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Solving a 31-year-old grand challenge in mathematics – the KLS conjecture
- Fundamental scientific breakthrough: Researchers resolved the Kannan-Lovász-Simonovits (KLS) conjecture, a 31-year-old problem widely regarded as one of the central open questions in high-dimensional geometry, with implications for statistics, optimization, algorithms, and computer science.
- A universal geometric principle: The result establishes a universal geometric principle for log-concave distributions, showing that simple flat cuts can capture their narrowest bottlenecks within a fixed factor, regardless of dimension.
- Human-AI collaboration: The breakthrough emerged from a human-directed agentic research process in which AI systems explored mathematical possibilities while researchers evaluated, pruned, and redirected the search.
- Independent confirmation: Multiple independent researchers have validated this research, identifying its central criterion as the key breakthrough, followed by a machine-checked formal verification.
For decades, a fundamental question about the difficulty of computing in high-dimensional spaces has resisted proof. New research resolves this question, removing a major theoretical obstacle to understanding the efficiency of randomized algorithms used across science and computing.
The Kannan–Lovász–Simonovits (KLS) conjecture was proposed in 1995. It asks whether, for a broad class of high-dimensional probability distributions, the best flat or hyperplane cut is always nearly as effective as the best cut of any shape. More precisely, KLS predicts that the two differ by no more than a universal constant, regardless of the number of dimensions. This would establish a dimension-free geometric principle with important consequences for high-dimensional geometry, probability, and theoretical computer science. Because the geometry of these cuts governs how quickly random walks can explore a distribution, KLS also plays a central role in the theory of high-dimensional sampling.
Figure 1: An illustration of the KLS Conjecture (simplified) on regular tetrahedron.Since 1995, mathematicians have accumulated evidence that the conjecture was true, but a complete proof remained elusive. Now, two researchers, including Xinzhi Zhang from the Machine Learning and Optimization group at Microsoft Research, have proved the KLS conjecture (opens in new tab). They have shown that the relationship holds with a fixed bound, regardless of how many dimensions a shape has. Before this work, the best known result (opens in new tab), established in July 2026, allowed that bound to grow slowly as the number of dimensions increased. This work establishes a fundamental geometric principle: high-dimensional spaces are better behaved than previously known, and the obstacles to navigating them do not grow without bound as dimensions increase.
The importance of the KLS conjecture was recognized across the field long before it was resolved. In its 2017-18 Annual Report, the Mathematical Sciences Research Institute (MSRI) (opens in new tab) called it “a central open problem in high-dimensional convex geometry.” The Simons Institute (opens in new tab) described it as “one of the most important open problems in convex geometry.” In the proceedings of the 2022 International Congress of Mathematicians (ICM) (opens in new tab), Ronen Eldan noted its broad implications for high-dimensional convex and computational geometry. Quanta Magazine (opens in new tab) wrote that KLS “lies at the heart of many questions in statistics and computer science.”
Technical detailsThe authors began by improving the July 2026 result in order to make the mathematical bound more precise. Working with AI agents in a structured, human-directed process, they explored more than 100 candidate approaches, many involving lengthy calculations with higher-order tensors. This produced a new mathematical criterion that became the foundation of the final proof.
The authors then discovered that the new criterion could be applied recursively. Each improved bound could be fed back into the same argument to produce a still tighter one. In the October 1, 2026 version of the paper, this reduced the dependence on dimension to the iterated logarithm. This function grows extraordinarily slowly, but it still grows with the dimension and therefore did not yet fully resolve the conjecture.
The final step was to repeat the entire recursive refinement, rather than applying it only once. This idea was inspired by the authors’ earlier work on fast algorithms for linear programming. The authors proved that the small errors introduced at each stage shrink fast enough that their total remains bounded by a universal constant, independent of the dimension. This eliminated the dependence on the number of dimensions and completed the proof in the October 4, 2026 version of the paper.
The recursive method, its repeated application, and the proof that the accumulated errors remain bounded are original contributions of the researchers. AI tools helped explore candidate approaches, carry out detailed derivations, prepare the manuscript, and perform internal proof checks. The researchers determined the mathematical direction, selected the promising ideas, assembled them into the final argument, and verified the proof.
Independent confirmationOn the same day that the authors posted their complete proof, a separate group of leading experts posted a full proof (opens in new tab) that they developed in parallel. Their work built upon the findings in the first version (opens in new tab) of the Microsoft paper, calling it “the crucial step in the proof.” A third proof (opens in new tab) which appeared separately on the same day relies on a closely related idea. In addition, a Lean 4 formalization (opens in new tab) was subsequently released, combining the key criterion from the first Microsoft paper with additional research.
Independent proofs are among mathematics’ strongest forms of validation because they demonstrate that a result does not rest on a single chain of reasoning. The subsequent appearance of alternative approaches and formal verification further strengthens confidence that the field has uncovered a genuine underlying principle rather than a fragile technical argument. The authors have also shortened their proof and verified the streamlined argument in Lean; they plan to release both after final review. Together, these developments provide complementary forms of confirmation.
Human-AI guidanceIn the process of proving KLS, this research also demonstrates the power of having researchers direct AI rather than simply asking AI to solve a complex problem through a single end-to-end run of a frontier model or agent. The authors used an agentic search process with iterative, human-assisted “pruning”: As multiple agents explored variations of an idea in parallel, the researcher examined their intermediate result, eliminated unpromising directions, and passed the most promising result to the next round. Roughly one hundred research trajectories were explored before the key breakthrough emerged.
In a separate track of the project, the authors made repeated unguided attempts to solve the same problem with several leading AI models, using roughly the same total token budget as the main process. That effort fell short of the goal. The eventual success depended on both the capabilities of the AI systems and the mathematical judgment of the researchers.
ConclusionTaken together, resolving KLS settles a central problem in high-dimensional geometry. A wide range of results that previously relied on the conjecture as an assumption can now be stated unconditionally. The proof therefore provides a stronger foundation for research in convex geometry, probability, and theoretical computer science.
The work also demonstrates how carefully guided human-AI collaboration can contribute to genuine scientific discovery while reinforcing, rather than replacing human insight. It highlights the continuing importance of scientific judgment in identifying promising directions, recognizing conceptual connections, and seeing when a partial insight points toward a deeper result. The authors are now simplifying the proof and extending its formal verification so that the mathematics and theoretical computer science communities can more easily examine the result and build on it.
AcknowledgementsThank you to our co-author Zhao Song for his contributions to this work, and Victor Reis (opens in new tab) and Ishai Menache for helpful discussions throughout the project.
Opens in a new tabThe post Solving a 31-year-old grand challenge in mathematics – the KLS conjecture appeared first on Microsoft Research.
ASUS Googlebook 14 Review: Being an early adopter isn't fun anymore
Have you ever shown up to a party only to realize that you're about 10 years too late? While I see some potential in the ASUS Googlebook 14, it feels like a clumsy effort that should've happened a long time ago. The extreme pricing certainly doesn't help, nor does my growing impatience for "early adopter" quirks.
PowerToys 0.102 has a fix for anyone tired of holding their mouse button
Microsoft has released PowerToys 0.102, following a major update in August that introduced Window Hopper along with several other improvements. This time, the focus shifts to two new mouse utilities, an upgraded Command Palette, voice-assisted screenshots, and a fresh set of command-line tools.
Blink's new security cameras have extreme range to cover your sprawling home
Amazon just made it easier to secure the farthest reaches of your home — even if you have a giant yard. Blink has introduced five new security cameras, including two with extra-long range.
5 powerful smart home automations you can build without buying any new devices
Setting up a smart home can be an expensive business. Not only do you need a device to run your smart home, but you also need all the devices for it to control. If you already have smart home devices set up, however, then there are plenty of incredibly useful automations that you can set up without needing to buy anything new.
This free Docker management tool replaced 5 of my most essentail containers
In most homelabs, Docker management involves more than running the applications you actually want to use. One container manages your other containers, another checks for image updates, and a separate service handles logs. Before long, you have several containers dedicated to managing the rest of your containers.
5 new multi-tools to buy in 2026, including a Leatherman that glows in the dark
Multi-tools are an essential gadget that I think everyone should own. With the right model, you'll have an invaluable tool perfect for everyday tasks around the house, on the job, or for your next outdoor adventure. And while many enthusiasts probably have a Leatherman they've owned for years, several exciting new multi-tools arrived in 2026 and are worth buying.
How to use the DROP function in Microsoft Excel
One of the most underused lookup and reference functions in Microsoft Excel is the DROP function. This powerful yet simple function lets you remove a specified number of rows or columns from the start or end of an array without altering the original dataset.
I made a pocket EDC toolbox that fits 6 tools (and attaches to my phone) [Update: Smaller version]
Those of us who are DIY-minded reach for a few common tools every day. Screwdriver, utility knife, tape measure, pencil, tweezers, and more. I wanted to find a way to keep these tools nearby, so I designed a pocket toolbox with magnets.
Music and podcasts sound better when you change these 4 Samsung Galaxy settings
The way you play your music, listen to your favorite podcasts, and immerse yourself in your comfort movie can be a deeply personal experience. This also calls for the best sound quality your device can deliver, but not all devices are set up by default to give you what you may be looking for.
4 historic power tools that might be hiding in your dad's garage
Most garages fill up with tools the same way attics fill up with boxes. You hang onto stuff because it seemed worth keeping at the time. If your dad was the type to buy quality once and hold onto it, there's a real chance some of what's sitting on his shelves is actually a piece of history. These aren't just fun finds for collectors. Each one changed how power tools were built, wired, or sold to contractors and homeowners. A few of them still work today, as long as you know what to check before you plug them in.
How to watch Como vs. Manchester United online for free
TL;DR: Live stream Como vs. Manchester United in the Champions League for free on Virgin Media Player. Access this free streaming platform from anywhere in the world with ExpressVPN.
The Champions League is a tough competition. Manchester United started their campaign with a comfortable victory over Sabah but suffered a disappointing defeat to Atlético Madrid in the second round. There's now some serious pressure on Michael Carrick's team as they head to Como.
Como are also sat on six points after two games, ahead of Manchester United by virtue of goal difference. We're expecting a close contest.
If you want to watch Como vs. Manchester United in the Champions League from anywhere in the world, we have all the information you need.
When is Como vs. Manchester United?Como vs. Manchester United in the Champions League kicks off at 12:45 p.m. ET on Oct. 21. This fixture takes place at the Giuseppe Sinigaglia Stadium.
How to watch Como vs. Manchester United for freeComo vs. Manchester United is available to live stream for free on Virgin Media Player.
Virgin Media Player is geo-restricted to Ireland, but anyone can access it for free with a VPN. These tools can hide your real IP address (digital location) and connect you to a secure server in Ireland, meaning you can unblock Virgin Media Player to stream the Champions League for free from anywhere in the world.
Live stream Como vs. Manchester United for free by following these simple steps:
Subscribe to a streaming-friendly VPN (we recommend ExpressVPN)
Download the app to your device of choice (the best VPNs have apps for Windows, Mac, iOS, Android, Linux, and more)
Open up the app and connect to a server in Ireland
Visit Virgin Media Player
Watch Como vs. Manchester United for free from anywhere in the world
The best VPNs for streaming are not free, but most do offer free trials or money-back guarantees. By leveraging these offers, you can access free live streams of the Champions League without actually spending anything. This obviously isn't a long-term solution, but it does give you enough time to stream Como vs. Manchester United (plus more Champions League fixtures) before recovering your investment.
What is the best VPN for Virgin Media Player?ExpressVPN is the best choice for bypassing geo-restrictions to stream live sport on Virgin Media Player, for a number of reasons:
Servers in 105 countries, including Ireland
Easy-to-use app available on all major devices, including iPhone, Android, Windows, Mac, and more
Strict no-logging policy so your data is secure
Fast connection speeds free from throttling
Up to 10 simultaneous connections
30-day money-back guarantee
A two-year subscription to ExpressVPN is on sale for $68.40 and includes an extra four months for free — 81% off for a limited time. This plan includes a year of free unlimited cloud backup and usually offers a generous 30-day money-back guarantee. Alternatively, you can get a one-month plan for just $12.99.
Live stream Como vs. Manchester United in the Champions League for free with ExpressVPN.
Martin Short roasts Conan OBrien for 5 brutal minutes
You exactly what to expect when Martin Short and Conan O'Brien get together, and that's a lot of roasting.
The Only Murders in the Building star appeared on the Conan O'Brien Needs a Friend podcast recently, and he didn't waste any time blasting O'Brien with zinger after zinger, starting with his recollection of a dinner the two shared recently in London.
"It's almost like I was seeing you in a new light, because that night I thought, 'He looks like the love-child between Lurch and Kathy Griffin', and I don't often feel that about people. Because you're very, you know, you're pale. You're very pale. You look like a cue tip with ketchup on it," says Short, while O'Brien cracks up laughing. "I mean, you're white. You look like a human surrender."
"Which I kind of am," O'Brien responds.
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Animol review: Ashley Walters tense and tender feature debut shines light on young offenders
The last place a 15-year-old wants to find himself is in a young offenders institution, where Animol shines its light.
In his feature directorial debut, acclaimed Top Boy star, recording artist, director, writer, and producer Ashley Walters explores the constant tension, threat, and camaraderie of boys whose lives have taken a serious turn. Co-written by Walters and Nick Love (Marching Powder) based on their experiences with such institutions, Animol boasts a talented young cast buoyed by an outstanding Tut Nyuot (The Long Walk), and supported by a characteristically brilliant Stephen Graham (Adolescence).
SEE ALSO: 'La Bola Negra' review: A magnificent gay epic that transcends timeWith superb cinematography and production design, commendably interior performances from an impeccable young cast, and unflinching authenticity in its detail, Animol presents an experience of young offenders, where being real feels impossible and redemption's just a glimmer.
Animol takes you inside a young offenders institution with grit and humanity Stephen Graham as Claypole in "Animol." Credit: SLNDAAwaiting incarceration in a young offenders institution, British teenager Troy prepares himself for the worst. Cast into a seriously adult situation, the 15-year-old instantly bonds with Polish boy Krystiyan (Ukrainian actor Vladyslav Baliuk). In the same breath, he's extorted into smuggling a burner phone by power player Dion (Boarders star Sekou Diaby). "You're stepping into my world now," Dion declares, and Troy soon finds out he's dead right. As soon as he moves in with mercurial cellmate Mason (The Jetty's Ryan Dean), Troy finds himself in a dangerous position between Dion and Mason, two very different ticking time bombs.
Trying to find his place while watching his back, Troy walks a knife's edge between security and exposure, with open assaults in the mess hall a regular occurrence and the idea of being his authentic self a laughable idea. However, in the midst of this constant suspicion, violence, and insomnia, Troy's tender bond with Krystiyan becomes a place of solace, of peace, of a yearning he's suppressed in himself.
Overseen by well-meaning welfare officer Claypole (Graham), Troy takes it day-by-day inside. Animol presents Troy's experience as one of constant self-doubt, isolation, hopelessness, and survival. His lifeline beyond the walls is his mother Joy (an impeccable Sharon Duncan Brewster), with their relationship strained under her struggle with addiction and sobriety. Over the course of the film, Troy and his fellow inmates grapple with a sense of identity behind bars, struggling to discern between friendship and manipulation, toxic masculine bravado and vulnerability, and the inability to communicate.
Animol uses unflinching cinematography to showcase a talented young cast Vladyslav Baliuk as Krystiyan and Tut Nyuot as Troy in "Animol." Credit: SLNDAWith Walters an actor's director, his connection with the cast is clear, allowing each to flourish in long close-up takes. Each scene of Animol, particularly Nyuot's intensely interior performance, is intimately shot by director of photography Tasha Back (In Camera) and edited by Danielle Palmer (Steve). The film allows silences to sit, unspoken words between characters to be amplified — a scene in which Diaby's Dion silently scrutinises Troy is an unsettling example. Nyuot finds balance between moments of adult survival and adolescent vulnerability, making tender scenes with Krystiyan a precious rarity, and scenes in which he's forced into brutality an anguish to watch. Troy holds so much, with no outlet safe.
As the two kings of the yard in Animol, Diaby and Dean bring contrasting approaches to Dion and Mason, hardened boys leaning into adult criminality and extreme violence to survive and dominate. Diaby's chilling veneer of composure and Dean's serpentine calculation make for formidable opposing forces, each a unique tinderbox for Troy.
Though seldom onscreen, it's a delight to see Graham reconnected with Walters, having worked together on A Thousand Blows and Adolescence. Drawing from his mother's experience as a social worker, Graham presents Claypole as a man not beaten by the system but finding humanity within it. An Animol highlight sees the empathetic welfare officer encouraging the boys to ditch their inhibitions and be themselves through unconventional action, a radically vulnerable scene in an institution where masks are key.
Notably, Animol doesn't sensationalise Troy's experience in the young offenders institute, with Swindle's sparing, impactful score and production designer Gini Godwin (Queenie, Champion) creating a world of state-run despair within dilapidated walls. Marks of previously incarcerated boys adorn the walls, reading "You are not animol," and giving the film its title. Sound designer Roland Heap builds a haunting, unsettling world around Troy, as Back's cinematography holds fast on his face night after night in his cell, enduring the taunts and rattles of the institution in his spartan bunk.
Ultimately, Walters crafts a compelling, harrowing, complex picture of life for young offenders, thrust into extreme survival mode in a place where toxic masculinity and homophobia run rife alongside loyalty and rare glimmers of friendship. What goes unsaid in Animol is its true power, with Walters allowing his talented cast to thrive in interior emotion and subtle action.
Animol was reviewed out of BFI London Film Festival and will be released in UK cinemas Oct. 30
Domino’s is giving away 20,000 free copies of Minecraft Dungeons II: How to claim
TL;DR: Domino’s and Minecraft Dungeons II are launching a block-shaped pizza collab with free game giveaways.
Do your weekend plans involve grinding through local co-op dungeons with a slice of pizza in hand? Domino’s and Minecraft just dropped the ultimate collab for you.
Starting Oct. 26, Domino’s is teaming up with Minecraft Dungeons II for a limited-time nationwide partnership. Order a new block-shaped pizza to unlock collectible character boxes, digital in-game cosmetics, and a chance at claiming a free digital copy of Minecraft Dungeons II.
How to score a free game code and digital lootWe showcase a lot of these free giveaways from major brands, and it's always a little disappointing when you have to jump through a million hoops to qualify for the promotion. That's not the case here. It's refreshingly straightforward.
Customers who purchase a Domino's block-shaped pizza will receive one of six boxes, each featuring a different Minecraft Dungeons II character: Corrupted Creeper, Prime Enchanter, Valorie, Zombie, Pig, and Creeper.
Domino's Rewards members who purchase a Domino's online can also unlock one of three exclusive, randomly awarded in-game items to use in Minecraft Dungeons II. The order automatically generates a promo code in your "My Rewards" tab redeemable for one of the random items: the Domino’s Skin, the Slice Slayer Cape, or the Cheesy Cube Pet.
Credit: Domino's / MinecraftThat's exciting, but the real draw of this collab is the free game giveaway. Between Oct. 26 and Nov. 4, purchase a pizza and submit your receipt at dominos.com/minecraft-dungeons-ii for a chance to win one of 20,000 free Minecraft Dungeons II game codes (2,000 codes awarded daily for PC and Xbox).
We love the characters, and the in-game items are cool, but giving away 20,000 full-game downloads turns a brand collab into a genuinely high-value opportunity. With 2,000 game tokens up for grabs daily across the 10-day sweepstakes window, your odds of scoring a free PC or Xbox copy are surprisingly solid if you submit proof of purchase early in the day.
Just note that game codes are only valid on PC and Xbox, so PlayStation or Nintendo Switch players can only redeem cosmetic item codes.
Stephen Graham giving Seth Meyers an acting lesson is a fun watch
If you could get an acting lesson from anyone in the world, you'd be hard-pushed to do better than Emmy-winning Adolescence star Stephen Graham.
In the clip, he gives Seth Meyers a brief bit of tuition mid-way through their interview, showing him a few of the different walks you can use to get into character.
Does Meyers struggle to know what to do with his arms? Absolutely. But you can't fault his effort.
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You can use Android Auto with a de-Googled phone, and it’s easier than you think
Everyone knows the obvious apps that you'll miss without Google: Gmail, Maps, Photos, etc. However, it's the Android features that rely on Google Play Services that are sneakier. One such feature is Android Auto, but it's easier than you might think to use on a de-Googled Android phone.
The Samsung SSD 990 PRO 4TB is $300 off at Amazon right now — bag the best early Black Friday SSD deal
SAVE $300.09: As of Oct. 21, the Samsung SSD 990 PRO 4TB is on sale for $799.90 at Amazon. That's a 27% discount on the list price.
Opens in a new window Credit: Samsung Samsung SSD 990 PRO 4TB $799.90 at Amazon$1,099.99 Save $300.09 Get Deal at Amazon
If you're running out of storage space or want to speed up your PC or gaming setup, the Samsung SSD 990 PRO 4TB is a seriously impressive upgrade option. It offers plenty of room for games, files, and other heavy workloads, and it's on sale at Amazon.
As of Oct. 21, this SSD is down from $1,099.99 to $799.90, saving you $300.
The Samsung 990 PRO SSD is built for fast loading and smooth performance, whether you're gaming, editing videos, or working with large files. It offers read speeds of up to 7,450 MB/s and write speeds of up to 6,900 MB/s.
Compared with the 980 PRO, this SSD delivers more than 55% better random performance, helping speed up transfers and demanding tasks. It's also up to 50% more efficient in performance per watt, so you can get more out of your system while using less power.
And there are capacities ranging from 1TB to 4TB, so there's plenty of space for all of your games and files, as well as different price options. The 1TB and 2TB devices are also on sale at Amazon, down from $319.99 to $259.84 and $639.99 to $409.99, respectively.
Find this deal at Amazon now.
NYT Connections hints today: Meanings for each word for Oct. 21, 2026
Looking for spoiler-free NYT Connections hints or just wondering why Connections is trending today? We've got what you need to understand the clues for today's puzzle without spoiling any of the answers.
Of course, Mashable has also provided daily hints and answers for Connections, Wordle, and Strands for years, so we can help you if that's also what you need.
While we are focused more on meanings than hints in this story, sometimes learning that many of the words have completely unrelated meanings is a clue in and of itself. Connections frequently includes clues that involve words within words and other visual clues.
SEE ALSO: NYT Connections hints today: Clues, answers for October 21, 2026 Duck Duck Goose meaningA traditional children's circle game.
Hot Potato meaningA controversial, difficult or problematic issue that no one wants to deal with..
Leapfrog meaningA traditional children's game in which one player crouches or bends over at the waist, and others take turns hopping over their back.
Musical Chairs meaningA party game where players walk or march around a row or circle of chairs while music plays.
Alpha dog meaningThe dominant leader or highest-ranking animal in a dog or wolf pack.
Big cheese meaningAn important, influential person who holds power, authority,or a top leadership position in an organization or company.
Heavyweight meaningSomeone or something of above-average weight.
Top banana meaningThe most important, powerful or leading person in a group, organization or activity
American Gothic meaningA 1930s oil painting of a Midwestern farmer holding a pitchfork and his unmarried grown daughter.
Campbell's Soup Can meaningA series of 32 paintings produced by American artist Andy Warhol.
Sunflowers meaningA tall, annual flowering plant in the daisy family, famous for its large, bright yellow flower heads and edible seeds.
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The Scream meaningAn iconic 1893 proto-expressionist painting by Norwegian artist Edvard Munch.
English horn meaningA double-reed woodwind musical instrument in the oboe family.
Grape-nuts meaningA classic American breakfast cereal made from whole grain wheat.
Mantis shrimp meaningCarnivorous marine crustaceans.
Sweetbread meaningA culinary name for the thymus or pancreas.
Have you learned the meanings and still want the things? Check out the hints and answers for today's NYT Connections puzzle.
Are you also playing NYT Strands? Get all the Strands hints you need for today's puzzle.
Meet The Mashable 101: Our list of the content creators shaping the internet today
If you're looking for more puzzles, Mashable's got games now! Check out our games hub for Mahjong, Sudoku, free crossword, and more.
Not the day you're after? Here's the solution to yesterday's Connections.
NYT Connections hints today: Clues, answers for October 21, 2026
The NYT Connections puzzle today is not too difficult if you're obedient.
Connections is the one of the most popular New York Times word games that's captured the public's attention. The game is all about finding the "common threads between words." And just like Wordle, Connections resets after midnight and each new set of words gets trickier and trickier—so we've served up some hints and tips to get you over the hurdle.
If you just want to be told today's puzzle, you can jump to the end of this article for today's Connections solution. But if you'd rather solve it yourself, keep reading for some clues, tips, and strategies to assist you.
SEE ALSO: Mahjong, Sudoku, free crossword, and more: Play games on Mashable What is Connections?The NYT's latest daily word game has become a social media hit. The Times credits associate puzzle editor Wyna Liu with helping to create the new word game and bringing it to the publications' Games section. Connections can be played on both web browsers and mobile devices and require players to group four words that share something in common.
This Tweet is currently unavailable. It might be loading or has been removed.Each puzzle features 16 words and each grouping of words is split into four categories. These sets could comprise of anything from book titles, software, country names, etc. Even though multiple words will seem like they fit together, there's only one correct answer.
If a player gets all four words in a set correct, those words are removed from the board. Guess wrong and it counts as a mistake—players get up to four mistakes until the game ends.
This Tweet is currently unavailable. It might be loading or has been removed.Players can also rearrange and shuffle the board to make spotting connections easier. Additionally, each group is color-coded with yellow being the easiest, followed by green, blue, and purple. Like Wordle, you can share the results with your friends on social media.
SEE ALSO: NYT Pips hints, answers for October 21, 2026 Here's a hint for today's Connections categoriesWant a hint about the categories without being told the categories? Then give these a try:
Yellow: Cease
Green: Servant
Blue: Facial hair
Purple: Animated roles
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Here are today's Connections categoriesNeed a little extra help? Today's connections fall into the following categories:
Yellow: Classic children's games
Green: Important person
Blue: Famous paintings
Purple: Double misnomers (neither word is an accurate description)
Ready for the answers? This is your last chance to turn back and solve today's puzzle before we reveal the solutions.
Drumroll, please!
The solution to today's Connections #1227 is...
What is the answer to Connections todayClassic children's games: DUCK DUCK GOOSE, HOT POTATO, LEAPFROG, MUSICAL CHAIRS
Important person: ALPHA DOG, BIG CHEESE, HEAVYWEIGHT, TOP BANANA
Famous paintings: AMERICAN GOTHIC, CAMPBELL'S SOUP CAN, SUNFLOWERS, THE SCREAM
Double misnomers (neither word is an accurate description): ENGLISH HORN, GRAPE-NUTS, MANTIS SHRIMP, SWEETBREAD
Looking for Wordle today? Here's the answer to today's Wordle.
Are you also playing NYT Strands? Get all the Strands hints you need for today's puzzle.
Meet The Mashable 101: Our list of the content creators shaping the internet today
If you're looking for more puzzles, Mashable's got games now! Check out our games hub for Mahjong, Sudoku, free crossword, and more.
Not the day you're after? Here's the solution to yesterday's Connections.


