Bookmarks 2025-12-15T15:58:12.671Z
by Owen Kibel
33 min read
Bookmarks for 2025-12-15T15:58:12.671Z
-
Curiosity Rover Makes Stunning Mars Discovery Before Holiday Break
Added: Dec 15, 2025Curiosity Rover Makes Stunning Mars Discovery Before Holiday Break
Site: The Daily Galaxy - Great Discoveries Channel
Curiosity rover is wrapping up its detailed exploration at Nevado Sajama, preparing to unveil crucial findings about Mars’ past habitability and ongoing mysteries.
-
Hollywood action star recoils at idea of President Newsom: ‘God forbid’ | Fox News Added: Dec 15, 2025
Hollywood action star recoils at idea of President Newsom: ‘God forbid’ | Fox News
-
With pro-journalism groups like these, who needs critics? Added: Dec 15, 2025
With pro-journalism groups like these, who needs critics?
Site: The Hill
We live in a world where awards named after our most famous journalists are given to actual clowns.
It would be nice if those who claimed to care about maintaining a strong, robust, and credible free press were to back up their words with action. Unfortunately, that is too much to ask. We don’t live in a world where many such groups exist. Instead, we live in a world where awards named after our most famous journalists are given to actual clowns. This is done not in the name of good journalism, but in the name of upholding ideological conformity. Jon Stewart and Rachel Maddow were among the honorees this week at USC Annenberg’s annual Walter Cronkite Awards for Excellence in Political Journalism, Deadline reported. “The message sent by honoring these winners is that the press isn’t ‘the enemy of the people,’” said Norman Lear Center founding director and USC Annenberg professor Martin Kaplan. “It’s the firewall between the public and disinformation, abuse of power and corruption.” Unfortunately, this isn't the lesson most people will take away from this award. Quite the contrary. We live in a time of extreme distrust of the press. Audiences hold us in lower regard than even Wall Street. And now, an awards event named after one of the most famous journalists of the 20th century is giving out honors to a clown who pretends to be a newsman, and a newswoman who is a clown. We are expected to see this as normal and acceptable for an industry that hasn’t even begun to address the allegations that it is heavily biased toward one political party. Rewarding Maddow was always going to be embarrassing. She is not a journalist, and she is a lousy one to the extent that she has ever tried to be one. Not everyone has forgotten the moment in 2017 when, with lots of hype and seemingly endless teases — all broken up by commercial breaks — Maddow promised she had the goods on President Trump and his tax returns. The “scoop” went nowhere, because the documents Maddow promoted contained no new or interesting information. Even Stephen Colbert, the patron saint of late-night anti-Trump “resistance” types, mocked Maddow for her botched, badly overblown “scoop.” No word yet on whether the Walter Cronkite Awards have a belated honor planned for Geraldo Rivera and his big Al Capone exclusive. But that 2017 incident is just one of many regarding Maddow’s long history of histrionic nonsense. Her Cronkite honor couldn’t have come at a worse time for media credibility, especially since it was less than a week ago that she appeared on Colbert’s show and repeated the thoroughly debunked conspiracy theory that Trump is somehow an asset of Moscow. “You know, Russia is a podunk country,” Maddow complained. “They’ve got a kleptocratic, sclerotic government run by a guy who’s never going to leave until he dies. The idea that we work for [Putin], that we work for them, is so humiliating and is such an abject failure on the part of Trump in terms of his weakness.” She added, “I don’t know what Putin has on him, but he works for Putin, and it’s an embarrassment to this country.” There is and was never anything to the claim that Trump is a Kremlin stooge, despite years of efforts by federal investigators and Pulitzer Prize-winning reporting (thanks only to the Pulitzer committee's retroactively embarrassing bias) that ultimately went nowhere. Maddow’s loyalty to the narrative goes beyond politics. It goes beyond simple stubbornness. It is the stuff of delusion — the blind faith of a religious zealot. Maddow today is the cable news equivalent of the Japanese soldier who kept fighting World War II on a remote island decades after Japan's surrender. So, who better to honor with an award named after Walter Cronkite than a wide-eyed, Kool-Aid-drinking evangelist of the church of resistance? Speaking of bad jokes, Jon Stewart is set to receive the inaugural Cronkite Award for comedic news and commentary. The kindest thing that can be said about Stewart is that, unlike Maddow, he seems to have some self-awareness. It is almost as if he finally understands the role he played in eroding trust in the news media. Stewart has always been a joker, and he remains so. However, around the middle of the George W. Bush administration and the start of the Obama era, his show became a go-to news source for many young viewers. This was unfortunate, because it coincided with Stewart’s full embrace of the role of Democratic hatchet man — splicing and dicing Republican and conservative guests in the most uncharitable ways, all to get cheers and laughs from an audience that clearly hated George W. Bush and loved Barack Obama. As it turns out, it’s not great that entire generations should grow up believing that a partisan who makes fart jokes between his commentaries on the news is a trustworthy and reliable source of information. Nevertheless, Stewart remains a hero to enough journalists that he is being given this award. Of all industries, the media seems to be the last to realize how its valorization of the TV comedian has helped normalize Americans getting their news from entertainers rather than news sources. Real journalists who’ve done the hard work of investigating scandals and breaking real news have not received even a fraction of the praise heaped upon Stewart, whose desk from his Comedy Central show was once even displayed at the now-closed Newseum — that belated and absurd monument to journalism’s undeserved high self-esteem. All of this despite Stewart becoming well known during his first run as a fake newsman for being factually sloppy, unethical, and deeply unfair to his interview subjects. Washington Post opinion columnist Megan McCardle wrote an article for Bloomberg News in 2014 with the blunt title, “Don’t ever appear on the ‘Daily Show.’” Despite all of this, Stewart has been treated like a king by the industry, with his first retirement announcement compared to the breakup of the Beatles. Now, years later, after numerous news cycles warning about the dangers of the public getting its news from non-traditional sources — especially the dreaded Joe Rogan — we see Stewart, the ultimate avatar of non-news news sources, being honored alongside journalists with an award named after a long-deceased and well-known newsman. There’s no good reason for either award, especially from a responsible and ethical journalism perspective. They are giving Stewart and Maddow the awards because they are part of the club. They will award people like Stewart and Maddow (and perhaps Colbert in some future year?) despite the obvious and subtle long-term damage they have caused to the industry’s credibility, because these people are more interested in enforcing the “correct” political view and values than they are in protecting journalism. Everything else is just posturing. And that’s the way it is. Becket Adams is a longtime journalist and media critic in Washington.
-
Grifters Are Rising Up, Taking Over The Conservative Movement - YouTube Added: Dec 15, 2025
Grifters Are Rising Up, Taking Over The Conservative Movement
Site: YouTube
NEW SONG, SILENT NIGHT, GET IT HERE: https://trashhousechristmas.com/SUPPORT THE SHOW BUY CAST BREW COFFEE NOW - https://castbrew.com/Join - https://www.yout...
-
The Loeb Scale: Astronomical Classification of Interstellar Objects | by Avi Loeb | Medium Added: Dec 15, 2025
The Loeb Scale: Astronomical Classification of Interstellar Objects
Site: Medium
by Omer Eldadi (1), Gershon Tenenbaum (1) and Avi Loeb (2)
-
FBI Thwarts New Years TERROR PLOT, Pro Palestine Group Accused | Tim Pool
Site: YouTube
Try my favorite sleep aid, Beam Dream. Visit https://shopbeam.com/TIMCAST and use code TIMCAST to get up to 35% off — limited time only!Become A Memberhttp:/...
-
Animal Farm Film IS PRO COMMUNIST Proving Orwell RIGHT | Tim Pool
Site: YouTube
Orwell Proven Right yet againBecome A Memberhttp://youtube.com/timcastnews/joinThe Green Room - https://rumble.com/playlists/aa56qw_g-j0BUY CAST BREW COFFEE ...
-
Site: X (formerly Twitter)
-
Australian PM rejects Netanyahu's linking of Palestine recognition to Bondi attack | The Times of Israel
Added: Dec 15, 2025Australian PM rejects Netanyahu's linking of Palestine recognition to Bondi attack | The Times of Israel
-
After Sydney attack, Netanyahu says he warned Canberra was ‘pouring fuel on antisemitic fire’ | The Times of Israel
Added: Dec 15, 2025After Sydney attack, Netanyahu says he warned Canberra was ‘pouring fuel on antisemitic fire’
Israeli politicians liken terror attack to Oct. 7, accuse Australia of ignoring anti-Jewish incidents in lead-up; some officials say victims' blood is on government's hands
-
Trump suggests Rob Reiner's killing was due to ‘TRUMP DERANGEMENT SYNDROME’ - POLITICO Added: Dec 15, 2025
Republicans rebuff Trump's post on Rob Reiner
Site: POLITICO
The president said the Hollywood icon suffered an “incurable affliction” at the time of his death.
-
Megyn Kelly Remembers Rob Reiner's Incredible Legacy After Shocking Death Reportedly at Hands of Son
Site: YouTube
Megyn Kelly remembers Rob Reiner's incredible legacy after shocking death reportedly at hands of son.LIKE & SUBSCRIBE for new videos everyday: https://bit.ly...
-
Trump's little-known link to Rob Reiner's wife revealed as son is arrested after parents were found dead at home: Live updates | Daily Mail Online Added: Dec 15, 2025
Nick Reiner could face the death penalty in parents' murder
Site: Mail Online
Investigators are treating the couple's death as a double homicide, and an unnamed family member is being questioned, a police source said.
-
JustHTML is a fascinating example of vibe engineering in action Added: Dec 15, 2025
JustHTML is a fascinating example of vibe engineering in action
Site: Simon Willison’s Weblog
I recently came across JustHTML, a new Python library for parsing HTML released by Emil Stenström. It’s a very interesting piece of software, both as a useful library and as …
-
Viewers Call Trump SNL Sketch Too Close To Reality Added: Dec 15, 2025
Everybody's Saying The Same Thing About The Trump And Leavitt "SNL" Sketch
Site: BuzzFeed
"This is the most unhinged cold open in a long time."
-
President Trump Participates in a Mexican Border Defense Medal Presentation
Site: YouTube
The White House
-
xiaomi-research/diffrhythm2
Added: Dec 15, 2025GitHub - xiaomi-research/diffrhythm2
Site: GitHub
Contribute to xiaomi-research/diffrhythm2 development by creating an account on GitHub.
-
billwuhao/ComfyUI_DiffRhythm2: DiffRhythm2 歌曲生成。
Added: Dec 15, 2025
GitHub - billwuhao/ComfyUI_DiffRhythm2: DiffRhythm2 歌曲生成。
Site: GitHub
DiffRhythm2 歌曲生成。. Contribute to billwuhao/ComfyUI_DiffRhythm2 development by creating an account on GitHub.
-
Musk Calls Earth Fusion Reactors Super Dumb Next to the Sun / X Added: Dec 15, 2025
Site: X (formerly Twitter)
-
Site: X (formerly Twitter)
-
Site: X (formerly Twitter)
-
The Anti-Tail of 3I/ATLAS is Larger Than the Distance to the Moon
Site: Medium
As of December 15, 2025, the interstellar object 3I/ATLAS arrived at a distance of about 270 million kilometers from Earth. By December 19…
-
Violence ERUPTS Over the Weekend, TERROR ATTACK In Australia ft. Libby Emmons
Site: YouTube
BUY CAST BREW COFFEE TO SUPPORT THE SHOW - https://castbrew.com/Become A Member And Protect Our Work at http://www.timcast.comHost:Tate Brown @realTate Brown...
-
Lexington Hills, California, USA 14 day weather forecast
Added: Dec 15, 2025Lexington Hills, California, USA 14 day weather forecast
Forecasted weather conditions the coming 2 weeks for Lexington Hills
-
10-Day Weather Forecast for Chemeketa Park, Lexington Hills, California - The Weather Channel | weather.com
Added: Dec 15, 202510-Day Weather Forecast for Chemeketa Park, Lexington Hills, California - The Weather Channel | weather.com
Site: The Weather Channel
Be prepared with the most accurate 10-day forecast for Chemeketa Park, Lexington Hills, California with highs, lows, chance of precipitation from The Weather Channel and Weather.com
-
How Neuro-Symbolic AI Breaks the Limits of LLMs | WIRED Added: Dec 15, 2025
How Neuro-Symbolic AI Breaks the Limits of LLMs
Site: WIRED
Combining neural learning with symbolic reasoning for more reliable AI.
While AI transforms subjective work like content creation and data summarization, executives rightfully hesitate to use it when facing objective, high-stakes determinations that have clear right and wrong answers, such as contract interpretation, regulatory compliance, or logical workflow validation. But what if AI could demonstrate its reasoning and provide mathematical proof of its conclusions? That’s where neuro-symbolic AI offers a way forward. The “neuro” refers to neural networks, the technology behind today’s LLMs, which learn patterns from massive datasets. A practical example could be a compliance system, where a neural model trained on thousands of past cases might infer that a certain policy doesn’t apply in a scenario. On the other hand, symbolic AI represents knowledge through rules, constraints, and structure, and it applies logic to make deductions. For example, in the same compliance scenario, symbolic AI might identify an edge case that makes the policy applicable—something the neural system could overlook. Neuro-symbolic AI brings these two approaches together by joining the inductive reasoning of neural networks with the rigor of symbolic logic. This allows AI systems to reason more reliably and generalize more effectively. And it represents a fundamental shift for business leaders: AI systems that don’t merely appear correct, but can demonstrate their correctness through verifiable logic. This form of AI is already in widespread operational use at Amazon. “Neuro-symbolic AI is helping us bring greater rigor and reliability to how AI operates across Amazon,” says Byron Cook, VP and distinguished scientist at Amazon. “By combining the pattern recognition of neural networks with the logical structure of symbolic reasoning, we’re able to build systems that reason more consistently and make decisions our customers can trust.” The technology enables confident AI deployment in mission-critical domains where accuracy isn’t simply preferred—it’s mandatory, Cook adds. “By blending these methods, AI systems can reason through problems step by step, reduce errors through verifiable checks, and apply their skills more effectively to new domains.” How Amazon Deploys Neuro-Symbolic AI Amazon has put this technology to work in production systems that handle a large number of customer interactions daily. From warehouse robots that ensure packages arrive on time to shopping assistants that understand customer requests, neuro-symbolic AI is demonstrating its value in real-world applications where reliability matters. To create a more efficient and dependable warehouse automation system, Amazon combines neuro-symbolic AI, machine learning, and Amazon’s new DeepFleet foundation model to uphold logical rules, optimize routes and workload distribution, and predict complex robot interactions. As a result, robot-fleet travel efficiency has improved by 10 percent, delivery times have dropped, operational costs are down, and energy usage has been reduced. Automated reasoning checks in Amazon Bedrock Guardrails uses symbolic reasoning to validate generated content against predefined knowledge bases, such as HR guidelines or operational manuals. Previously, systems would treat these materials as probabilistic references, but with neuro-symbolic AI, they’re now understood as definitive sources of truth, ensuring outputs are grounded in verified facts. This generative AI safeguard identifies correct model responses with up to 99 percent verification accuracy, providing organizations with provable assurance in minimizing hallucinations while also detecting ambiguity. On the customer-facing side, Amazon has introduced Rufus, a new generative AI-powered conversational shopping experience. It uses neuro-symbolic AI via models that can reason and call APIs, improving its ability to understand customer requests and take appropriate actions. “The future of trustworthy AI agents starts with automated reasoning,” says Cook, who is also the founder of the Automated Reasoning Group at AWS. “Amazon has invested over a decade building this expertise to prove correctness in security and cloud infrastructure, and we’re now applying those same rigorous techniques to verify the safety and reliability of AI systems and autonomous agents.” For business leaders evaluating AI adoption, this operational track record demonstrates the technology’s maturity beyond laboratory settings. It also lays the foundation for the neuro-symbolic techniques now embedded in training of Amazon’s newly released reasoning model Amazon Nova 2 Lite. Advancing Reasoning Capabilities Amazon recently released Nova 2 Lite, a reasoning foundation model trained using neuro-symbolic AI. The team used Lean4, which is an open-source automated reasoning tool popular among machine learning practitioners, during model training. This approach enhances the model’s credibility, consistency, and performance on complex reasoning tasks. For example, consider how auditors approach financial reviews: The conclusion matters, but the verifiable trail of logic matters more. A clean audit opinion without supporting documentation is almost worthless. Neuro-symbolic AI introduces a structural advance in LLM training by embedding automated reasoning directly into the training loop. This uses formal logic and mathematical proof to mechanically verify whether a statement, program, or output used in the training data is correct. A tool such as Lean,4 is precise, deterministic, and gives provable assurance. The key advantage of automated reasoning is that it verifies each step of the reasoning process, and not just the final answer. The integration of automated reasoning happens across three stages of model development: pre-training, supervised fine-tuning, and reinforcement learning. In pre-training, Amazon added automated reasoning code and textbooks to the training data, giving the model a foundational grasp of reasoning science. Next, a specialized dataset combined automated reasoning proofs written in Lean4 with natural-language reasoning traces, exposing Nova not only to correct solutions but also to the thought process behind them. “This approach drove statistically significant gains across reasoning-intensive tasks,” says Kanna Shimizu, Senior Manager, Applied Science, at Amazon. Finally, Nova was challenged with a large set of mathematical statements in automated reasoning, with real-time validation providing direct feedback on reasoning quality. This improves the model’s ability to generate valid proofs, says Spyros Matsoukas, VP, Distinguished Scientist, AGI, at Amazon. By combining neural learning with symbolic reasoning, Amazon Nova 2 Lite, available in Amazon Bedrock, shows stronger results in mathematics, coding, and science benchmarks. It is learning to reason—to construct step-by-step justifications, apply logic in domains like mathematics and coding, and generalize those reasoning skills to new areas, from scientific discovery to planning tasks such as policy interpretation, regulatory compliance, or strategic decision analysis. Looking Ahead The implications extend far beyond current applications. Neuro-symbolic AI enables AI deployment in high-stakes environments where complex problem-solving, logical consistency, and verifiable outcomes are critical. “We see neuro-symbolic approaches as an important step toward AI that reasons more consistently and reliably. Over time, these methods could help broaden how AI supports scientific discovery, autonomous systems, and real-world decision-making—areas where rigor and trust will matter most,” Matsoukas says. As AI moves from supporting creative and analytical tasks to informing binding business decisions, the ability to verify reasoning becomes increasingly valuable. Amazon is advancing research in this area through technologies such as autoformalization—converting natural language into formal logic—and collaborative efforts with academic partners to establish new benchmarks for measuring reasoning progress. “The early applications we see today, from policy interpretation to risk assessment, indicate growing demand for verifiable AI capabilities. Organizations that understand these reasoning capabilities now will be better positioned as AI models become more sophisticated in handling complex business logic,” Cook says. “Understanding these developments helps inform longer-term AI strategy decisions.”
-
The End of Debugging – O’Reilly
Added: Dec 15, 2025The End of Debugging
Site: O’Reilly Media
Software Now Writes, Runs, and Repairs Itself—Our Job Is Shifting from Control to Description.
-
Israeli officials blame Australia for antisemitism before Sydney attack | Fox News
-
Republican lawmakers slam Trump's "inappropriate" posts on Rob Reiner Added: Dec 15, 2025
Republican lawmakers slam Trump's "inappropriate" posts on Rob Reiner
Site: Axios
"Most Americans want more and better from our president," said one House Republican.
-
The great AI hype correction of 2025 Added: Dec 15, 2025
The great AI hype correction of 2025
-
The Good, Bad and Ugly of AI - WSJ Added: Dec 15, 2025
-
Australia allowed Jewish hate to fester with cowardly appeasement and foolish immigration decisions | New York Post Added: Dec 15, 2025
Australia allowed Jewish hate to fester with cowardly appeasement and foolish immigration decisions
Site: New York Post
On Sunday, this slice of paradise became the latest battlefront of the anti-Jew bloodshed that has seized the world since Israel was attacked by Palestinian terrorists on Oct. 7, 2023.
-
Australia’s government failed its Jews in the long runup to Bondi Beach attack
Site: New York Post
In the wake of Sunday’s Bondi Beach terror attack on a gathering to celebrate the start of Hanukkah, Australia’s leaders should be facing some very tough questions about their failure to fight anti…
-
Republicans rebuff Trump's post on Rob Reiner
Site: POLITICO
The president said the Hollywood icon suffered an “incurable affliction” at the time of his death.
-
Trump admin says it's "escalating" review of Mark Kelly to an "official" investigation
Site: Axios
"There is no legitimate basis for any type of proceeding against Senator Kelly," his attorney said.
-
Australian leaders dodge questions over how Bondi shooter was licensed gun carrier | The Times of Israel
Added: Dec 15, 2025
Australian leaders dodge questions over how Bondi shooter was licensed gun carrier | The Times of Israel
-
Where have all the male poets gone in modern literature and poetry today | Fox News Added: Dec 15, 2025
Where have all the male poets gone in modern literature and poetry today | Fox News
The article explores how male voices in poetry have been marginalized over the past 50 years, arguing that society wrongly views poetry as feminine rather than masculine.
-
Google Warns Noindex Can Block JavaScript From Running
Added: Dec 15, 2025Google Warns Noindex Can Block JavaScript From Running
Site: Search Engine Journal
Google updated its JavaScript SEO documentation to clarify that noindex tags may prevent rendering and JavaScript execution, blocking changes.
-
MAGA breaks with Trump on mocking Rob Reiner's killing
Site: Axios
"A man and his wife were murdered last night. This is NOT the appropriate response."
-
ADHD Isn’t Just a Deficit: New Study Reveals Powerful Psychological Strengths Added: Dec 15, 2025
ADHD Isn’t Just a Deficit: New Study Reveals Powerful Psychological Strengths
Site: SciTechDaily
Adults with ADHD who understand and apply their personal strengths experience better well-being and fewer mental health difficulties.
-
How to levitate objects sans magic
Added: Dec 15, 2025How to levitate objects sans magic
Site: Science News
It’s possible to defy gravity using sound waves, magnets or electricity, but today’s methods can’t hoist heavy items high in the sky.
-
Generative AI hype distracts us from AI’s more important breakthroughs
-
Astronauts Are About to Wear Radiation-Proof Clothes for the Moon—And You Might Want One Too!
Added: Dec 15, 2025
Astronauts Are About to Wear Radiation-Proof Clothes for the Moon—And You Might Want One Too!
Site: The Daily Galaxy - Great Discoveries Channel
Introducing a fabric that warns you about radiation by changing color, no batteries required. Protecting astronauts and potentially you too!
-
Psilocybin Breaks Depressive Cycles by Rewiring The Brain, Study Suggests : ScienceAlert
Added: Dec 15, 2025Psilocybin Breaks Depressive Cycles by Rewiring The Brain, Study Suggests
Site: ScienceAlert
Scientists have used a specially engineered virus to help track the brain changes caused by psilocybin in mice, revealing how the drug could be breaking loops of depressive thinking.
-
Over 100 Years Later, Ramanujan's Unexpected Formulas Are Still Unraveling The Mysteries Of The Universe | IFLScience
Added: Dec 15, 2025Ramanujan's Unexpected Formulas Are Still Unraveling The Mysteries Of The Universe
Site: IFLScience
“[In] any piece of beautiful mathematics, you almost always find that there is a physical system which actually mirrors the mathematics.”
There are few things more pleasing to your average mathematician than when a result surprises you. Take e, for example – a transcendentally irrational number equal to a little more than 2.7 – and raise it to the power of π multiplied by the imaginary unit i. Add one to your total, and you get… zero. Why should that be the case? It’s baffling – and for that, it’s truly beautiful. And if anybody personified this surprising mathematical beauty, it would have to be Srinivasa Ramanujan. He’s now remembered as one of the most prodigious minds known to math, making substantial contributions to analytic number theory and leaving behind reams of revolutionary results in unpublished notebooks after his death. His ideas would go on to influence areas of math and science he could never have heard of in his own lifetime; often, as a new paper from a pair of researchers at the Indian Institute of Science shows, they turn up totally unexpectedly in already-known phenomena, and it’s left to us to figure out why. But back in the early 1910s, when he first started reaching out to respected English mathematicians with some of his results, he couldn’t have been more unexpected. The story of a nobody A miserably poor man from a tiny village southwest of Chennai in India, Ramanujan had no university degree or formal mathematical training – which might be why the first couple of mathematicians he approached with his ideas assumed he was little more than a crank. But then he sent a letter to G.H. Hardy – cricketer, philosopher, and one of the leading mathematicians in all of England – and finally, he got a response. “I was exceedingly interested by your letter and by the theorems which you state,” Hardy replied on February 8, 1913. “Your results seem to me to fall into roughly three classes: (1) there are a number of results that are already known, or easily deducible from known theorems; (2) there are results which, so far as I know, are new and interesting, but interesting rather from their curiosity and apparent difficulty than their importance; (3) there are results which appear to be new and important.” “Important” may have been, if anything, underselling it. Hardy would later write that “a single look at [the results] is enough to show that they could only be written down by a mathematician of the highest class.” He compared Ramanujan to Euler and Jacobi, and said that his results “must be true because, if they were not true, no one would have had the imagination to invent them.” “Here was a man who could work out modular equations, and theorems of complex multiplication, to orders unheard of,” Hardy would later write in Ramanujan’s 1920 obituary ; “whose mastery of continued fractions was, on the formal side at any rate, beyond that of any mathematician in the world, who had found for himself the functional equation of the Zeta-function, and the dominant terms of many of the most famous problems in the analytic theory of numbers.” Ramanujan, even then, had found results whose importance would not be fully appreciated for decades: identities that would open new mathematical worlds and close monstrous conjectures. He found ways of calculating pi that, while obviously correct and incredibly fast, seemed to have arisen more or less from divine inspiration – but which, now, have been shown to reflect some of the deepest truths in modern physics. “[In] any piece of beautiful mathematics, you almost always find that there is a physical system which actually mirrors the mathematics,” said Faizan Bhat, first author of the new paper and former PhD student at the Indian Institute of Science, in a statement. “Ramanujan’s motivation might have been very mathematical, but without his knowledge, he was also studying black holes, turbulence, percolation, all sorts of things.” A modern man There are many reasons to be a fan of pi. It’s got strong geometry cred; it’s both eminently calculable and frustratingly not ; and, of course, it puts you in mind of a delicious dessert. But in the modern world, we like pi because it means we get to show off. Specifically, we use pi to boast about how powerful our computers are: calculating the constant to ever-higher degrees of accuracy is “a computational challenge,” David Harvey, an associate professor at the University of New South Wales, told The Guardian in 2021. “There’s plenty of other interesting constants in mathematics: if you’re into chaos theory there’s Feigenbaum constants, if you’re into analytic number theory there’s Euler’s gamma constant,” he pointed out. “There’s lots of other numbers you could try to calculate: e, the natural logarithm base, you could calculate the square root of 2.” But “you do pi because everyone else has been doing pi,” he said. “That’s the particular mountain everyone’s decided to climb.” The world record for how many digits pi can be calculated to is not one that stands for very long, these days – it’s been broken four times since the beginning of 2024 alone – but the method for doing it is more hardy. Since 2010, every breakthrough has come thanks to y-cruncher, a one-time high school project by Alexander Yee – and that, in turn, has owed its success to Ramanujan. “Scientists have computed pi up to 200 trillion digits using an algorithm called the Chudnovsky algorithm,” explained Aninda Sinha, Professor at CHEP and senior author of the new study. “These algorithms are actually based on Ramanujan’s work.” That Ramanujan could have discovered these formulae at all, given his (lack of) formal mathematical background, is surprising enough – but “we wanted to see whether the starting point of his formulas fit naturally into some physics,” Sinha said. “In other words, is there a physical world where Ramanujan’s mathematics appears on its own?” As with so many of Ramanujan’s results before this one, the answer turned out to be “yes”. Specifically, the formulas turn up in so-called conformal field theory – an area of theoretical physics that combines quantum mechanics, field theory, and relativity to describe phenomena like string theory and condensed matter physics. It’s a bit of physics that didn’t even exist for more than 60 years after Ramanujan’s death – and yet, somehow, he figured them out. Alone. “We were simply fascinated by the way a genius working in early 20th century India, with almost no contact with modern physics, anticipated structures that are now central to our understanding of the universe,” Sinha said. A tragic end Ramanujan was evidently a genius – but his untutored approach needed training. Before long, he and Hardy were exchanging letters regularly – and it was ever-more evident to Hardy that Ramanujan’s raw, instinctive talent needed refining and polishing. “The limitations of his knowledge were as startling as its profundity,” Hardy recalled in his obituary. Despite his accomplishments, Ramanujan “had never heard of a doubly periodic function or of Cauchy’s theorem, and had, indeed, but the vaguest idea of what a function of a complex variable was.” “[These] were things of which it was impossible that he should remain in ignorance,” Hardy wrote. “It was impossible to allow him to go through life supposing that all the zeroes of the Zeta-function were real. So I had to try to teach him.” He sent out an invitation to Cambridge via a finagled scholarship to the University of Madras, and – after some soul-searching over the morals of traveling overseas as a Brahmin – Ramanujan came to England. It was a move that would change the mathematical world. “In 1916 Ramanujan got his BA [the equivalent of a modern PhD] from Cambridge and his research went from strength to strength,” wrote Béla Bollobás, Professor of Pure Mathematics at the University of Cambridge, in a 2016 article for The Conversation. “He published one excellent paper after another, with a great deal of Hardy’s help in the proofs and presentation. They also collaborated on several great projects, and published wonderful joint papers.” But personally, it was probably a mistake. Ramanujan suffered from ill health almost immediately, thanks in part to the UK’s 1914 entrance into World War One, partly due to cultural misunderstandings, and partly due to the sometimes institutional, sometimes naked racism of the England around him. He attempted suicide – and was promptly arrested for doing so – and spent years confined to sanatoria for tuberculosis and vitamin deficiencies. “By early 1919 Ramanujan seemed to have recovered sufficiently, and decided to travel back to India,” Bollobás wrote. A year later, he wrote to Hardy once again: the letter “contained some examples of his latest discovery, mock theta functions, which have turned out to be very important.” “A main conjecture about them was solved 80 years later, and these functions are now seen as interesting examples of a much larger class of mock modular forms in mathematics,” he explained, “which have applications to elliptic curves, Borcherds products, Eichler cohomology and Galois representations – and the nature of black holes.” Sadly, his recovery was not to last. Ramanujan was only 32 when, in April 1920, he died from the ill health that had plagued him for so long. It would take decades for his results, including those in his famous “ Lost Notebook ”, to be fully understood – a few conjectures bearing his name are still open – and, as this new work makes clear, fresh slants on his ideas are constantly being found. “I had to try to teach him, and in a measure I succeeded,” Hardy wrote. “Though obviously I learnt from him much more than he learnt from me.” “He would probably have been a greater mathematician if he had been caught and tamed a little in his youth; he would have discovered more that was new, and that, no doubt, of greater importance,” he concluded. “On the other hand, he would have been less of a Ramanujan […] and the loss might have been greater than the gain.” The study is published in Physical Review Letters.
-
Site: X (formerly Twitter)
-
I used Nano Banana Pro to create 20 social media posts, the response they got was shocking - Digital Trends
Added: Dec 15, 2025I used Nano Banana Pro to create 20 social media posts, the response they got was shocking
Site: Digital Trends
Google Gemini now lets you generate images using Nano Banana Pro. I tested whether the bot can make compelling social media graphics.
-
This shark fits in your pocket and glows in the dark - Earth.com Added: Dec 15, 2025
This shark fits in your pocket and glows in the dark
Site: Earth.com
A small bioluminescent shark so rare that there are only two specimens in the entire world has been discovered in the Gulf of Mexico.
-
Trump says Rob Reiner was "very bad for our country" in new attacks
Site: Axios
"I wasn't a fan of Rob Reiner at all in any way, shape or form," Trump said.
-
Brown Shooter AT LARGE, People FURIOUS As Cops WITHHOLD FOOTAGE | Tim Pool
Site: YouTube
Why wont the police release more footage to find the brown shooter?Become A Memberhttp://youtube.com/timcastnews/joinThe Green Room - https://rumble.com/play...
