I have a tendency to… misplace

I asked AI to modify mission-critical code, and what happened next haunts me

Tsuba_sa/iStock/Getty Images Plus Follow ZDNET: Add us as a preferred source on Google. ZDNET's key takeaways AI repeated major sections in a mission-critical coding plan. Mission-critical coding work is too risky to delegate to AI. AI is fine for new features, not core infrastructure. I woke up in a cold sweat. In my nightmare, I was being chased by tens of thousands of people, all of whom were enraged because I destroyed their privacy. They were all holding laptops over their heads, swin

Best Labor Day Mattress Sales (2025)

Labor Day is here and along with it comes a bunch of bedding sales. If you've been looking for a sign from the universe to upgrade your bed, consider these Labor Day mattress deals—we don't expect to see sleep sales this good until Black Friday. I've been a professional mattress tester for five years, so I'm plugged in to what's going on in the mattress world (we're constantly scoping out new additions to our best mattresses list) and can keep track of the sales that really are the ones to watch