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    Can Math Help AI Chatbots Stop Making Stuff Up?

    Chatbots like ChatGPT get stuff wrong. But researchers are building new A.I. systems that can verify their own math — and maybe more.On a recent afternoon, Tudor Achim gave a brain teaser to an A.I. bot called Aristotle.The question involved a 10-by-10 table filled with a hundred numbers. If you collected the smallest number in each row and the largest number in each column, he asked, could the largest of the small numbers ever be greater than the smallest of the large numbers?The bot correctly answered “No.” But that was not surprising. Popular chatbots like ChatGPT may give the right answer, too. The difference was that Aristotle had proven that its answer was right. The bot generated a detailed computer program that verified “No” was the correct response.Chatbots like ChatGPT from OpenAI and Gemini from Google can answer questions, write poetry, summarize news articles and generate images. But they also make mistakes that defy common sense. Sometimes, they make stuff up — a phenomenon called hallucination.Mr. Achim, the chief executive and co-founder of a Silicon Valley start-up called Harmonic, is part of growing effort to build a new kind of A.I. that never hallucinates. Today, this technology is focused on mathematics. But many leading researchers believe they can extend the same techniques into computer programming and other areas.Because math is a rigid discipline with formal ways of proving whether an answer is right or wrong, companies like Harmonic can build A.I. technologies that check their own answers and learn to produce reliable information.Google DeepMind, the tech giant’s central A.I. lab, recently unveiled a system called AlphaProof that operates in this way. Competing in the International Mathematical Olympiad, the premier math competition for high schoolers, the system achieved “silver medal” performance, solving four of the competition’s six problems. It was the first time a machine had reached that level.We are having trouble retrieving the article content.Please enable JavaScript in your browser settings.Thank you for your patience while we verify access. If you are in Reader mode please exit and log into your Times account, or subscribe for all of The Times.Thank you for your patience while we verify access.Already a subscriber? Log in.Want all of The Times? Subscribe. More

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    Time to Say Goodbye to the B.M.I.?

    The body mass index has long been criticized as a flawed indicator of health. A replacement has been gaining support: the body roundness index.Move over, body mass index. Make room for roundness — to be precise, the body roundness index.The body mass index, or B.M.I., is a ratio of height to weight that has long been used as a medical screening tool. It is one of the most widely used health metrics but also one of the most reviled, because it is used to label people overweight, obese or extremely obese.The classifications have been questioned by athletes like the American Olympic rugby player Ilona Maher, whose B.M.I. of 30 technically puts her on the cusp of obesity. “But alas,” she said on Instagram, addressing online trolls who tried to shame her about her weight, “I’m going to the Olympics and you’re not.”Advocates for overweight individuals and people of color note that the formula was developed nearly 200 years ago and based exclusively on data from men, most of them white, and that it was never intended for medical screening. Even physicians have weighed in on the shortcomings of B.M.I. The American Medical Association warned last year that B.M.I. is an imperfect metric that doesn’t account for racial, ethnic, age, sex and gender diversity. It can’t differentiate between individuals who carry a lot of muscle and those with fat in all the wrong places.“Based on B.M.I., Arnold Schwarzenegger when he was a bodybuilder would have been categorized as obese and needing to lose weight,” said Dr. Wajahat Mehal, director of the Metabolic Health and Weight Loss Program at Yale University.“But as soon as you measured his waist, you’d see, ‘Oh, it’s 32 inches.’”So welcome a new metric: the body roundness index. B.R.I. is just what it sounds like — a measure of how round or circlelike you are, using a formula that takes into account height and waist, but not weight.We are having trouble retrieving the article content.Please enable JavaScript in your browser settings.Thank you for your patience while we verify access. If you are in Reader mode please exit and log into your Times account, or subscribe for all of The Times.Thank you for your patience while we verify access.Already a subscriber? Log in.Want all of The Times? Subscribe. More

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    Eliyahu Rips, Who Claimed to Find Secret Codes in the Torah, Dies at 75

    His work provided the basis for the worldwide best seller “The Bible Code,” but he later rejected the book as unscientific.It sounds like a headline ripped from a supermarket tabloid: In 1994, three Israeli researchers claimed to have found a secret code embedded in Genesis, the first book of the Old Testament.But this wasn’t junk science. The paper in which they revealed their findings appeared in an esteemed, peer-reviewed journal. And the academic reputations of the three authors — Eliyahu Rips, Yoav Rosenberg and Doron Witztum — were unimpeachable, especially that of Dr. Rips.A math prodigy born to Holocaust survivors in Latvia, he had received his doctorate from, and spent his career at, Hebrew University in Jerusalem, where he became known for his work in a field called geometric group theory.He had also become convinced that statistical tools and newer, more powerful computers that were becoming available in the 1980s could be used to identify hidden meaning within the Bible, and he teamed up with his two partners to discover them. Their biggest finding was the names of 32 Jewish scholars in the text, along with their birth or death dates; several of the scholars had lived thousands of years after Genesis was written.Their results, reported in the journal Statistical Science, set off a tempest in the worlds of biblical scholarship and statistical analysis. In 1997, Michael Drosnin, a journalist, used the team’s tools to write “The Bible Code,” a global best seller that claimed to find not just rabbis’ birthdays but also predictions about world events, including the assassination of Israeli Prime Minister Yitzhak Rabin in 1995, all embedded in the Torah, or the first five books of the Old Testament. (Mr. Drosnin died in 2020.)The book put Dr. Rips in an international spotlight. Magazine and newspaper profiles proliferated; with his Gandalfian white beard and wide-brimmed hat, he seemed to embody the intersection of science and Jewish mysticism.We are having trouble retrieving the article content.Please enable JavaScript in your browser settings.Thank you for your patience while we verify access. If you are in Reader mode please exit and log into your Times account, or subscribe for all of The Times.Thank you for your patience while we verify access.Already a subscriber? Log in.Want all of The Times? Subscribe. More

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    A Mammoth DNA Discovery Helps Map an Ancient Genome in 3-D

    In 2018 an international team of scientists — from labs in Houston, Copenhagen, Barcelona and beyond — got their hands on a remarkable biological specimen: a skin sample from a 52,000-year-old woolly mammoth that had been recovered from the permafrost in Siberia. They probed the sample with an innovative experimental technique that revealed the three-dimensional architecture of the mammoth’s genome. The resulting paper was published on Thursday in the journal Cell.Hendrik Poinar, an evolutionary geneticist at McMaster University in Canada, was “floored” — the technique had successfully captured the original geometry of long stretches of DNA, a feat never before accomplished with an ancient DNA sample. “It’s absolutely beautiful,” said Dr. Poinar, who reviewed the paper for the journal.The typical method for extracting ancient DNA from fossils, Dr. Poinar said, is still “kind of cave man.” It produces short fragments of code composed of a four-letter molecular alphabet: A (adenine), G (guanine), C (cytosine), T (thymine). An organism’s full genome resides in cell nuclei, in long, unfragmented DNA strands called chromosomes. And, vitally, the genome is three-dimensional; as it dynamically folds with fractal complexity, its looping points of contact help dictate gene activity.“To have the actual architectural structure of the genome, which suggests gene expression patterns, that’s a whole other level,” Dr. Poinar said.“It’s a new kind of fossil, a fossil chromosome,” said Erez Lieberman Aiden, a team member who is an applied mathematician, a biophysicist and a geneticist and directs the Center for Genome Architecture at Baylor College of Medicine in Houston. Technically, he noted, it is a non-mineralized fossil, or subfossil, since it has not turned to stone.Erez Lieberman Aiden, director of the Center for Genome Architecture at Baylor College of Medicine in Houston.Brandon Thibodeaux for The New York TimesThe trunk of a 39,000-year-old woolly mammoth nicknamed Yuka that also yielded fossil chromosomes in the study.Love Dalén/Stockholm UniversityWe are having trouble retrieving the article content.Please enable JavaScript in your browser settings.Thank you for your patience while we verify access. If you are in Reader mode please exit and log into your Times account, or subscribe for all of The Times.Thank you for your patience while we verify access.Already a subscriber? Log in.Want all of The Times? Subscribe. More

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    What Improv Can Do for Mathematicians

    Coaching sessions at the People’s Improv Theater were aimed at helping math experts connect with laypeople and give engaging presentations.Good morning. It’s Wednesday. Today we’ll solve for x and y, where x is a group of high-level mathematicians and y is an improvisational theater workshop. This one’s easy, even if you’re not very good at math. We’ll also look at Mayor Eric Adams’s fund-raising.Michelle V. Agins/The New York TimesWhat’s funny about quadratic equations? Is there something to laugh at in Euclidean geometry?Those questions went unanswered in unusual coaching sessions last week, and no wonder: The instructor’s background is not in Cartesian geometry or matrix algebra but in improvisational theater and standup comedy.The students were mathematicians from across the country — assistant professors, postdoctoral students and a few who are months away from their Ph.D.s, along with Cindy Lawrence, the executive director and chief executive of the National Museum of Mathematics, which arranged the three-day workshop.The sessions were “not so much about being funny,” explained the instructor, Kihresha Redmond, the artistic director of the People’s Improv Theater, a comedy theater and improv training center on West 29th Street that is also known as the PIT. The purpose was to show the mathematicians how to do engaging presentations for laypeople.“You don’t get a Ph.D. because you’re just so-so at something,” Lawrence said, but mathematicians “may not be quick at responding to an audience and they may not be comfortable in front of a room of strangers. Improv helps you build those kinds of skills.”Redmond did not mention it to the group, but she knew something about math. “I thought it was something I was going to major in” when she went to college, she confided one morning last week, before the group arrived. “It was a last-minute left turn to theater.”One session with the mathematicians involved no scripts, no carefully rehearsed “to be or not to be” moments — and no math. It began with Redmond leading some loosening-up exercises. Later, as a drill in thinking fast and talking in front of an audience, she had the mathematicians conduct mock news conferences. They made up companies and products to promote and assigned someone in the group to be the spokeswoman fielding questions. The others in the group played reporters.Angela Avila, a Ph.D. candidate at the University of Texas at Arlington, said the think-on-your-feet training would be useful in her work, which involves using math to solve agricultural problems, like how many more cows could be fed in a given pasture if a dairy farmer increased the nutrient yield.She said she could use artificial intelligence and “big fancy equations” to come up with an answer, but if she explained it that way, there would probably be a lot of head-scratching.“If I am speaking line from line on my research paper, they’d get lost,” she said, “but if I connect with them and read the energy in the room, that won’t happen.”Lawrence, from the math museum, said she had invited women to the workshop because women are underrepresented in mathematics and in science, technology and engineering. “It’s a problem that self-perpetuates because young women who don’t see female mathematicians get the impression that math is a field that’s not for them, it’s for men,” she said.She wants the participants to help bring about more balance by serving as role models for girls: Each workshop participant is to present a talk about her specialty in a setting like a middle school. She said the idea was “to incentivize women who maybe already have an interest in reaching the younger generation to do so” before their focus is on the publish-or-perish pressures of tenure-track academics.“One of the women told me she was not looking forward to improv and went along with it because it was part of the program,” Lawrence said. “She said this turned her mind completely around.”WeatherOn a partly sunny day with a high near the mid-80s, prepare for a chance of showers and thunderstorms persisting through the evening. At night, temps will drop into the low 70s.ALTERNATE-SIDE PARKINGIn effect until Aug. 15 (Feast of the Assumption).The latest New York newsJohnny Milano for The New York TimesGilgo Beach killings: The wife of Rex Heuermann, the suspect in the Gilgo Beach murders, was away when the killings happened and has not been charged. Experts say it’s not unusual for the spouses of serial killers to be unaware of their crimes. Rikers management: The federal judge in charge of deciding whether New York City jails will be taken over by an outside authority expressed disapproval of how Rikers Island and other lockups are managed.Housing moves: Gov. Kathy Hochul announced a series of executive actions to promote residential real estate development and ease the state’s housing crisis.Museum director: Stephanie Hill Wilchfort, who most recently served as the president and chief executive of the Brooklyn Children’s Museum, will be the next director and president of the Museum of the City of New York.Remembering Chisholm: City officials approved designs for a monument in Prospect Park to Shirley Chisholm, the first Black woman elected to Congress.Landmarks’ protector: Beverly Moss Spatt, who battled real estate and political interests as chairwoman of the city’s Landmarks Preservation Commission in the 1970s, died on Friday. She was 99.Amassing cash for a campaign that’s two years awayBenjamin Norman for The New York TimesEric Adams was a prodigious fund-raiser when he ran for mayor in 2021. Now, with his eye already on a second term, he is raising big money for 2025 — $1.3 million since January.My colleagues Emma G. Fitzsimmons and Nicholas Fandos write that Adams appears to be eager to amass a large war chest to fend off serious competitors. He faced seven serious opponents in the Democratic primary two years ago and won by only 7,197 votes.With matching funds that Adams campaign officials expect to receive under the city’s public financing system, his re-election effort is expected to have about $4.6 million on hand by the time the 2025 campaign gears up. The matching funds program can turn a $10 contribution from someone who lives in New York City into $90 for a campaign.Adams could be difficult to beat, despite recent setbacks. Chris Coffey, a Democratic strategist who was a campaign manager for Andrew Yang, an Adams opponent two years ago, said the mayor’s low approval rating was not terribly worrisome — it fell to 46 percent in a Siena College poll last month. Coffey noted that Michael Bloomberg’s approval rating dipped as low as 24 percent in his second year in office, but he went on to win two more terms.Among Adams’s donors are Marc Holliday and Steve Green, the chief executive and founder, respectively, of the city’s largest commercial landlord, SL Green. Each gave $2,100. Also on the list of Adams contributors are Alexander and Helena Durst, from the Durst real estate dynasty. In addition, the mayor has taken in $12,600 from people who work for Top Rock Holdings, a real estate investment firm.A fund-raiser for the mayor at a performance of the Broadway musical “New York, New York” last month was lucrative despite lackluster reviews for the show. Seats went for as much as $2,100 apiece. Adams’s campaign took in about $600,000 from the event, which a campaign spokesman said was organized by Frank Carone, Adams’s former chief of staff.The real estate industry is also making donations to Gov. Kathy Hochul, whose term runs through 2026. Of the $4.5 million her campaign raised from January through June, more than $885,000 came from developers and real estate investors. Among the donors contributing $18,000 — the new legal maximum for statewide candidates — were Holliday; members of the Durst family; and Scott Rechler and Jeff Blau. Both are Democratic megadonors whose firms are competing with Holliday’s for a casino license for the New York City area.METROPOLITAN diaryA sliceDear Diary:He carried the box while they held each other’s hands, their sweat stuck between warm, tanned palms.They walked down the cobblestone street, and she kept her heels out of cracks in the ground. New York heat held her neck. It smelled like new deodorant, smoke, like summertime.She put her head near his ear.They sat at the bottom of a Brooklyn stoop — the lights were on — and he passed her a slice.Their elbows touched.She wiped the corner of his lip and put her leg over his.He traced constellations between spots of orange oil on her scabby knees.“It tastes good,” she said.“The cheese?” he asked with a laugh.“Yeah.”He whispered in her ear.“But we’re on the street,” she said.“Come on,” he said, and took her hand again.— Laila Hartman-SigallIllustrated by Agnes Lee. Send submissions here and read more Metropolitan Diary here.Glad we could get together here. See you tomorrow. — J.B.P.S. Here’s today’s Mini Crossword and Spelling Bee. You can find all our puzzles here.Melissa Guerrero, Shivani Gonzalez and Ed Shanahan contributed to New York Today. You can reach the team at nytoday@nyimes.com.Sign up here to get this newsletter in your inbox. More

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    Pandemic Learning Loss

    The role remote education played.Months into the current school year, most American students are still trying to make up for what they lost during the pandemic. This fall, we saw some of the clearest evidence yet of the extent to which the pandemic — and the school closures that came with it — hurt children’s education.Nine-year-olds lost the equivalent of two decades of progress in math and reading, according to an authoritative national test. Fourth and eighth graders also recorded sweeping declines, particularly in math, with eighth-grade scores falling in 49 of 50 states.The data comes from the National Assessment of Educational Progress, a rigorous exam that evaluates thousands of children across the country and is overseen by a research arm of the U.S. Education Department.Today, I’ll break down the factors that drove these declines and explain an important trend that helps show why these results are so sobering.Remote learning’s roleFirst, to address one of the most common questions I hear as an education reporter: To what degree is remote learning responsible for these setbacks? The answer is both simple and complicated.At a basic level, there is good evidence and a growing consensus that extended remote learning harmed students. Some state test results from 2021 help show the damage. In Ohio, researchers found that districts that stayed fully remote during the 2020-21 school year experienced declines up to three times greater than those of districts that mostly taught students in person.More recently, the national test results capture both the initial academic declines and any recovery, and they offer some nuance. While there was a notable correlation between remote learning and declines in fourth-grade math, for example, there was little to no correlation in reading. Why the discrepancy? One explanation is that reading skills tend to be more influenced by parents and what happens at home, whereas math is more directly affected by what is taught in school.So remote learning does not explain the whole story. What else does? In a sophisticated analysis of thousands of public school districts in 29 states, researchers at Harvard and Stanford Universities found that poverty played an even bigger role in academic declines during the pandemic.“The poverty rate is very predictive of how much you lost,” Sean Reardon, an education professor at Stanford who helped lead the analysis, told me.Comparing two California school districts, one wealthier and the other poorer, illustrates this point. Cupertino Union, a Silicon Valley school district where about 6 percent of students qualify for free or reduced lunch (a marker that researchers use to estimate poverty), spent nearly half of the 2020-21 school year remote. So did Merced City in the Central Valley, where nearly 80 percent of students are eligible for free or reduced lunch, according to the Harvard-Stanford analysis.Yet despite spending roughly the same amount of time attending classes remotely, students in the wealthier Cupertino district actually gained ground in math, while students in poorer Merced City fell behind.High vs. low performersWhile the overall declines in student achievement were stark, the averages mask even deeper divergences between student groups. For example, Black and Hispanic students, who had started out behind white and Asian students in fourth-grade math, lost more ground than those groups during the pandemic.Notably, the gap is also growing between the country’s highest-achieving students and low-performing students who struggle the most.That gap — driven by declines among lower performers — was most clear for younger students and in reading. (Middle-school math declines were more significant across the board.)In fourth grade, the average reading score on the national exam fell three points. But results for students in the top 90th percentile did not fall at all, while those for students in the bottom 10th percentile plunged six points, double the overall average.In other words: The students who had the least ground to lose lost the most.There may be a twofold explanation. Recent research from NWEA, a nonprofit academic assessment organization, found that students at the bottom of their classes both experienced sharper setbacks at the start of the pandemic and showed less improvement last school year.I am sometimes asked: If the pandemic affected all students, how much does it matter? Isn’t everyone behind?What the latest data affirmed is that while the pandemic affected all students, it did not affect all students equally. That was true with remote learning, and it is playing out now in recovery. The students who had the greatest needs coming into the pandemic have the steepest challenge — and will need the most help — in the future.Related: On “The Daily,” I explained what schools can do to help students recover.THE LATEST NEWSProtests in ChinaDemonstrators in Beijing.Kevin Frayer/Getty ImagesChina has witnessed its most defiant eruption of public anger in years, after a deadly apartment fire last week set off nationwide protests against Covid lockdowns.Anger with Xi Jinping, China’s leader, helps explain how the demonstrations gained momentum.Chinese spam flooded Twitter and obscured news about the protests, The Washington Post reported.PoliticsA strong midterm performance eased some Democrats’ fears about President Biden’s potential re-election bid.Attorney General Merrick Garland is recalibrating his political approach as the Justice Department investigates Donald Trump.Biden’s sweeping marijuana pardons do not apply to many people with minor convictions.Other Big StoriesGunmen in explosive vests stormed a hotel in Somalia, trapping government officials in an ongoing siege. The militant group Al Shabab claimed responsibility.A small plane crashed into power lines in Maryland, injuring two people and knocking out electricity to roughly 117,000 customers.Many developed countries have reduced roadway deaths, but the U.S. has failed to keep up.“I simply wanted to save the family I found”: Another patron helped stop the shooter during the attack on an L.G.B.T.Q. nightclub in Colorado Springs.Millions of people in Houston were told to boil drinking water and schools were closed after a power failure at a purification plant.OpinionsGail Collins and Bret Stephens discuss gun violence.Just ignore Donald Trump, Patti Davis, a daughter of Ronald Reagan, writes.To protect patients, give older doctors competency assessments, Dr. Sandeep Jauhar writes.MORNING READSA wind farm in the North Sea.Francesca Jones for The New York TimesGreen transition: Oil and gas workers are finding jobs on Scotland’s wind farms.Vows: They met in an elevator and danced their way to a “beautifully intoxicating” romance.Metropolitan diary: The upside of a forgotten phone.Quiz time: Take our latest news quiz, and share your score (the average was 9.4).Advice from Wirecutter: The best advent calendars.Lives Lived: Irene Cara was an Oscar-winning singer who performed the title tracks for “Flashdance” and “Fame.” She died at 63.SPORTS NEWS FROM THE ATHLETICEagles beat Packers: Philadelphia maintained the N.F.L.’s best record with a 40-33 win over the Packers late last night. Aaron Rodgers left the game with a rib injury.No. 1 goes down: The Alabama men’s basketball team upset top-ranked North Carolina in four overtimes.WORLD CUPMorocco’s Zakaria Aboukhlal scores against Belgium.Amr Abdallah Dalsh/ReutersShock: Morocco upset Belgium, leading to riots in Brussels. And Canada is out after losing to Croatia. Manager John Herdman’s ill-fated bravado before the match proved disastrous.Powers draw even: Germany kept its tournament hopes alive with a 1-1 tie against Spain.Taking stock: Do all these upsets make for a more exciting tournament?Protest battle: Iran called for the U.S. to be expelled from the competition over a social media post featuring an altered flag.Photo collage: A V.I.P. entrance at Qatar’s showpiece stadium replaced a mural celebrating migrant workers.Today: Cameroon is playing Serbia, and Brazil will face Switzerland this afternoon — though without its star, Neymar, who is injured. Here are the latest scores.ARTS AND IDEAS The modern wine barPlace des Fêtes in Brooklyn.Karsten Moran for The New York TimesThey’re popping up all over New York City. But what is a wine bar, anyway?American wine bars used to be a novelty — a space for customers to learn about the intricacies of a bottle’s taste and production. They have evolved over the last few decades, finding success with a new formula: simple food, casual atmosphere, inexpensive wine by the glass.This relaxed approach sets wine bars apart from restaurants. “Good wine bars are informal neighborhood gathering places rather than destinations, with occasional exceptions,” our critic Eric Asimov writes. Some of his favorite wine bars introduce new trends, like natural and orange wines.For more: Eric picks New York’s best wine bars.PLAY, WATCH, EATWhat to CookPeter DaSilva for The New York TimesCacio e Pepe is simple but incredible.What to seePuerto Rican artists at the Whitney.What to WatchAn “Unsolved Mysteries” reboot from an executive producer of “Stranger Things,” and six other shows to binge.Now Time to PlayThe pangram from yesterday’s Spelling Bee was workload. Here is today’s puzzle.Here’s today’s Mini Crossword, and a clue: Moon goddess (four letters).And here’s today’s Wordle. After, use our bot to get better.Thanks for spending part of your morning with The Times. See you tomorrow.P.S. Amanda Choy and Mantai Chow are joining Times Cooking to produce documentary-style videos.Here’s today’s front page. “The Daily” is about the World Cup.Matthew Cullen, Lauren Hard, Lauren Jackson, Claire Moses, Ian Prasad Philbrick, Tom Wright-Piersanti and Ashley Wu contributed to The Morning. You can reach the team at themorning@nytimes.com.Sign up here to get this newsletter in your inbox. More