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TK King caught the go-ahead touchdown pass for New Mexico State to win the 102nd Battle of I-10 with 21 seconds left, 34-31 over UTEP on Saturday afternoon in the regular season finale for both teams.
DELAND, Fla. (AP) — Ethan Copeland scored 25 points as Stetson beat VMI 99-80 on Saturday as part of the ASUN/SoCon Challenge.
COLLEGE STATION, Texas (AP) — Marcel Reed threw three touchdown passes in the first quarter before sitting down early in the second as No. 3 Texas A&M built a huge early lead and rolled to a 48-0 win over FCS school Samford on Saturday. Texas A&M is 11-0 for the first time since going 12-0 [...]
The rise of Ja Morant from overlooked collegiate player to full-blown NBA superstar is wild. The two-time All-Star remains one of the league’s most popular players thanks to highlight reel plays and his unmatched charisma.
UNIVERSITY PARK, Texas — One more win like Saturday’s 38-6 rout of Louisville — which recently sat 15th in the College Football Playoff rankings and came into Ford Stadium eight points shy of an undefeated season — and SMU could...
(The Hill) -- The FBI this week concluded its probe into the first assassination attempt against President Trump during a Pennsylvania campaign rally last year, finding that the deceased suspect acted alone and without motive. FBI Director Kash Patel, in an interview with Fox News, said Trump was informed of the FBI's conclusion to its [...]
LSU leads Western Kentucky 7-3 at halftime, Saturday, November 22, 2025, at Tiger Stadium in Baton Rouge, La.
D4vd is no longer cooperaitng with police on the investigation into the death of Celeste Rivas. Insider claim the LAPD is eyeing a second suspect.
![HIGH SCHOOL FOOTBALL: Saratoga Springs vs. Middletown [PHOTO GALLERY]](https://www.saratogian.com/wp-content/uploads/2025/11/IMG_8549.jpg?h=683&w=1024)
COLONIE, N.Y. — Saratoga Springs defeated Middletown, 28-18, in the NYSPHSAA Class AA regional quarterfinals, on Nov. 22, 2025, at Colonie High School, in Colonie, N.Y.
Arch Manning finished with four passing touchdowns, a rushing touchdown and even a receiving touchdown as the Texas Longhorns beat the 2-9 Razorbacks at DKR.
This marks the first public engagement on the project since Austin City Council approved $104 million in May to fund various roadway elements.
(KRON) -- The California Golden Bears and the Stanford Cardinal both wore helmet stickers honoring beloved coach John Beam who was killed in a shooting at Laney College. KRON4's Ben Ross posted images of the adorned helmets in a post on X Saturday night. Coach Beam, 66, was fatally wounded on Nov. 13 near Laney [...]
The framework seeks to ensure that mineral-producing countries, particularly in the Global South, derive maximum benefit from their resources, moving beyond mere raw material exports
The IDF intercepted 17 Hamas terrorists fleeing Rafah tunnels, killing 11 and arresting six, as an observation officer described how her unit led the...
A Northern California judge issued the restraining order in the trademark dispute, and asked OpenAI to justify its use of the name 'Cameos.'
A Predator silhouetted by an explosion in Predator Badlands
The best season of a controversial cancelled fantasy series is streaming free (but its 2 other seasons are still missing)
Julio Bardini is a Senior Author at Collider who focuses on sci-fi, historical works, and analysis. He also writes for Cinema Com Rapadura in Brazil.
Fox News Channel offers its audiences in-depth news reporting, along with opinion and analysis encompassing the principles of free people, free markets and diversity of thought, as an alternative to the left-of-center offerings of the news marketplace.
Los Angeles Clippers point guard Chris Paul hinted at potential retirement after this season.
SMU is still in contention to reach another ACC title game after Kevin Jennings accounted for four touchdowns in a 38-6 win over Louisville.
The University of Oklahoma's iconic covered wagon mascot, the Sooner Schooner, has been pulled onto Owen Field in Norman for 60 years.
President Donald Trump’s chaotic political universe has at least one consistent law that rises above any other.
San Francisco 49ers receiver Brandon Aiyuk has had $27 million in guaranteed money voided from his contract.
LSU edge Patrick Payton (6) and LSU defensive tackle Jacobian Guillory II (90) tackle Western Kentucky running back Marvis Parrish (21) on the carry in the first half between the Tigers and the Hilltoppers, Saturday, November 22, 2025, on the...
LSU edge Patrick Payton (6) and LSU defensive tackle Jacobian Guillory II (90) tackle Western Kentucky running back Marvis Parrish (21) on the carry in the first half between the Tigers and the Hilltoppers, Saturday, November 22, 2025, on the...
LSU edge Jack Pyburn (44) drives around Western Kentucky tight end Noah Meyets (81) in the first half between the Tigers and the Hilltoppers, Saturday, November 22, 2025, on the campus of LSU in Baton Rouge, La.
LSU wide receiver Barion Brown (6) runs the ball as Western Kentucky defensive back Jaylen Lewis (7) closes in on the stop in the first half between the Tigers and the Hilltoppers, Saturday, November 22, 2025, on the campus of...
President Donald Trump says he's teaming up with legendary golfer Jack Nicklaus to revamp the golf courses at Joint Base Andrews.
Mike the Tiger does the worm in the end zone during a timeout in the first half between the Tigers and the Hilltoppers, Saturday, November 22, 2025, on the campus of LSU in Baton Rouge, La.
LSU edge Jack Pyburn (44) celebrates after sacking Western Kentucky quarterback Rodney Tisdale Jr. (16) in the first half between the Tigers and the Hilltoppers, Saturday, November 22, 2025, on the campus of LSU in Baton Rouge, La.
LSU edge Jack Pyburn (44), LSU edge Dylan Carpenter (97) and LSU defensive tackle Ahmad Breaux (16) celebrate after sacking Western Kentucky quarterback Rodney Tisdale Jr. (16) in the first half between the Tigers and the Hilltoppers, Saturday, November 22,...
LSU defensive coordinator and linebackers coach Blake Baker calls his players over during a timeout in the first half between the Tigers and the Hilltoppers, Saturday, November 22, 2025, on the campus of LSU in Baton Rouge, La.
LSU running back Harlem Berry (22) runs the ball before the stop by Western Kentucky linebacker Anthony Brackenridge (3) in the first half between the Tigers and the Hilltoppers, Saturday, November 22, 2025, on the campus of LSU in Baton...
5 Of The Best Ryobi Black Friday Deals Under $30We may receive a commission on purchases made from links.Ryobi tools are not always necessarily cheaper at Home Depot, though many are currently discounted as part of the hardware retailer's Black Friday sale. Because of the close relationship...
Josh Hoover threw for 293 yards and two touchdowns and TCU took advantage of No. 25 Houston’s missed field goal in the final minute to beat the Cougars 17-14.
LSU athletics director Verge Ausberry, left, holds up a commemorative football jersey honoring fallen Baton Rouge Police Sgt. Caleb Eisworth as Eisworth’s family and colleagues are recognized on the field in the first half between the Tigers and the Hilltoppers,...
After two weeks of negotiations, this year’s United Nations climate talks have ended with what critics are calling a weak compromise.
US To Launch "New Phase" Of Venezuela Operations, Options Include Overthrowing Maduro: Report One day after the FAA issued a Notice to Air Missions (NOTAM), or an alert notifying pilots of potential serious hazards in certain airspace, for the Maiquetía Flight Information Region above Venezula, Reuters reported that the US is poised to launch a new phase of Venezuela-related operations in the coming days, citing four U.S. officials.Amid a sharp escalation of pressure by the Trump administration on President Nicolas Maduro's government, including proliferating reports of looming action as the US military deployed forces to the Caribbean amid worsening relations with Venezuela, two of the sources said covert operations would likely be the first part of the new action against Maduro, while two US officials told Reuters the options under consideration included attempting to overthrow Maduro.A senior administration official on Saturday told Reuters that nothing had been ruled out regarding Venezuela."President Trump is prepared to use every element of American power to stop drugs from flooding into our country and to bring those responsible to justice," said the official, speaking on the condition of anonymity.Before the Reuters report, six airlines had already cancelled flights to Venezuela on Saturday after the US aviation regulator warned major airlines of dangers from "heightened military activity" amid a major buildup of American forces in the region, as well as a "potentially hazardous situation" when flying over Venezuela and urged them to exercise caution.Spain's Iberia, Portugal's TAP, Chile's LATAM, Colombia's Avianca, Brazil's GOL and Trinidad and Tobago's Caribbean have suspended their flights to the country, said Marisela de Loaiza, president of the Venezuelan Airlines Association (ALAV). Panama's Copa Airlines, Spain's Air Europa and PlusUltra, Turkish Airlines, and Venezuela's LASER are continuing to operate flights for now.The Trump administration has been weighing Venezuela-related options to combat what it has portrayed as Maduro’s role in supplying illegal drugs that have killed Americans. He has denied having any links to the illegal drug trade. Maduro, under whose rule Venezuela has experienced crushing hyperinflation and a collapse in its oil production sector amid staggering corruption, has contended that Trump seeks to oust him and that Venezuelan citizens and the military will resist any such attempt. He also has characterized U.S. actions as an effort to take control of Venezuela's oil.A military buildup in the Caribbean has been underway for months, and Trump has authorized covert CIA operations in Venezuela. The United States plans on Monday to designate the Cartel de los Soles a foreign terrorist organization for its alleged role in importing illegal drugs into the United States, officials said. The Trump administration has accused Maduro of leading Cartel de los Soles, which he denies.Washington in August doubled its reward for information leading to Maduro's arrest to $50 million. But U.S. Defense Secretary Pete Hegseth said last week that the terrorist designation "brings a whole bunch of new options to the United States."Trump has said the upcoming designation would allow the United States to strike Maduro's assets and infrastructure in Venezuela, but he also has indicated a willingness to potentially pursue talks in hopes of a diplomatic solution.Maduro said earlier this week that the countries' differences should be resolved through diplomacy and that he is willing to hold face-to-face talks with anyone interested. Two U.S. officials acknowledged conversations between Caracas and Washington. It was unclear whether those conversations could impact the timing or scale of potential U.S. operations.The U.S. Navy's largest aircraft carrier, the Gerald R. Ford, arrived in the Caribbean on November 16 with its strike group, joining at least seven other warships, a nuclear submarine and F-35 aircraft.U.S. forces in the region so far have focused on counter-narcotics operations, even though the assembled firepower far outweighs anything needed for them. U.S. troops since September have carried out at least 21 strikes on alleged drug boats, killing at least 83 people, mostly in the Caribbean, although vessels in the Pacific Ocean also have been targeted. Tyler DurdenSat, 11/22/2025 - 21:35
Former Florida coach Urban Meyer, a two-time national champion with the Gators, will be inducted into the team’s ring of honor next season.
DEAR ABBY: My 19-year-old niece didn’t finish high school and has been in and out of rehab for years. She’s about to leave a residential program and is looking for a place to live. Her parents have implemented “house rules” she doesn’t like, notably staying drug-free and away from her boyfriend.I...
Samsung’s A-series usually gets a predictable refresh every year. The 2025 Galaxy A56, for instance, will get a successor in 2026 in the form of the A57. However, the company hasn’t touched its Galaxy A7x series in years. The last model in the series was Galaxy A73 from 2022, and Samsung never followed it with [...]The post Samsung’s dormant A7-series might finally return, thanks to a new Geekbench leak appeared first on Gizmochina.
The QCinema Project Market concluded its third edition by distributing over PHP18 million ($310,000) in production, post-production, development and marketing support to filmmakers across Southeast Asia. The event carries added significance following Quezon City’s recent designation as a UNESCO Creative City of Film, positioning the Philippines capital alongside recognized global cinema centers. The industry arm [...]
This band which got its start as a TV show on Nickelodeon had to address its audience during a Kraków, Poland when one of its members gashed his knee open
Walmart's early Black Friday deals are here, with big discounts on laptops, kitchen gadgets, and more (including the lowest-ever prices on AirTags, AirPods, and Apple Watches).
Norfolk Southern railroad worked with the state of Ohio and Youngstown State University to revive plans for a $20 million first responder training center near the site of the worst derailment in a decade in East Palestine, Ohio. A training...
Makita may not offer the wide variety of power tools and equipment that Milwaukee does, but the teal brand still has a few options you won't find anywhere else.
New Fortress Energy faces major losses and cash crunch, risking shareholder value.
In a world where everyone prefers individualism, conventionality, and routine over spontaneity and new experiences, one of the biggest adventures in life could be seeking one’s true colors. That is what you’ll learn in “Spirit Fingers,” TVING’s new K-drama adaptation. Based on Han Kyung Chal’s original story, it follows an interesting journey of self-discovery, friendship,... Continue reading 5 Reasons To Watch Youth Romance K-Drama “Spirit Fingers” The post 5 Reasons To Watch Youth Romance K-Drama “Spirit Fingers” appeared first on Soompi.
In one California city, apartments up to six stories can now be built with a single stairwell, a surprisingly buzzy cause. But there are concerns.
Saturday Night Live is standing firm behind their episode which featured Bad Bunny as a host and aired a week after he was chosen to be the NFL Super Bowl Halftime performer
New CEO to Lead Company from Groundbreaking Science to Commercial Launch in Maternal Mental Health Diagnostics SEATTLE, Nov. 22, 2025 /PRNewswire/ -- Dionysus Health, a precision diagnostics company revolutionizing maternal mental health through Epigenetics and Artificial Intelligence,...
Phillip Bradford returned an interception 21 yards for a key fourth-quarter score, the McNeese defense stopped a 2-point conversion attempt to preserve a two-point lead, and the Cowboys defeated Lamar 21-19. The loss may be very damaging for Lamar, ranked...
Richard Kahn and Darren Indyke worked for the convicted sex offender for years. The men deny they knew about Epstein’s crimes.
Local financial sector has had $8bn worth of deals involving foreign companies
The US-brokered Gaza cease-fire is teetering on the brink of collapse, with Hamas threatening to walk away from the deal -- as the terror group traded barbs with Israel Saturday over who was first to violate the fragile truce.
Find out how eSIMs are changing the nature of our traveling experience. Experience real-time global connectivity with less hassle when working remotely.
Michigan went further down the depth chart at running back — and still produced a 100-yard rusher. Bryson Kuzdzal was asked to step up in the absence of Justice Haynes and Jordan Marshall, and he ran for 100 yards and...
Molten Ventures Plc (LON:GROW – Get Free Report) crossed below its 50-day moving average during trading on Thursday . The stock has a 50-day moving average of GBX 412.54 and traded as low as GBX 411. Molten Ventures shares last traded at GBX 411.80, with a volume of 6,834,727 shares changing hands. Analyst Upgrades and [...]
Galaxy Resources Limited (OTCMKTS:GALXF – Get Free Report) crossed below its 50-day moving average during trading on Thursday . The stock has a 50-day moving average of $3.57 and traded as low as $3.38. Galaxy Resources shares last traded at $3.57, with a volume of 3,700 shares trading hands. Galaxy Resources Stock Performance The business [...]
Shares of BlackRock Municipal Income Quality Trust (NYSE:BYM – Get Free Report) crossed below its 50 day moving average during trading on Thursday . The stock has a 50 day moving average of $10.98 and traded as low as $10.83. BlackRock Municipal Income Quality Trust shares last traded at $10.83, with a volume of 63,990 [...]
Shares of SysGroup plc (LON:SYS – Get Free Report) crossed below its fifty day moving average during trading on Thursday . The stock has a fifty day moving average of GBX 16.82 and traded as low as GBX 16. SysGroup shares last traded at GBX 16, with a volume of 83,823 shares trading hands. SysGroup [...]
Associated British Foods PLC (OTCMKTS:ASBFY – Get Free Report)’s share price passed below its fifty day moving average during trading on Thursday . The stock has a fifty day moving average of $28.87 and traded as low as $27.46. Associated British Foods shares last traded at $27.59, with a volume of 24,638 shares trading hands. [...]
easyJet plc (OTCMKTS:ESYJY – Get Free Report) passed below its fifty day moving average during trading on Thursday . The stock has a fifty day moving average of $6.27 and traded as low as $5.91. easyJet shares last traded at $5.91, with a volume of 1,152 shares changing hands. Analysts Set New Price Targets A [...]
Pure Egy Minrls (OTCMKTS:PEMIF – Get Free Report)’s stock price passed below its fifty day moving average during trading on Thursday . The stock has a fifty day moving average of $0.18 and traded as low as $0.1763. Pure Egy Minrls shares last traded at $0.1880, with a volume of 13,886 shares changing hands. Pure [...]
Command Security Co. (NYSEAMERICAN:MOC – Get Free Report) shares passed below its fifty day moving average during trading on Thursday . The stock has a fifty day moving average of $2.85 and traded as low as $2.82. Command Security shares last traded at $2.85, with a volume of 51,100 shares changing hands. Command Security Stock [...]
M�nchener R�ckversicherungs-Gesellschaft (OTCMKTS:MURGY – Get Free Report) passed below its fifty day moving average during trading on Thursday . The stock has a fifty day moving average of $12.66 and traded as low as $12.11. M�nchener R�ckversicherungs-Gesellschaft shares last traded at $12.13, with a volume of 482,442 shares. M�nchener R�ckversicherungs-Gesellschaft Stock Performance The company has [...]
Check out the following guide to the process of creating an explainer video in the following article below.
John F. Kennedy’s granddaughter has disclosed that she has terminal cancer and may live for only about another year. Tatiana Schlossberg is the daughter of Kennedy’s daughter, Caroline Kennedy, and Edwin Schlossberg. She shared her diagnosis in an essay published...
Shield AI's Hivemind autonomy software will be integrated onto Destinus’ Ruta and Hornet unmanned aerial systems.
OSAKA -- Billboards in Osaka's splashy Dotonbori district are unapologetically huge. The area's best-known landmark signage -- the 20-meter-tall Glico running man exulting in victory with his arms raised to the sky -- is just one of many oversized corporate logos and product names crowding the...
JD Vance says he pushed Jeff Bezos to hire Breitbart staff at The Washington PostInstead of attending Dick Cheney's funeral, Vance flattered Breitbart's Matt Boyle on a White House live stream.Screenshot: Theo Von/YouTubeYesterday was Dick Cheney’s funeral in Washington, D.C., which attracted a...
Spencer Jakab at The Wall Street Journal makes the case that we could use a long bear market:He explains:The average time to reach the previous high when a bear market was accompanied by a recession was 81 months. It took just 21 without a recession. Over the past 16 years, downturns have lasted...
The Problem Of Fake Science Authored by Jeffrey Tucker via The Epoch Times,Last week, I was able to generate from artificial intelligence a fake study that proved that eating waffles increases baldness. It was filled with footnotes, citations, and complicated math and models. It was kind of...
Fifteen years ago, when I started studying the international dating industry, few people took the subject seriously. The term "mail-order bride" was treated as a punch line—something outdated, associated with lonely men and poor women who migrated from Eastern Europe, Asia or other places to meet their new husbands in the United States.
In a 2020 research project code-named Project Mercury, Meta scientists worked with survey firm Nielsen to gauge the effect of deactivating Facebook and Instagram, according to Meta documents
This year's COP30 comes after the international Agreement on Marine Biological Diversity of Areas beyond National Jurisdiction (BBNJ) finally acquired the required number of ratification votes by United Nations member states.
Researchers have taken a significant step toward creating a standardized language for describing the aromas of cannabis and hemp.
Meta shut down internal research into the mental health effects of Facebook and Instagram after finding causal evidence that its products harmed users’ mental health, according to unredacted filings in a class action by U.S. school districts against Meta and other social media platforms.
The surface of the Earth is finite. We can measure it. If it was expanding, then its size would grow with time. And once again, good ol’ Earth helps us understand what the universe might be doing beyond our observable horizon.
We have more power than we might think. As the luminous Sun forms a cooperative sextile with transformative Pluto at 2:20 PM EST, we can recognize where steady effort invites meaningful change. Morning conversations might reveal unexpectedly simple fixes. Meanwhile, afternoon choices flow smoothly as we align intentions with actions and share support. By evening, the mood should steady. Small promises kept rebuild trust and help us close the day feeling more capable and a little lighter. Choose one doable change and stick with it!
AI stocks aren't going anywhere over the next three years.
Researchers successfully teleported quantum information between photons from different sources, marking a major step toward practical quantum repeaters and a future fiber-based quantum internet.
A new technique was adapted to study slag waste that was a byproduct of ancient copper smelting.
Large language models (LLMs) have astounded the world with their capabilities, yet they remain plagued by unpredictability and hallucinations – confidently outputting incorrect information. In high-stakes domains like finance, medicine or autonomous systems, such unreliability is unacceptable. Enter Lean4, an open-source programming language and interactive theorem prover becoming a key tool to inject rigor and certainty into AI systems. By leveraging formal verification, Lean4 promises to make AI safer, more secure and deterministic in its functionality. Let's explore how Lean4 is being adopted by AI leaders and why it could become foundational for building trustworthy AI.What is Lean4 and why it mattersLean4 is both a programming language and a proof assistant designed for formal verification. Every theorem or program written in Lean4 must pass a strict type-checking by Lean’s trusted kernel, yielding a binary verdict: A statement either checks out as correct or it doesn’t. This all-or-nothing verification means there’s no room for ambiguity – a property or result is proven true or it fails. Such rigorous checking “dramatically increases the reliability” of anything formalized in Lean4. In other words, Lean4 provides a framework where correctness is mathematically guaranteed, not just hoped for.This level of certainty is precisely what today’s AI systems lack. Modern AI outputs are generated by complex neural networks with probabilistic behavior. Ask the same question twice and you might get different answers. By contrast, a Lean4 proof or program will behave deterministically – given the same input, it produces the same verified result every time. This determinism and transparency (every inference step can be audited) make Lean4 an appealing antidote to AI’s unpredictability.Key advantages of Lean4’s formal verification:Precision and reliability: Formal proofs avoid ambiguity through strict logic, ensuring each reasoning step is valid and results are correct.Systematic verification: Lean4 can formally verify that a solution meets all specified conditions or axioms, acting as an objective referee for correctness.Transparency and reproducibility: Anyone can independently check a Lean4 proof, and the outcome will be the same – a stark contrast to the opaque reasoning of neural networks.In essence, Lean4 brings the gold standard of mathematical rigor to computing and AI. It enables us to turn an AI’s claim (“I found a solution”) into a formally checkable proof that is indeed correct. This capability is proving to be a game-changer in several aspects of AI development.Lean4 as a safety net for LLMsOne of the most exciting intersections of Lean4 and AI is in improving LLM accuracy and safety. Research groups and startups are now combining LLMs’ natural language prowess with Lean4’s formal checks to create AI systems that reason correctly by construction.Consider the problem of AI hallucinations, when an AI confidently asserts false information. Instead of adding more opaque patches (like heuristic penalties or reinforcement tweaks), why not prevent hallucinations by having the AI prove its statements? That’s exactly what some recent efforts do. For example, a 2025 research framework called Safe uses Lean4 to verify each step of an LLM’s reasoning. The idea is simple but powerful: Each step in the AI’s chain-of-thought (CoT) translates the claim into Lean4’s formal language and the AI (or a proof assistant) provides a proof. If the proof fails, the system knows the reasoning was flawed – a clear indicator of a hallucination. This step-by-step formal audit trail dramatically improves reliability, catching mistakes as they happen and providing checkable evidence for every conclusion. The approach that has shown “significant performance improvement while offering interpretable and verifiable evidence” of correctness.Another prominent example is Harmonic AI, a startup co-founded by Vlad Tenev (of Robinhood fame) that tackles hallucinations in AI. Harmonic’s system, Aristotle, solves math problems by generating Lean4 proofs for its answers and formally verifying them before responding to the user. “[Aristotle] formally verifies the output... we actually do guarantee that there’s no hallucinations,” Harmonic’s CEO explains. In practical terms, Aristotle writes a solution in Lean4’s language and runs the Lean4 checker. Only if the proof checks out as correct does it present the answer. This yields a “hallucination-free” math chatbot – a bold claim, but one backed by Lean4’s deterministic proof checking.Crucially, this method isn’t limited to toy problems. Harmonic reports that Aristotle achieved a gold-medal level performance on the 2025 International Math Olympiad problems, the key difference that its solutions were formally verified, unlike other AI models that merely gave answers in English. In other words, where tech giants Google and OpenAI also reached human-champion level on math questions, Aristotle did so with a proof in hand. The takeaway for AI safety is compelling: When an answer comes with a Lean4 proof, you don’t have to trust the AI – you can check it.This approach could be extended to many domains. We could imagine an LLM assistant for finance that provides an answer only if it can generate a formal proof that it adheres to accounting rules or legal constraints. Or, an AI scientific adviser that outputs a hypothesis alongside a Lean4 proof of consistency with known physics laws. The pattern is the same – Lean4 acts as a rigorous safety net, filtering out incorrect or unverified results. As one AI researcher from Safe put it, “the gold standard for supporting a claim is to provide a proof,” and now AI can attempt exactly that.Building secure and reliable systems with Lean4Lean4’s value isn’t confined to pure reasoning tasks; it’s also poised to revolutionize software security and reliability in the age of AI. Bugs and vulnerabilities in software are essentially small logic errors that slip through human testing. What if AI-assisted programming could eliminate those by using Lean4 to verify code correctness?In formal methods circles, it’s well known that provably correct code can “eliminate entire classes of vulnerabilities [and] mitigate critical system failures.” Lean4 enables writing programs with proofs of properties like “this code never crashes or exposes data.” However, historically, writing such verified code has been labor-intensive and required specialized expertise. Now, with LLMs, there’s an opportunity to automate and scale this process. Researchers have begun creating benchmarks like VeriBench to push LLMs to generate Lean4-verified programs from ordinary code. Early results show today’s models are not yet up to the task for arbitrary software – in one evaluation, a state-of-the-art model could fully verify only ~12% of given programming challenges in Lean4. Yet, an experimental AI “agent” approach (iteratively self-correcting with Lean feedback) raised that success rate to nearly 60%. This is a promising leap, hinting that future AI coding assistants might routinely produce machine-checkable, bug-free code.The strategic significance for enterprises is huge. Imagine being able to ask an AI to write a piece of software and receiving not just the code, but a proof that it is secure and correct by design. Such proofs could guarantee no buffer overflows, no race conditions and compliance with security policies. In sectors like banking, healthcare or critical infrastructure, this could drastically reduce risks. It’s telling that formal verification is already standard in high-stakes fields (that is, verifying the firmware of medical devices or avionics systems). Harmonic’s CEO explicitly notes that similar verification technology is used in “medical devices and aviation” for safety – Lean4 is bringing that level of rigor into the AI toolkit.Beyond software bugs, Lean4 can encode and verify domain-specific safety rules. For instance, consider AI systems that design engineering projects. A LessWrong forum discussion on AI safety gives the example of bridge design: An AI could propose a bridge structure, and formal systems like Lean can certify that the design obeys all the mechanical engineering safety criteria. The bridge’s compliance with load tolerances, material strength and design codes becomes a theorem in Lean, which, once proved, serves as an unimpeachable safety certificate. The broader vision is that any AI decision impacting the physical world – from circuit layouts to aerospace trajectories – could be accompanied by a Lean4 proof that it meets specified safety constraints. In effect, Lean4 adds a layer of trust on top of AI outputs: If the AI can’t prove it’s safe or correct, it doesn’t get deployed.From big tech to startups: A growing movementWhat started in academia as a niche tool for mathematicians is rapidly becoming a mainstream pursuit in AI. Over the last few years, major AI labs and startups alike have embraced Lean4 to push the frontier of reliable AI:OpenAI and Meta (2022): Both organizations independently trained AI models to solve high-school olympiad math problems by generating formal proofs in Lean. This was a landmark moment, demonstrating that large models can interface with formal theorem provers and achieve non-trivial results. Meta even made their Lean-enabled model publicly available for researchers. These projects showed that Lean4 can work hand-in-hand with LLMs to tackle problems that demand step-by-step logical rigor.Google DeepMind (2024): DeepMind’s AlphaProof system proved mathematical statements in Lean4 at roughly the level of an International Math Olympiad silver medalist. It was the first AI to reach “medal-worthy” performance on formal math competition problems – essentially confirming that AI can achieve top-tier reasoning skills when aligned with a proof assistant. AlphaProof’s success underscored that Lean4 isn’t just a debugging tool; it’s enabling new heights of automated reasoning.Startup ecosystem: The aforementioned Harmonic AI is a leading example, raising significant funding ($100M in 2025) to build “hallucination-free” AI by using Lean4 as its backbone. Another effort, DeepSeek, has been releasing open-source Lean4 prover models aimed at democratizing this technology. We’re also seeing academic startups and tools – for example, Lean-based verifiers being integrated into coding assistants, and new benchmarks like FormalStep and VeriBench guiding the research community.Community and education: A vibrant community has grown around Lean (the Lean Prover forum, mathlib library), and even famous mathematicians like Terence Tao have started using Lean4 with AI assistance to formalize cutting-edge math results. This melding of human expertise, community knowledge and AI hints at the collaborative future of formal methods in practice.All these developments point to a convergence: AI and formal verification are no longer separate worlds. The techniques and learnings are cross-pollinating. Each success – whether it’s solving a math theorem or catching a software bug – builds confidence that Lean4 can handle more complex, real-world problems in AI safety and reliability.Challenges and the road aheadIt’s important to temper excitement with a dose of reality. Lean4’s integration into AI workflows is still in its early days, and there are hurdles to overcome:Scalability: Formalizing real-world knowledge or large codebases in Lean4 can be labor-intensive. Lean requires precise specification of problems, which isn’t always straightforward for messy, real-world scenarios. Efforts like auto-formalization (where AI converts informal specs into Lean code) are underway, but more progress is needed to make this seamless for everyday use.Model limitations: Current LLMs, even cutting-edge ones, struggle to produce correct Lean4 proofs or programs without guidance. The failure rate on benchmarks like VeriBench shows that generating fully verified solutions is a difficult challenge. Advancing AI’s capabilities to understand and generate formal logic is an active area of research – and success isn’t guaranteed to be quick. However, every improvement in AI reasoning (like better chain-of-thought or specialized training on formal tasks) is likely to boost performance here.User expertise: Utilizing Lean4 verification requires a new mindset for developers and decision-makers. Organizations may need to invest in training or new hires who understand formal methods. The cultural shift to insist on proofs might take time, much like the adoption of automated testing or static analysis did in the past. Early adopters will need to showcase wins to convince the broader industry of the ROI.Despite these challenges, the trajectory is set. As one commentator observed, we are in a race between AI’s expanding capabilities and our ability to harness those capabilities safely. Formal verification tools like Lean4 are among the most promising means to tilt the balance toward safety. They provide a principled way to ensure AI systems do exactly what we intend, no more and no less, with proofs to show it.Toward provably safe AIIn an era when AI systems are increasingly making decisions that affect lives and critical infrastructure, trust is the scarcest resource. Lean4 offers a path to earn that trust not through promises, but through proof. By bringing formal mathematical certainty into AI development, we can build systems that are verifiably correct, secure, and aligned with our objectives.From enabling LLMs to solve problems with guaranteed accuracy, to generating software free of exploitable bugs, Lean4’s role in AI is expanding from a research curiosity to a strategic necessity. Tech giants and startups alike are investing in this approach, pointing to a future where saying “the AI seems to be correct” is not enough – we will demand “the AI can show it’s correct.”For enterprise decision-makers, the message is clear: It’s time to watch this space closely. Incorporating formal verification via Lean4 could become a competitive advantage in delivering AI products that customers and regulators trust. We are witnessing the early steps of AI’s evolution from an intuitive apprentice to a formally validated expert. Lean4 is not a magic bullet for all AI safety concerns, but it is a powerful ingredient in the recipe for safe, deterministic AI that actually does what it’s supposed to do – nothing more, nothing less, nothing incorrect.As AI continues to advance, those who combine its power with the rigor of formal proof will lead the way in deploying systems that are not only intelligent, but provably reliable.Dhyey Mavani is accelerating generative AI at LinkedIn. Read more from our guest writers. Or, consider submitting a post of your own! See our guidelines here.
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![Daimler CEO just dropped some pretty WILD pro-hydrogen claims [update]](https://electrek.co/wp-content/uploads/sites/3/2025/09/hydrogen_semi.jpg?quality=82&strip=all&w=1600)
Daimler Truck AG CEO Karin Rådström hopped on LinkedIn today and dropped some absolutely wild pro-hydrogen talking points, using words like “emotional” and “inspiring” while making some pretty heady claims about the viability and economics of hydrogen. The rant is doubly embarrassing for another reason: the company’s hydrogen trucks are more than 100 million miles behind Volvo’s electric semis.UPDATE 22NOV2025: Daimler just delivered five new hydrogen semis for trials. more...
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