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
In brief The discovery of penicillin nearly 100 years ago started a gold rush to find new antimicrobials. Scientists mined microscopic bacteria and fungi for compounds that could help fight off infection. But over time the rate of antimicrobial discoveries slowed to a crawl. Now, modern-day bioprospectors are using genomics, synthetic biology, and AI to dig deeper than they ever have before. A new golden age of antibiotics may be upon us, say some on the hunt, though getting a drug candidate int
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
The Open Source Technology Improvement Fund is proud to share the results of our security audit of Ruby on Rails. Ruby on Rails (or “Rails”) is an open source full stack web-application framework. Thanks to the help of X41 D-Sec, GitLab, and the Sovereign Tech Agency, Rails can provide more secure versions of the tools needed for users to create database-backed web applications following the Model-View-Controller pattern. Audit Process: The audit work for this engagement took place over Decemb
The Algebra of an Infinite Grid of Resistors In a previous note we discussed the well-known problem of determining the resistance between two nodes of an “infinite” square lattice of resistors. The most common approach is to superimpose two “monopole” solutions, one representing the field for one amp of current entering a given node and flowing “to infinity”, and the other representing the field for one amp of current being withdrawn from a given node flowing in from infinity. If the two nodes
In the fast-paced world of CI/CD, understanding the performance and behaviour of your pipelines is crucial. GitHub Actions has become a popular choice for automating builds and deployments, but anyone who's debugged a flaky workflow or long-running job knows how challenging it can be to get visibility into what's happening under the hood. We usually rely on build logs, timing data, or guesswork when something goes wrong. Wouldn't it be nice to trace a pipeline run step-by-step, or have metrics o
Does RL scale? Over the past few years, we've seen that next-token prediction scales, denoising diffusion scales, contrastive learning scales, and so on, all the way to the point where we can train models with billions of parameters with a scalable objective that can eat up as much data as we can throw at it. Then, what about reinforcement learning (RL)? Does RL also scale like all the other objectives? Apparently, it does. In 2016, RL achieved superhuman-level performance in games like Go and C
The Art of Lisp & Writing Ignorance more frequently begets confidence than does knowledge. Charles Darwin Lisp is the language of loveliness. With it a great programmer can make a beautiful, operating thing, a thing organically created and formed through the interaction of a programmer/artist and a medium of expression that happens to execute on a computer. Taught that programmingor the worse "developing software"is like a routine engineering activity, many find difficulty seeing writing
When Superstorm Sandy made a beeline for New York City in October 2012, it flooded huge swaths of downtown Manhattan, leaving 2 million people without electricity and heat and damaging tens of thousands of homes. The storm followed a sweltering summer in New York City, with a procession of heat waves nearing 100 degrees. For those who were pregnant at the time, enduring these extreme conditions wasn’t just uncomfortable—it may have left a lasting imprint on their children’s brains. That’s accor
We're barely into June, but July-like weather has descended on parts of the country, including the Northeast, where 90-plus temperatures are expected. But you've still got to eat -- and cook -- which means hot kitchens that can cause a domino effect, raising the temperature in the entire home. Read more: Best Foods for Staying Hydrated During Hot Weather Using appliances that don't produce as much heat and planning your meals so that cooking doesn't coincide with the hottest part of the day a
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
When legendary game designer Hideo Kojima announced to the world that Death Stranding 2 would soon be released, he made it known that Covid-19 had completely changed his idea for this sequel. “We released Death Stranding before the Covid-19 pandemic, when the world was moving toward isolation and division—as with Brexit. The idea behind it was ‘Let's connect. We’ll face disaster if we don’t connect.’ The theme, the story, and the gameplay of the first chapter all revolved around that idea,” Koj
A short while ago, I was browsing Apple deals on Amazon (as one does) – and something stuck out to me. High-end iPad Pros, particularly 12.9-inch models, are surprisingly cheap. I saw M1 models with 1TB and cellular for under $700. Given the recent iPadOS 26 overhaul that makes the iPad much more Mac-like, I figured these deals would be worth a share. While renewed iPad deals are the focus here because of their affordability, new iPad deals are also mentioned at the end. Renewed M1 iPad Pro de
This is a spoiler-free preview of the first five episodes of season three. Star Trek: Strange New Worlds ended its second season with arguably the single strongest run of any streaming-era Trek. The show was made with such confidence in all departments that if there were flaws, you weren’t interested in looking for them. Since then, it’s gone from being the best modern Trek, to being the only modern Trek. Unfortunately, at the moment it needs to be the standard bearer for the show, it’s become
This article has been reviewed according to Science X's editorial process and policies . Editors have highlighted the following attributes while ensuring the content's credibility: Electron microscopy image showing a haltere developed under normal conditions (left) and a deformed haltere in a genetically modified fruit fly model (right). Credit: Instituto de Neurociencias UMH CSIC A team from the Institute for Neurosciences (IN), a joint center of the Spanish National Research Council (CSIC) a
Please visit the sponsor! Cray versus Raspberry Pi I fondly recall the era when the pinnacle of supercomputing was the Cray 1. Even the shape of this computer was massively different to anything that came before and it was so futuristic that it could have come straight from a scifi movie. While almost all other computers of the 1970s were just a collection of huge rectangular cabinets with blinky lights and perhaps a few tape drives, the Cray 1 looked more like a piece of space-age furnitu
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'There's a huge amount that we don't understand': Why sperm is still so mysterious 20 hours ago Share Save Katherine Latham Share Save How do sperm swim? How do they navigate? What is sperm made of? What does a World War Two codebreaker have to do with it all? The BBC untangles why we know so little about this mysterious cell. With every heartbeat, a man can produce around 1,000 sperm – and during intercourse, more than 50 million of the intrepid swimmers set out to fertilise an egg. Only a f
A few months ago, security researcher Thomas Roche presented his fundamental research on secure elements used in the YubiKey 5. The security element is the Infineon SLE78, which contains a proprietary implementation of the Elliptic Curve Digital Signature Algorithm (ECDSA). Using side-channel attacks and a great deal of smart research, the author discovered a vulnerability in Infineon Technologies' cryptographic library and, as a result, was able to extract the ECDSA secret key from the secure
I’ve been playing chess a long time now, and I’ve always been a good deal better (maybe a couple hundred ELO points) at blitz (3+0 or 5+0) than bullet (1+0). Well, I may have just fixed that. I changed how I move pieces this afternoon and have gained about 100 ELO already. When I play on a computer, I usually drag-and-drop pieces. But it turns out you can also move pieces by clicking first on your piece and then the target square. An analysis of my recent games indicates this shift saved me abou
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The restoration is printed on a very thin polymer film, in the form of a mask that can be aligned and adhered to an original painting. It can also be easily removed. Kachkine says that a digital file of the mask can be stored and referred to by future conservators, to see exactly what changes were made to restore the original painting. Still, there has been no way to translate digital restorations directly onto an original work, until now. In a paper appearing today in the journal Nature, Alex
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Only have a minute? Here are our key takeaways. 🚀 New MI355X GPU: 2x AI FLOPs, more HBM, 40% better tokens/$ than NVIDIA. 🧠 Software Wins: ROCm 7 with big performance boosts and day-0 support. 🖧 Rack-Scale Wins: New turnkey solutions using AMD CPU + GPU + Network. 📈 Roadmap Wins: Next-Gen in 2026 with 4x performance, HBM4 and scale. 🌱 Efficiency Wins: Roadmap to 20× rack-scale energy efficiency by 2030. Thanks for reading More Than Moore! This post is public so feel free to share it. Share
How To Bring Back Oddly Shaped App Icons in macOS 26 Tahoe June 11, 2025 macOS 26 Tahoe replaces the oddly shaped app icons that once brought joy and personality to the Dock with the familiar squircle icons from iOS. Here's what that looks like. The lovely Things icon now sits awkwardly on a glass background 😢 I strongly dislike this change. Part of the Mac’s soul was in its expressive, varied app icons, a case of character over conformity. Fortunately, there's a way to bring back the perso
You can't move for hit British crime shows right now. Whether it's Dept. Q or Adolescence on Netflix; MobLand on Paramount Plus; or Slow Horses on Apple TV Plus (even if that one's technically more of a spy show), gritty and binge-worthy content is showing up on the best streaming services, all delivered in a vibrant array of British accents. Deep Cover feels like a real crowd-pleaser. Peter Mountain/Metronome Film But a shift is happening. We're about to enter cozy-crime summer, when the genr
Of all the jarring things I’ve witnessed on the National Mall, nothing will beat the image of the first thing I saw after I cleared security at the Army festival: a child, sitting at the controls of an M119A3 Howitzer, being instructed by a soldier on how to aim it, as his red-hatted parents took a photo with the Washington Monument in the background. The primary stated reason for the Grand Military Parade is to celebrate the US Army’s 250th birthday. The second stated reason is to use the even
In a nutshell: As nations set ever more ambitious targets for renewable energy and electrification, the humble high-voltage cable has emerged as a linchpin – and a potential chokepoint – in the race to decarbonize the global economy. A Bloomberg interview with Claes Westerlind, CEO of NKT, a leading cable manufacturer based in Denmark, explains why. A global surge in demand for high-voltage electricity cables is threatening to stall the clean energy revolution, as the world's ability to build n
Terraforming, the act of radically transforming a planet's climate and environment to make it suitable for human habitation, currently belongs to the realm of science-fiction. But it's possible, at least in theory, and the idea of terraforming our nearest candidate planet for off-world colonization, Mars, has captivated us for generations. But how would we even begin to pull off such a monumental feat of engineering? You can basically boil it down to three simple steps, argue the authors of a r