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What Apple's controversial research paper really tells us about LLMs

CHRISTOPH BURGSTEDT/SCIENCE PHOTO LIBRARY/Getty Generative AI models quickly proved they were capable of performing technical tasks well. Adding reasoning capabilities to the models unlocked unforeseen capabilities, enabling the models to think through more complex questions and produce better-quality, more accurate responses -- or so we thought. Last week, Apple released a research report called "The Illusion of Thinking: Understanding the Strengths and Limitations of Reasoning Models via the

Mathematical Illustrations: A Manual of Geometry and PostScript

This manual has been available on this site since about 1996, with improvements taking place frequently. The current version has been published as a book of about 350 pages by Cambridge University Press. By agreement with the Press, however, it will remain posted on this web site. Many improvements in the current version over previous ones are due to the (anonymous) referees of the Press, whom I wish to thank heartily. I also wish to thank Lauren Cowles, of the New York office of the Press, for

I replaced my Kindle and iPad within hours of testing this tablet - and didn't regret it

ZDNET's key takeaways The TCL Tab 10 Nxtpaper 5G is a full-color, color paper, and ink paper tablet available at Verizon for $239. It's a great entertainment tablet for daily use that also functions very well as an e-reader. Although the screen is versatile, don't expect the graphics to compare to those on an iPad or other high-end tablets. View now at Verizon For a limited time, Verizon is running an offer for the TCL Tab 10 Nxtpaper 5G that nets you $100 off the tablet when you purchase it

iPad Air vs reMarkable Paper Pro: Which tablet is best for note taking? [Updated]

Over the past few months, I’ve had the pleasure of testing out the reMarkable Paper Pro. You can read my full review here, but in short, it gets everything right about the note taking experience. Despite being an e-ink tablet, it does get quite pricey. However, there are certainly some fantastic parts of the experience that make it worth comparing to an iPad Air, depending on what you’re looking for in a note taking device for school, work, or whatever else. Updated June 15th to reflect reMark

Do reasoning AI models really ‘think’ or not? Apple research sparks lively debate, response

Join the event trusted by enterprise leaders for nearly two decades. VB Transform brings together the people building real enterprise AI strategy. Learn more Apple’s machine-learning group set off a rhetorical firestorm earlier this month with its release of “The Illusion of Thinking,” a 53-page research paper arguing that so-called large reasoning models (LRMs) or reasoning large language models (reasoning LLMs) such as OpenAI’s “o” series and Google’s Gemini-2.5 Pro and Flash Thinking don’t a

Would you switch browsers for a chatbot?

is editor-at-large and Vergecast co-host with over a decade of experience covering consumer tech. Previously, at Protocol, The Wall Street Journal, and Wired. Hi, friends! Welcome to Installer No. 87, your guide to the best and Verge-iest stuff in the world. (If you’re new here, welcome, happy It’s Officially Too Hot Now Week, and also you can read all the old editions at the Installer homepage.) I also have for you a much-awaited new browser, a surprise update to a great photo editor, a neat

Using `make` to compile C programs

I have never been a C programmer but every so often I need to compile a C/C++ program from source. This has been kind of a struggle for me: for a long time, my approach was basically “install the dependencies, run make , if it doesn’t work, either try to find a binary someone has compiled or give up”. “Hope someone else has compiled it” worked pretty well when I was running Linux but since I’ve been using a Mac for the last couple of years I’ve been running into more situations where I have to

Seven replies to the viral Apple reasoning paper and why they fall short

The Apple paper on limitations in the “reasoning” of Large Reasoning Models, which raised challenges for the latest scaling hypothesis, has clearly touched a nerve. Tons of media outlets covered it; huge numbers of people on social media are discussing. My own post here laying out the Apple paper in historical and scientific context was so popular that well over 150,000 people read it, biggest in this newsletter’s history. The Guardian published an adaptation of my post (“When billion-dollar AI

Do reasoning models really “think” or not? Apple research sparks lively debate, response

Join the event trusted by enterprise leaders for nearly two decades. VB Transform brings together the people building real enterprise AI strategy. Learn more Apple’s machine-learning group set off a rhetorical firestorm earlier this month with its release of “The Illusion of Thinking,” a 53-page research paper arguing that so-called large reasoning models (LRMs) or reasoning large language models (reasoning LLMs) such as OpenAI’s “o” series and Google’s Gemini-2.5 Pro and Flash Thinking don’t a

Frontier AI Models Are Getting Stumped by a Simple Children's Game

Earlier this week, researchers at Apple released a damning paper, criticizing the AI industry for vastly overstating the ability of its top AI models to reason or "think." The team found that the models including OpenAI's o3, Anthropic's Claude 3.7, and Google's Gemini were stumped by even the simplest of puzzles. For instance, the "large reasoning models," or LRMs, consistently failed at Tower of Hanoi, a children's puzzle game that involves three pegs and a number of differently-sized disks t

AMD CTO: power constraints, not compute, will shape tomorrow's supercomputers

In a nutshell: In his keynote at ISC 2025, AMD CTO Mark Papermaster emphasized that the next wave of supercomputers will demand breakthroughs in efficiency, reliability, and adaptability, not just raw performance. He noted that industry leaders are now grappling with the realities of explosive growth and the increasingly complex challenges it brings. Papermaster began by highlighting the continued surge in demand for high-performance computing, driven primarily by artificial intelligence. He po

10 productivity gadgets that will help you work smart in 2025

Dedication and determination can go a long way, but it’s also true that the right equipment can make you much more productive. Some products are made with productivity in mind, from the concept’s inception all the way up to the production line. Here at Android Authority, we are a content and productivity machine, and we’ve tried it all. Take a look at our productivity gadgets to catch a boost when you most need it! SPONSORED PLAUD.AI NOTE and NotePin PLAUD.AI NOTE PLAUD.AI NOTE MSRP: $159.00 Ef

Android 16 QPR1 Beta 2 Wallpaper Studio offers a home for its best customization tools

Joe Maring / Android Authority TL;DR Google’s been refreshing its Wallpapers & style app for Android 16 QPR1 with new features like Magic Portrait and theme support. With QPR1 Beta 2 the company has started grouping together its wallpaper creation and editing tools under a new Wallpaper Studio banner. This replaces the previous “suggested photos” view. When you’re interested in customizing the look and feel of your Pixel phone, there’s probably nowhere better to start than Google’s own Wallp

You can now get the official macOS Tahoe 26 wallpapers

With the WWDC 2025 keynote officially in the books, Apple has released the first developer beta for macOS Tahoe 26. The new system comes with light and dark default wallpapers to match their updated design language, and you can download them right here. macOS Tahoe 26 wallpapers Alongside iOS 26, iPadOS 26, and the rest of the renamed OS lineup, macOS 26 brings the new Liquid Glass refreshed look, new Continuity experiences with the Phone app and Live Activities, improved Spotlight, and the ne

Download the new iPadOS 26 light and dark wallpapers

If you’ve already refreshed your setup with the official iOS 26 and macOS Tahoe 26 wallpapers, here’s your chance to complete the set. You can now download the brand-new iPadOS 26 light and dark wallpapers. If you’ve seen the iOS 26 wallpapers, there is not much of a surprise here. The iPadOS 26 design is essentially an expanded, more spaced-out reinterpretation of the iOS 26 wallpaper, featuring the same translucent arcs and layered glass gradients as its iPhone counterpart. Be sure to click

DeepSeek Open Infra: Open-Sourcing 5 AI Repos in 5 Days

Hello, DeepSeek Open Infra! 202502 Open-Source Week We're a tiny team @deepseek-ai pushing our limits in AGI exploration. Starting next week, we'll open-source 5 repos – one daily drop – not because we've made grand claims, but simply as developers sharing our small-but-sincere progress with full transparency. These are humble building blocks of our online service: documented, deployed and battle-tested in production. No vaporware, just code that moved our tiny moonshot forward. Why? Becaus

Topics: ai link open paper week

How I used this portable, ink-free printer to declutter my workstation (and it's 60% off)

ZDNET's key takeaways This battery-powered printer is perfect for taking on the road, and it connects to devices using Bluetooth or USB Thermal printing means there are no ink cartridges to replace, but the downside is the printer cannot use regular paper Installing the Windows and Mac drivers is a bit painful and unintuitive. $69.91 at Amazon I like to joke that whenever someone asks me if I own a printer, I say, "I don't need one where I live." When they inevitably ask where that is, I repl

I replaced my Kindle and iPad within hours of using this tablet (and it's on sale)

ZDNET's key takeaways The TCL Tab 10 Nxtpaper 5G is a full-color, color paper, and ink paper tablet available at Verizon for $239. It's a great entertainment tablet for daily use that also functions very well as an e-reader. Although the screen is versatile, don't expect the graphics to compare to those on an iPad or other high-end tablets. View now at Verizon Reading has always been my favorite way to unwind before bed, and for 13 years, Kindles were my go-to e-readers. But after trying TCL'

You don’t need to buy an iPhone 16e to use Apple’s latest wallpaper

Another new iPhone can only mean one thing: new Apple wallpapers! Fortunately, you don’t need to go out and buy the new iPhone 16e if you just want to try Apple’s latest wallpaper. Download the new iPhone 16e wallpaper The new iPhone 16e replaces the iPhone SE and iPhone 14 in the lineup. It also introduces a new device-specific wallpaper. While you’ll only get the dynamic version on the actual hardware, you can download the still shot below to sport the new look on any smartphone: Download t