How multiplication is defined in Peano arithmetic
Mathematician Keith Devlin is the Executive Director of the Human-Sciences and Technologies Advanced Research Institute ( H-STAR ) at Stanford University and The Math Guy on NPR's Weekend Edition
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Mathematician Keith Devlin is the Executive Director of the Human-Sciences and Technologies Advanced Research Institute ( H-STAR ) at Stanford University and The Math Guy on NPR's Weekend Edition
A meta-analysis of three different notions of software complexity I want to discuss three different notions of software complexity: Rich Hickey’s notion of complexity, as explained in his talk Simple Made Easy. John Ousterhout’s notion of complexity, as explained in his book A Philosophy of Software Design. Zach Tellman’s notion of complexity, as explained in his newsletter Explaining Software Design. I’ve picked these three because I’ve found them to be at least somewhat coherent, and the
For some people, however, it might be helpful to think through what software you need to run and which operating systems it runs best on will help you determine the hardware you need. And let's not forget: ChromeOS and Linux are still alternative options. So, here's how the four available operating systems break down. Windows: Windows is the stalwart default OS. Windows is the broadest and most widely used operating system, supporting the largest number of applications and hardware. It may be r
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Space Draft Space tourism company Axiom Space has had to postpone its fourth chartered SpaceX flight to the International Space Station after NASA announced it needs more time to investigate an air leak affecting the orbital lab. For five years, NASA and its Russian counterpart Roscosmos have been hunting down leaks in the station, which has been continuously occupied for 25 years. The issue has since been traced back to the Russian segment of the ISS, specifically the Zvezda service module, a
Calvin Wankhede / Android Authority I hate nothing more than advertising online that blends into the rest of the content. That’s especially true when it shows up in places where I least expect it, like my email inbox. In the Gmail app, the biggest offender is the “Sponsored” emails pictured above. These ads often show up like a regular message and look almost the same as any other email — sender, subject line, and all. Some ads are even worse and take up significant real estate to show you prod
It's been a big week or so in the video game realm between the arrival of the Nintendo Switch 2 (our review is now live) and Summer Game Fest. During the Xbox Games Showcase on Sunday, Microsoft announced handheld gaming PCs that will have deep Xbox integration as well as support for storefronts such as Battle.net. Steam, GOG and Ubisoft Connect. If Microsoft and its partner ASUS stick the landing, the Xbox Ally systems could be a strong option for powering through your backlog of games, big and
ZDNET's key takeaways The Anker Solix EverFrost 2 is available for $1,349 but currently on sale. This cooler works as a portable mini-fridge, with dual-zone cooling and the capacity to freeze or refrigerate. The Anker Solix EverFrost 2 is bulky and heavy, and it only comes with one battery so you have to purchase the second to reach the full 3.2 day capacity. View now at Best Buy View now at Amazon more buying choices The Anker Solix EverFrost 2 58L electric cooler is typically $1,349, but it
ZDNET's key takeaways The 47mm Samsung Galaxy Watch Ultra normally retails for $650 on Amazon, although it occasionally goes on sale. It's a stylish-looking smartwatch with a slew of safety features and a long-lasting battery. However, it's only available in a single size (47mm, to be exact), meaning it may not be a good fit for folks with smaller wrists. $404.04 at Amazon At Amazon, the Samsung Galaxy Watch Ultra received a $250 discount, bringing it significantly down from its retail price
Squid Game has been one of Netflix’s biggest hits in recent memory, and we’ve known for quite a while that the show was reaching the finish line. With just two weeks to go, Netflix has doled out one last trailer to remind auidneces how far Seong Gi-hun/456 has come and how much he’s playing for keeps. Last season ended with Gi-hun learning his new game buddy In-ho/001 was actually the Front Man, who then killed his other game buddy, Jung-bae. That’s made for one more death weighing on Gi-hun’s
With the latest robot vacuum models from Roborock now easily topping $2,000, it’s refreshing (and downright unbelievable) to see a device as capable as the Q7 Max robot vacuum and mop available for just $159 on Amazon: This limited-time deal marks a dramatic discount from the original list price of $599 (even if it’s now available at a regular price of $299 at Amazon). As you can imagine, it’s a new all time low price for this vacuum. See at Amazon Strong 4,200Pa of Suction Power The Roborock
One of the biggest surprises of the Nintendo Switch 2’s reveal was its proposed accessibility. For years, Nintendo has been known for accidentally stumbling on accessibility solutions while stubbornly refusing to engage with the broader subject. Yet, in the Switch 2, there appeared a more holistic approach to accessibility for which disabled players have been crying out. This was supported by a webpage dedicated to the Switch 2’s hardware accessibility. However, specifics were thin and no furth
He wrote me a prescription; he said “You are depressed I'm glad you came to see me to get this off your chest Come back and see me later, next patient please Send in another victim of industrial disease” Industrial Disease, Dire Straits The Google campus doesn’t look as friendly as it used to. (this ia actually from Bartertown in Mad Max 3 - you can see Thunderdome in the middle) Since the start of 2023, more than half-a-million tech workers have been laid off. This isn’t the impact of COV
Four senior executives of tech giants like Meta and Palantir are being sworn into the Army Reserve as direct-commissioned officers at the unusually high rank of lieutenant colonel as part of a new program to recruit private-sector experts to speed up tech adoption. The Army calls the program to recruit Silicon Valley executives Detachment 201: The Army’s Executive Innovation Corps. One of the executives, Andrew Bosworth of Meta (formerly Facebook) posted on X that the “201” monicker was a nod t
Back in 2017–2020, while I was on the Blaze team at Google, I took on a 20% project that turned into a bit of an obsession: sandboxfs. Born out of my work supporting iOS development, it was my attempt to solve a persistent pain point that frustrated both internal teams and external users alike: Bazel’s poor sandboxing performance on macOS. sandboxfs was a user-space file system designed to efficiently create virtual file hierarchies backed by real files—a faster alternative to the “symlink fore
Yep, they're definitely coming for our jobs. Package Deal Earlier this year, humanoid robotics company Figure showed off its Figure 02 robot using a sophisticated visual language system called Helix to sort packages at a logistics warehouse. Footage showed a small army of the humanoid robots deftly picking up packages of various sizes, shapes, and hardnesses, and manipulating their orientation. Just three months later, the company has published an update about its Helix learning-based approa
Ryan Haines / Android Authority If you’re looking to get a new set of wireless earbuds, the Samsung Galaxy Buds 3 Pro are among our favorites, especially if you already use a Samsung smartphone. They are quite pricey at about $249.99, though. It’s a good idea to wait for a good discount, and boy, do we have a good one today! In fact, it’s the cheapest we’ve seen these go for! Buy the Samsung Galaxy Buds 3 Pro for just $119.99 ($130 off) This offer is available from Woot.com, an Amazon-owned de
Pixar just announced the next movie on its always exciting upcoming slate and, for the first time in a long time, it feels a little like the studio is chasing trends instead of setting them. Which probably isn’t the case, but the timing does make it hard to ignore. Just announced at the Annecy International Animation Film Festival, Pixar’s 2027 film is called Gatto. Directed by Luca helmer Enrico Casarosa, the film is set in Venice, Italy and follows a black cat named Nero who, “after years of
If you caught some morsels from A Minecraft Movie on social media -- videos of theater audiences going wild over a chicken jockey or Jack Black passionately singing about cooking chicken with lava -- next week you can stream the flick that started it all. The Max streaming service, which will soon take on the title of HBO Max again, previously announced that the video game movie would premiere in June. Now it's shared the exact release date for the PG-rated comedy. A Minecraft Movie stars Black
This week on streaming, get ready for crime of every kind. True crime, crime thrillers -- it's all in there. Over on Apple TV Plus, Julianne Moore stars in the new film Echo Valley as a mother who helps her daughter cover up a murder. Peacock also just released its latest true crime show, The Gilgo Beach Killer: House of Secrets, a three-part series about a Long Island serial killer that lived a double life, working as an architect in Manhattan by day, and preying on women by night. For someth
is a reviewer with 10 years of experience writing about consumer tech. She has a special interest in mobile photography and telecom. Previously, she worked at DPReview. Some of us take a kind of “I eat to live” rather than an “I live to eat” approach to gadgets. They’re tools that help you get things done, not something you want to invest a lot of time or money in. If that’s you — and there’s no judgment here from a certifiable gadget nerd — then you can probably think of more worthwhile ways t
Rufus is a small utility that helps format and create bootable USB flash drives. Oh, and Rufus is fast. It can be especially useful for cases where: You need to create USB installation media from bootable ISOs (Windows, Linux, UEFI, etc.) You need to work on a system that doesn't have an OS installed You need to flash a BIOS or other firmware from DOS You want to run a low-level utility Despite its small size, Rufus provides everything you need. Non-exhaustive list of ISOs Rufus is known
Don’t throw all your popcorn at the screen, but A Minecraft Movie begins streaming exclusively on HBO Max (which used to be Max, which used to be HBO Max) on June 20. The big studio adaptation of the best-selling video game of all time was something of a surprise hit for those unfamiliar with the game’s mammoth audience. Movie adaptations of video games can be really hit or miss. The Super Mario Bros. Movie set the box office record for the highest-grossing video game movie of all time and was
Austin Z. Henley Associate Teaching Professor Carnegie Mellon University [email protected] @austinzhenley github/AZHenley The fastest way to detect a vowel in a string 6/13/2025 I was nerdsniped recently: What is the best way to detect if a string has a vowel in it? This is trivial, right? But as I started getting into it, I realized there is much more to this. I challenged myself to come up with as many ways to detect a vowel as possible. I even asked a few friends to give it a go. Whi
TL;DR: Microsoft and Asus recently announced two new Xbox-branded handheld devices: the ROG Xbox Ally and ROG Xbox Ally X. While these represent a new step for Xbox gaming on portable devices, a new report suggests that Microsoft has internally shelved its own Xbox handheld project – one that was never officially announced but had been the subject of considerable speculation. According to The Verge, Microsoft has "essentially canceled" its native Xbox handheld to focus on the Xbox software plat
Joe Maring / Android Authority TL;DR Google has reportedly been working on a new AI-powered assistance tool for Pixel devices since 2023. The system would monitor your screen and actions in apps, and offer “personal predictive suggestions.” First known as Pixie, and then Pixel Sense, a new leak suggests Google has renamed the tool to Magic Cue. Who doesn’t love a good mystery? In the smartphone world, upcoming high-profile devices sometimes leak so much that it feels like there’s nothing lef
In recent years, there has been increasing interest in tools and programming languages that can automatically detect common types of bugs, in order to improve product quality and programmer productivity. Most commonly, this is done via static type systems, but traditional static type systems require large amounts of manual annotation by programmers, making them difficult to work with. Therefore, modern programming languages make increasing use of type inference, which provides the same benefits
luxe A lovingly crafted cross platform game engine About luxe is a cross platform, rapid development game engine to make games for Mac, Linux, Windows, and Web, with console support in development. luxe is an easy to learn game engine for making 2D or 3D games. As an engine it prioritizes design and workflow for rapidly expressing ideas. Designed as a 2D first engine, luxe aims to provide a strong 2D toolset ready to make games. This applies whether it's a one hour or one+ year project.
marian / Getty Images Proxy servers are the middlemen of cyberspace. Acting as gateways between our devices and the Internet, proxy servers are used by businesses and individuals worldwide for a variety of tasks. While proxy servers were once almost exclusively used by companies to redistribute traffic and load or for caching purposes, they now offer a degree of online anonymity for individuals. Requests you make are first sent to the proxy and then forwarded -- and this process assigns you a
Samsung has announced its latest lineup of AI-assisted smart monitors with 4K resolution, active voice amplifier technology for cleaner audio, and a new QD-OLED option for high-end workstations. Right now, when you reserve a new AI smart monitor at Samsung, you'll get an exclusive $100 discount as well as the chance to win a Samsung Galaxy AI Ecosystem bundle that includes a Galaxy Tab S10 Ultra, Galaxy Watch Ultra, and Galaxy Ring. Also: The Samsung Galaxy Ring comes with a free $100 gift card