Why Evolution is True is a blog written by Jerry Coyne, centered on evolution and biology but also dealing with diverse topics like politics, culture, and cats.
We have a short RWP today as there are more posts to come. First we hear from Robert Lang, who sees a surprising amount of wildlife near his home in the eastern LA “suburb” of Altadena. Robert’s intro is indented, and you can enlarge the photo by clicking on it.
Although every day sees another few housing starts in post-fire Altadena, it’s still mostly empty of people, but after a year that included plenty of rain, the vacant lots are lush with plants—a mix of native coastal sage scrub, invasive weeds, and landscaping gone wild. This temporary rewilding provides plenty of cover for the local wildlife to come down out of the hills and hang out. Yesterday the workers at our site reported that a bear had stopped by and done a walk-through of the framed house (fortunately, just lookie-looing, no damage). Today I did a short hike on the Gabrielino Trail above my old stomping ground of JPL and saw a different (younger) California black bear (Ursus americanus californiensis) just off the trail, and I shot the photo below. . .
. . . also this video.
This isn’t the bear species on the California state flag, which is the California grizzly bear (Ursus arctos californicus); that was native to this area but was hunted to extinction in the early 20th century. In the 1930s, 28 “problem bears”, California black bears, were taken from Yosemite and released in the San Gabriel and San Bernardino Mountains of Southern California. The black bear species is highly variable in coloration, ranging from black through brown, blond, and even white (the so-called “spirit bears” of British Columbia). Most of the bears we see in Altadena are brown, like this youngster, all descended from the original Problematic Twenty-Eight.
JAC: Here’s the California state flag sporting a grizzly:
Original: Donald Graeme Kelley. Vectorization: Devin Cook, Public domain, via Wikimedia Commons
Welcome to Sunday, May 31, Sabbath for goyische cats and World Parrot Day. I can do no better than show a great photograph of a very rare and unusual parrot, the Australian Golden-shouldered parrot (Psephotellus chrysopterygius), here photographed by Scott Ritchie. The parrot is endangered, with a total population of about 1000 birds. And it’s the world’s only parrot that lives in termite mounds. Further, it has a symbiotic relationship with a moth species!. From Wikipedia:
The golden-shouldered parrot breeding season occurs from March to August. They construct nests in termite mounds, with a strong preference for conical shaped mounds. A 50–350 mm (2.0–13.8 in) long tunnel is excavated into the mound, ending in the nesting chamber. The clutch size is between 3–6 eggs, which are incubated by the female for 20 days. The termite occupants of the mound use a natural form of air conditioning to preserve the climatic conditions of their colony and this process regulates the temperature of the parrot’s nest chamber at around 28–30 °C (82–86 °F). Temperature surveys have shown, however, a range of 13–35 °C (55–95 °F). These conditions have led to the parrots developing a habit of leaving the eggs at night beginning around the 10th day after hatching. A symbiotic relationship is present between the golden shouldered parrot and the moth species Trisyntopa scatophaga, the antbed parrot moth. Found in around half of parrot nests, the moths seek out the newly dug nest tunnels and deposit their eggs in the entrance. The hatching moth larvae consume the faeces of the nestling parrots therefore helping to keep the nest chamber clean. Whether the parrots receive any other benefits from the presence of moths is arguable as not all nests contain moth larvae.
Scott tells me that the moth larvae also line the parrot’s burrow with silk, giving an easier ride to the incubating eggs. Amazing! Here’s Scott’s photo:
I slept poorly last night, though I had a series of dreams. I remember only one, right before I awoke. My sister was leading me through some village that harbored dozens of cats that were underfoot. She pointed one of them out to me, a Siamese/tabby hybrid with an amiable expression and huge paws. I was told its name was “Pawsome.” That’s all I remember.
Readers are welcome to mark notable events, births, or deaths on this day by consulting the May 31 Wikipedia page.
US forces attacked a cargo ship they claimed was attempting to breach their naval blockade of Iran on Saturday.
Centcom said Lian Star ignored over 20 warnings before its forces struck the Gambia-flagged vessel’s engine room with a missile, stranding it in the Gulf of Oman.
The incident came as Tehran awaits the US president’s response to a proposed peace deal, as efforts to bring an end to the war drag on.
A senior official accused Trump of “betraying diplomacy for the third time”. Mohsen Rezaei pointed at the continuing naval blockade and what he called the president’s excessive demands in negotiations as he blamed the White House for failure to reach a peace deal.
Meanwhile, in Lebanon, Israeli troops pushed beyond the Litani river and seized the Crusader-era Beaufort fortress in their deepest invasion of the neighbouring country in over 25 years.
The military said it was prepared “to expand the operation if needed”.
On Friday morning, it issued a fresh evacuation warning for residents south of the Zahrani River in southern Lebanon.
And from the NYT on Lebanon:
Once again, there has been a cease-fire in Lebanon for weeks.
And, once again, the fighting has not stopped.
Israel is still bombarding much of the south and east of the country. Israeli drones are still buzzing low over the skies in Beirut, the capital. Hezbollah is still attacking Israeli troops occupying Lebanese territory, and firing rockets into Israel. The death toll is still rising.
And now — though a truce was declared in April, and there has been talk this week of a potential U.S. deal with Iran, Hezbollah’s sponsor — resignation is setting in across Lebanon that a meaningful end to the war between Israel and Hezbollah is not coming anytime soon.
The blockade on ships leaving Iran, or trying to enter Iranian ports, is apparently still in effect, no matter what flag they’re flying, and Hezbollah is still refusing to disarm. (The chances of that are about equal to the chances that Hamas will disarm. Both are supposed to, but that ain’t gonna happen.) The war is going to continue for a while, and I don’t see a cease-fire in Lebanon.
A federal judge ordered on Friday that the John F. Kennedy Center for the Performing Arts remove President Trump’s name from the building’s facade and all official branding and temporarily blocked the institution from shuttering this summer for renovations.
Mr. Trump railed against the judge’s ruling in an incensed social media post, suggesting that he was considering casting theKennedy Center aside as one of his personal projects. The president wrote that unless he was free to decide the center’s trajectory, he had “no interest in continuing what could only be a hopeless journey.”
“Unfortunately, Judge Cooper and the Radical Left would rather see it DIE than have President Trump transform it into something that everyone could be proud of, much as I have done, in many cases, throughout my life,” he wrote.
Judge Christopher R. Cooper, of the Federal District Court in Washington, determined that the board’s decision to add Mr. Trump’s name to the Kennedy Center violated a law passed by Congress in 1964 that made “crystal clear” the institution was to be named for former President John F. Kennedy.
“Congress gave the Kennedy Center its name, and only Congress can change it,” the judge wrote in a 94-page opinion. He ordered that the 18 letters added to the center’s front portico be removed within two weeks.
The center’s board of trustees, a vast majority of whom are allies of Mr. Trump, voted in December to add the president’s name to the performing arts center. Less than a day later, new lettering was added to the building’s marble facade, which now reads: “The Donald J. Trump and the John F. Kennedy Memorial Center for the Performing Arts.”
Here’s the last big of Trump’s Truth Social post on the kerfuffle (link above; it’s too long to quote in full). It reads like the gibberish of someone who’s partly demented: full of caps and braggadocio. “Your favorite President, ME. . . “, “Unless I am free to do what I do better than anyone else. . . “, etc.
Therefore, based on the fact that the Radical Left Democrats care more about opposing your favorite President, ME, than saving a dying Performing Arts Center, almost all of which lose large amounts of money throughout the Country, we are going to be working with Congress to transfer this failing Institution back to them so they can make a determination as to what to do with it. Judge Cooper was given a presentation by leading Building and Construction Experts as to how structurally dangerous the Building is, with rotting beams, parking areas that are subject to collapse, and various other Life and Safety problems, in addition to the fact that it also needs a MAJOR renovation, from an aesthetic standpoint, but he was not “swayed,” and said he wants the Building to, incredibly, remain open and, therefore, dangerous. Judge Cooper should be ashamed of himself! I cannot be involved with a situation where danger to the Public is allowed to flourish in plain and open sight. Unless I am free to do what I do better than anyone else, bring this Institution back, physically, financially, and artistically, I have no interest in continuing what could only be a hopeless journey into “NEVER NEVER LAND.” There has never been a President of the United States who has been treated so unfairly by the Courts as I but, that’s OK, I will continue to do, what is considered to be, a great job for the wonderful people of our Country. I have instructed the Department of Commerce to make all necessary arrangements with Congress to allow a full and complete transfer of this Institution, giving them the responsibility for its Operation, Maintenance, and Management. Thank you for your attention to this matter! President DONALD J. TRUMP
I wonder if this one will go all the way up to the Supreme Court. Trump is both a narcissist and persistent, so I wouldn’t be surprised.
The United Nations on Friday added Israel and Russia to a U.N. blacklist of countries suspected of committing sexual violence in conflict zones, a move that prompted Israel’s foreign ministry to say it would sever all ties with U.N. Secretary-General Antonio Guterres.
Guterres’ annual report to the U.N. Security Council on conflict-related sexual violence, opens new tab goes a step further than last year, when he put Israel and Russia “on notice” that they could be added to the list of parties “credibly suspected of committing or being responsible for patterns of rape or other forms of sexual violence.”
The latest report does that and contains harrowing descriptions of abuses at the hands of Israeli and Russian armed and security forces.
Israel’s arch enemy Hamas, whose October 7, 2023, attack on southern Israel triggered the war in Gaza, was already on the blacklist and in a post on X on Thursday, Israel’s U.N. Ambassador Danny Danon said ranking Israel with the militant group marked a “new low”.
. . . “This is a political decision! Disconnected from the facts and reality!” Danon said in another post by the Israeli mission to the U.N. which said he was informed about it during a phone call with Guterres.
. . . The U.S. ambassador to the United Nations, Mike Waltz, posted on X that it was “ridiculous for the UN to put a democracy like Israel — with robust rule of law that conducts investigations and holds criminals accountable — on the same level as terrorist organizations like Hamas.”
. . . Being added to the list does not automatically carry specific punitive measures such as sanctions, although public naming and shaming can cause significant reputational damage for the states involved, and those repeatedly listed are barred from U.N. peacekeeping operations.
. . . Danon said Israel had responded in detail to each allegation and had invited U.N. representatives to visit and examine the situation, but that they had chosen not to do so.
. . . This year’s report said that in 2025, “the United Nations verified multiple incidents of conflict-related sexual violence, including as a form of torture, inflicted against 14 men, seven women, nine boys and one girl from the Gaza Strip and the West Bank.”
It said 13 of the cases occurred in 2025, and 18 in 2023 and 2024.
“Violations consisted of rape, including with objects, gang rape, attempted rape, physical violence to the genitals, instances of targeted shooting of the genitals, touching of breasts and genitals, strip and cavity searches conducted without apparent security justification, forced nudity and threats of rape,” it said.
“Rape and gang rape, in some cases repeated, were perpetrated against nine victims, the majority from Gaza,” it said, adding that perpetrators included Israeli armed and security forces and occurred primarily during detention and interrogation and across several sites, including military camps and also at checkpoints and during Israeli military operations in the Occupied Palestinian Territory.
It said survivors included journalists and human rights defenders and that in some cases, the violations were filmed or photographed, including one case of rape.
What bothers me is the UN’s refusal to meet with Israel to discuss the evidence as well as hear Israel’s response to the allegations. Of course one can’t say that all the claims our false, but evidence is needed and it’s bothersome that the UN refuses to meet with Israel—especially after Israel issued a documented report on the many cases of sexual attacks by Hamas on Israelis.
That of course doesn’t mean that any victimization of prisoners by Israel is okay, for one is too many, and it’s against Israeli law. But if you assume that Israel has 20,000 prisoners, and that the UN is correct in claiming a total of 31 victims of Israeli sexual violence over three years (some were only threatened with sexual violence), and assume further that the U.S. has 2.2% annual allegations of sexual violence or abuse of prisoners by staff in a nationwide prison population of 1.25 million (all figures from AI)—then the U.S. has an annual rate of sexual violence/abuse of prisoners by staff 44 times higher than Israel’s. The UN should add the U.S. to their list.
President Trump “remains in excellent physical health,” according to a memo from his physician released late Friday by the White House, following the president’s physical at Walter Reed National Military Medical Center earlier this week.
The president’s physician, Navy Capt. Sean Barbabella, said in a memo that the Tuesday exam, Trump’s third since returning to office, included comprehensive and preventive laboratory testing “as well as consultations with twenty-two specialty providers from multiple academic institutions.”
Barbabella said in the report that “preventive counseling was provided, including guidance on diet, recommendation to take a low-dose aspirin, increased physical activity, and continued weight loss.” The president weighed 238 pounds, 14 pounds more since his 2025 exam, according to Barbabella, a career military doctor who served in Iraq and Afghanistan.
He added that the president’s “cognitive and physical performance are excellent” and Trump “is fully fit to carry out all duties of the commander in chief and Head of State.” The physician concluded after neurological and cognitive function tests that the president “demonstrated normal mental status.”
Trump, who will turn 80 years old on June 14, is the oldest person to ever assume the presidency. The results of his physical come amid increased scrutiny about presidential health. Former President Joe Biden faced questions about slipping physical fitness and mental acuity, which Trump bolstered on the campaign trail.
. . .Barbabella previously diagnosed Trump with chronic venous insufficiency, a condition in which valves inside the veins don’t work properly and allow blood to collect or transmit down the leg. The physician provided an update on the swelling in Trump’s lower legs, describing it as “slight” and an “improvement from last year.”
Barbabella reported that Trump takes two medications to treat high cholesterol, Rosuvastatin and Ezetimibe, as well as aspirin as a preventive heart measure. The physician noted that Trump benefits from “lifelong abstinence from tobacco and alcohol.”
Barbabella wrote that Trump’s “demanding daily schedule, including multiple high-level meetings, public engagements, and regular physical activity, continues to support his overall well-being.”
Aside from golf, Trump doesn’t get regular exercise, and he is known to consume a diet heavy on salty and fatty foods, such as hamburgers and french fries.
Given his horrible diet and sedentary lifestyle, I suppose he is in good shape for 80. I woiuldn’t wish illness or death on anyone, including Trump, and perhaps some may be glad that he stays alive for 2.5 more years because it keeps Vance from becoming President.
Over the course of his early tenure as mayor, Zohran Mamdani has filled out City Hall’s upper ranks with people he trusts to implement his democratic socialist-inflected agenda in New York City, the nation’s financial capital.
But one arm of city government continues to bedevil him: the Economic Development Corporation, whose mission is to leverage city real estate and tax incentives to attract private capital and drive job growth across the five boroughs.
Five months into the mayor’s tenure, the nonprofit corporation remains officially rudderless, with City Hall officials considering at least 10 candidates for E.D.C. president, including a consumer protection advocate and pro-business types. But the mayor’s team has been unable to coalesce around any of them, illustrating an internal debate over how to direct the organization.
The uncertainty surrounding the E.D.C.’s leadership and direction has fed the notion, widespread among business leaders and moderate Democratic politicians, that Mr. Mamdani is insufficiently attuned to the health of New York City’s economy, and that his inattention potentially comes at his, and the city’s, peril.
It also raises larger and more fundamental questions: What kind of economic policy does the mayor want to embrace? And is Mr. Mamdani quietly withdrawing from City Hall’s traditional role of courting business and using the E.D.C.’s power to support a thriving economic climate in New York?
“I have not heard one statement yet about how it is that the city sees industry growth, how the city wants to maximize talent, and, certainly, the absence of an E.D.C. head this far into the administration is a concern,” said Gregory Morris, the chief executive of the New York City Employment and Training Coalition.
When the mayor talks about the economy, he largely talks about his ambitious universal day care and housing programs, and how they will redound to the city’s economic benefit — a prediction that some analyses agree with.
But some business and work force development leaders argue that Mr. Mamdani cannot fulfill his vision for a more expansive government without a robust, tax-generating economy. They note that affordability requires not just cheaper goods, but also better-paying jobs. And they worry that he has yet to articulate what business growth in the Mamdani era will be, at a time when the challenges facing New York’s economy are legion.
The city’s job numbers are lackluster, even as office leasing has strengthened. Some financial sector jobs have migrated to Texas. The war in Iran continues to cast a haze over the country’s economic prospects. City officials are eyeing the coming disruptions from artificial intelligence with alarm. International tourism has declined.
Here’s Sam Harris’s take on Mamdani; and I agree with Sam’s take that the Mayor is a “none too closeted Islamist, or at minimum an apologist for Islamists.” As for his wife’s social media “likes”, it’s not clear that that is any reflection of Mamdani’s beliefs.
Szaron: Do you think it’s safe there?
Hili: I think so, it looks like the dog is locked up.
In Polish:
Szaron: Myślisz, że tam jest bezpiecznie?
Hili: Chyba tak, wygląda na to, że pies jest zamknięty.
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From TherionArms, another great medieval letter with commentary:
Masih is still at war with AOC’s desire to “respect” local customs, which involved her wearing a hijab and speaking to a sex-segregated crowd (men in front, women in back):
You find hijab “fun.” #MahsaAmini called it a death sentence.
That’s not a custom. That’s not a fun learning experience. That’s a woman’s life. Women live under Sharia laws are not your cultural tourism. We are dying for the freedom you… https://t.co/bhGNSdbOFkpic.twitter.com/c2TsajV7SO
From Luana; Jonathan Kay continues his exposé of the paucity of empirical evidence for these bodies, which nobody has bothered to investigate thoroughly:
Today is the 5th anniversary of the 1st fake news reports that “bodies of 215 children” were found in Kamloops. (No bodies were ever found.) The 1st to report was local radio station CJFC. Here is the historic tweet that set off the biggest journalistic disgrace in Cdn history… https://t.co/aD2UMDtZ3s
Do not hurt opossums! They are wonderful! Look at all those babies holding on:
Don’t harm opossums! They’re harmless and actually really useful. They keep pests in check (eating ticks, roaches, rats, and scorpions), clean up dead animals, and help spread seeds. Basically, they’re nature’s cleanup crew pic.twitter.com/Qiz3jJYuJq
And one from Dr. Cobb. Look at those cute pink babies!
Deborah Sandidge Photography"A dedicated pair of Roseate Spoonbills watch over the nest, taking good care of the chicks. They spend time reinforcing the nest together. Each branch placement ensures the chicks stay safe, a process they continue as they grow up in their wetlands home."
Here’s the latest opinion/comedy bit from Friday’s Real Time show with Bill Maher, with the episode called “Let’s be frank.” Maher starts out by citing the recent Democratic Party Autopsy (here) about why the party lost the Presidency and Congress in 2024. But he then faults both parties for having politicians in office who won’t be honest (surprise!).
Honesty, he avers, can be found only in books politicians write after they have left office. Maher gives several examples, including Republicans who admit, after they leave office, that Trump is paying off the January 6 insurrectionists with a “slush fund.” And don’t forget, he adds, Eisenhower’s warning about the “military industrial complex,” issued just three days before he left office.
The key diagnosis, Maher says, was made by the late Barney Frank when he was in hospice. It’s cited in the Times of Israel:
“The key to liberal democracy being able to come back is to get rid of the perception that we have allowed to grow, that the entire Democratic Party is committed to a series of very drastic social reconstructions that go beyond the politically acceptable,
Maher says, “And there, in one sentence, is the autopsy the Democrats have been so desperately searching for.” True! And of course this explains the capitalized “Frank” in the title.
The theme, then, is that Democrats say the truth about the party only when they have nothing to lose for speaking up.
Finally, Maher notes that some red states are better than his own “progressive” state—California—in education and in green energy. The last bit: “Democrats: these are your issues: education, race, the environment. And I say this with love: you’re losing to the Waffle House car-on-the-lawn states.” Well, we’ll see how the Democrats do in this fall’s midterms, though the most crucial election is in 2028.
The guests for this episode were astrophysicist Neil deGrasse Tyson, MS Now news correspondent Katy Tur, and former Speaker of the House Kevin McCarthy. Tyson is not shown in this segment.
I don’t wholeheartedly embrace AI, for I think it will be the death of liberal education. In both the humanities and science, I fear that students will lose any ability they have to write, and will not improve their writing because they’ll be using bots. This will degrade their ability to communicate. (Scientists too need to communicate, and if they rely solely on bots, which can write papers for them, they’ll also degrade their ability to think.) Take-home assignments will vanish (AI can do them, and are doing them now), and all that’s left are in-class verbal participation and in-class exams. This is fine for students who just think of college as a way to purchase accreditation and not a chance to glory in the joys of learning, but so be it.
However, AI is good for some things, including analyzing data, doing statistics, doing preliminary literature searches, and, in the article from the WSJ screenshot below, solving difficult math problems. The article shows that a problem posed by the famous and eccentric Hungarian mathematician Paul Erdös—the “unit distance problem” has been solved by AI. Open AI, which created the program that did it, describes it this way—but it’s not that simple:
For nearly 80 years, mathematicians have studied a deceptively simple question: if you place nn points in the plane, how many pairs of points can be exactly distance 1 apart?
This is the planar unit distance problem, first posed by Paul Erdős in 1946. It is one of the best-known questions in combinatorial geometry, easy to state and remarkably difficult to resolve. The 2005 book Research Problems in Discrete Geometry, by Brass, Moser, and Pach, calls it “possibly the best known (and simplest to explain) problem in combinatorial geometry.” Noga Alon, a leading combinatorialist at Princeton, describes it as “one of Erdős’ favorite problems.” Erdős even offered a monetary prize for resolving this problem.
The “distance 1” thing confused me, and Wikipedia explains it a different way:
A problem posed by Paul Erdős known as the unit distance problem asks for the maximum possible number of unit-distance pairs determined by n points in the Euclidean plane; equivalently, it asks for the maximum number of edges in a unit distance graph on n vertices.
It gives a figure described as “a unit distance graph with 16 vertices and 40 edges”.
Wikipedia describes such unit distance graphs this way:
“In mathematics, particularly geometric graph theory, a unit distance graph is a graph formed from a collection of points in the Euclidean plane by connecting two points whenever the distance between them is exactly one.”
That’s what is confusing me, for if the theorem deals only with points in a two-dimensional plane, why aren’t unconnected dots not joined that are closer than some connected dots? (Look at the four dots around the center of the graph above. None of them are connected to each other, though more distant one are.) I presume some math-savvy reader will enlighten us.
Anyway, Open AI and the WSJ tells us that the problem has been solved by AI. If you want to see the solutions, open AI says this:
But the WSJ gives more comprehensible details. Click screenshot to read (if you subscribe):
An excerpt:
“If you are a mathematician,” one of the world’s leading mathematicians recently wrote, “you may want to make sure you are sitting down before reading further.”
And you’ll definitely need to sit down if you’re not a mathematician.
Because a famous math problem that stumped humans for the better part of a century has finally been toppled—by AI.
Not long ago, the most advanced AI models couldn’t do basic math. By last year, they were performing at gold-medal levels at the International Mathematical Olympiad. Now they are solving classic problems in combinatorial geometry using algebraic number theory. In no time at all, artificial intelligence has gone from stupid to frighteningly smart.
But even mathematicians were astonished when OpenAI announced that one of its models resolved a puzzle known as the unit distance problem without the help of any humans scribbling a bunch of equations on chalkboards.
It was fed this prompt:
And produced this proof, giving the maximum number of unit-distance pairs:
Apparently the proof was accepted by mathematicians. More from the WSJ:
And everyone in math lost their minds.
For those who aren’t fluent in numbers, OpenAI helped translate its findings by presenting them alongside 19 pages of companion remarks from prominent mathematicians.
. . .Just looking at formulas is enough to hurt my brain, but I wanted to know more about what the AI found, how we humans missed it—and why this breakthrough matters to those of us who would like to permanently distance ourselves from math problems.
When I spoke with OpenAI employees, they told me this result would have sounded completely bananas one year ago.
“Forget one year ago,” researcher Sebastien Bubeck said. “A month ago.”
There are endorsements by mathematicians, and a history of the problem, which Erdös considered quite difficult. So difficult, in fact, that he offered what was then a pretty hefty sum for anybody who could solve it: $500. I think the money will be given to the OpenAI team.
OpenAI’s researchers were stunned. They had given this Erdős problem to an internal model as a test of its capabilities—to find out whether it was better than previous models. They found out how much better it was once they took a peek at the solution. “I initially didn’t believe it,” said Mehtaab Sawhney, a Columbia mathematician at OpenAI. So they searched for errors, verified the results with outsiders and checked the AI’s work using the company’s AI coding agent. “With enough reading and enough Codexing,” Sawhney said, “it seemed believable—and pretty remarkable.”
Long before AI, mathematicians who solved Erdős problems often framed their checks instead of cashing them. For them, the money was worth less than the glory. When I asked OpenAI researchers about their plans for the prize, they hadn’t given it much thought.
But they did have lots of thoughts about my next question: Why did AI succeed where humans failed?
The first explanation is that this particular solution happens to be highly counterintuitive.
Most people who tackled this problem tried to prove Erdős’s conjecture, rather than disprove it. Only by defying conventional wisdom and experimenting with seemingly improbable strategies did the model find an unexpected path forward.
The second is that humans specialize while AI synthesizes.
While mathematicians tend to focus on their specific areas of expertise, AI models use their vast knowledge to spot connections that we couldn’t possibly see ourselves. In this case, that meant pulling from both algebraic number theory and discrete geometry, which have about as much in common as the marathon and pole vault.
The third explanation is that AI has time, attention, patience, focus and the persistence to stick with methods that humans might abandon—and the solution to this Erdős problem demanded it.
“It’s the kind of idea that you try for a bit, it doesn’t work, and you think maybe you were just too hopeful,” said Mark Sellke, a Harvard statistician at OpenAI. “So you give up and move on.”
AI doesn’t move on. It keeps plugging away without taking breaks to eat, sleep, answer emails, pick the kids up from school and watch the Knicks.
And it can think coherently for so long that even an abridged version of the model’s “chain of thought” ran more than 75,000 words—the length of the first “Harry Potter” book.
Was it an elegant proof? Well, the article implies “no,” but it’s apparently a proof:
“It’s fair to say that we haven’t seen yet the spark of genius that you could attribute to some of the grandest proofs in the history of humanity,” Bubeck told me.
And how long did the computation take? Less than a day and a half:
After reading it, a former OpenAI researcher did some back-of-the-envelope math and estimated it took less than 32 hours and $1,000 in tokens, a bargain for a result of this caliber. The researchers wouldn’t confirm the exact amount of time and compute, but Bubeck described the costs as “really nothing crazy at all.”
At any rate, this is what AI is good for, and I wonder if, say, it could solve Fermat’s Last Theorem, which took Andrew Wiles eight years of work to solve (he was knighted for it). And I wonder if there are any seemingly intractable math problems that can’t be solved by AI, especially if they were or will be solved by humans.
Now I don’t think there are any practical implications of this results, but that’s true of much mathematical theory. I’m just amazed at what AI can do.
From People magazine (also at the UPI), we hear about a brave moggy whjo chased off a coyote. Click on the screenshot to read:
An excerpt:
A Pico Rivera, California, resident captured some surprising footage: a cat fighting off a coyote in the middle of the day.
“I was in shock,” Debbie Beltran, the cat’s owner, told KTLA-TV, after viewing the video. “It took me a while to see—is that our cat or somebody else’s? And no, it’s our cat.”
Beltran said she was at work on May 1 when a neighbor sent security camera footage of her cat ferociously fighting a coyote outside. The video shows the cat standing its ground outside the family’s yard on Manzanar Avenue before it climbs a tree and escapes the coyote.
“Coyotes usually come out when the sun goes down,” Beltran said. “So to see this happen in broad daylight, that was shocking.”
Beltran said her cat, named Mama, has been with her family for about 5 years and is believed to be about 10 years old. She notes that Mama has always been a courageous cat who doesn’t back down from a fight.
“She’s always been feisty, this type of cat, and has got into fights before, so it doesn’t surprise me,” the pet parent told KABC.
Unfortunately, this isn’t the first time a coyote has attacked one of Beltran’s pets. She said that last year, one of her cats died in a coyote attack. Now, she’s giving Mama some extra attention since her caught-on-camera battle.
The video is below (turn off the closed captions, as they interfere with seeing the scrap). Mama is a brave cat: watch at her bristle, hump her back, and chase the d*g! However, cats should really be kept indoors because not all predators are so timorous.
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From IHeartCats, we here about a high-tech way Dubai has developed to feed street cats. Click headline below to read.
An excerpt with a video below:
As people stroll through Dubai’s carefully maintained parks and busy public spaces, a quieter sign of compassion is beginning to appear beside the city’s modern landscape. New feeding stations for stray animals are being introduced across several locations, giving homeless cats a cleaner and more dependable place to find food and water. For years, many residents relied on leaving bowls wherever they could stop to help, often hoping hungry street cats would discover them in time. Now, Dubai is taking a more organized approach that blends kindness, sanitation, and public care into one thoughtful effort designed to support both animals and the shared spaces around them.
Dubai has launched a pilot program featuring 12 feeding units placed in parks and other public areas. The project is designed to support stray animals while also improving cleanliness and organization in shared spaces. For years, many residents and volunteers have cared for street cats on their own, stopping to leave food and water wherever they could. While compassionate, those efforts often created scattered feeding spots that were difficult to maintain.
Now, the city is taking a more structured approach.
The stations aim to make feeding more consistent and sanitary while helping caretakers provide support in designated locations. It reflects a growing recognition that animal welfare is connected to a city’s overall health and appearance. Instead of treating stray-cat care as an informal act left entirely to volunteers, Dubai is weaving compassion into its public infrastructure.
For the cats wandering through busy streets and quiet parks, the change could mean something deeply important: reliability.
Street animals often survive day by day, never knowing when food or water will appear. Many endure extreme heat, exhaustion, and long stretches of uncertainty. Having fixed feeding stations creates a sense of stability for animals that spend their lives navigating harsh outdoor conditions. Even a simple sheltered feeding spot can offer relief and comfort.
Dubai’s decision also highlights how cities are beginning to rethink the relationship between urban development and animal care. Modern public spaces are usually designed around people first, but this initiative acknowledges that stray animals are part of the environment, too.
The feeding stations are intended to reduce mess and discourage random food waste while still allowing residents to help animals responsibly. By centralizing feeding efforts, the city can better manage sanitation concerns without removing the compassion that inspired people to feed the cats in the first place.
The idea transforms what was once a scattered, individual effort into something shared and supported at a civic level.
Not only that, but the station combines feeding with recycling: if you put a can or bottle into the station, cat food is dispensed into the station. See the video below. Great idea!
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From The Animal Rescue Site we hear of an unholy interspecific friendship between a cat and a d*g species: “Wild fox befriends cat“, by Malorie Thompson. Here’s an excerpt, with a video below:
Cats and foxes seem like two of the same, but it’s rare that we see them interact.
They’re both sly and cunning, playful and adorable. Yet, they’re different species and they likely rarely cross paths in a meaningful way.
However, a wildlife photographer managed to capture a sweet exchange between the two animals and you have to see it to believe it.
Turkish wildlife photographer Ali ihsan Öztürk (@aliihsanozturk.65) shared a video of a cat and a fox hanging out on Instagram and it’s really something special.
He captioned the post (translated): “Fox and cat’s friendship. I couldn’t believe even while taking the picture. what a beautiful friendship.”
In the video, you can see the cat come up behind the fox and nuzzle the wild animal. Surprisingly, the fox didn’t seem to mind one bit and took it as an invitation for friendship!
The two animals continued to nuzzle each other in a playful way. It’s easy to see why Ali was so surprised to witness it!
Below is the Facebook post, which you can also see by clicking on the picture. Here’s the entire text:
In January 2026, a story began spreading online that many people could not stop thinking about: two stray animals who soon became known as the “street brothers.”
A fox and a cat had somehow learned to survive together outdoors. They shared warmth, protection, and the feeling of not being alone. Life on the street was hard, but they always stayed close to each other. The fox, a little bigger and stronger, often let the injured cat lie right by his side. On cold nights, it almost seemed as if he was quietly keeping watch so nothing would happen to his small companion.
When rescuers finally brought them to safety, the cat received the medical care it urgently needed. But at the shelter, something became obvious right away: whenever the two were separated, both became visibly stressed. Restlessness, searching, whining — as if the most important support in their lives had suddenly been taken away. Their closeness had long become more than a habit. It was their home.
So the team did everything they could to keep them together. Eventually, their story reached a kindhearted person who did not want a half-solution. He did not adopt only the cat — he took in the fox too, so the two would never be torn apart again.
Their journey is a reminder of what loyalty really means. And that friendship sometimes appears where no one expects it. Family does not always have to be the same species — sometimes it is simply the same bond holding two hearts together.
Fox-and-cat-friends videos are not rare: here are two more. All of these, oddly, feature cats that are mostly white.
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Lagniappe: From Reese: “Our Michael” from Archaeology & Art on Facebook, featuring an old photograph that was apparently for sale on eBay but that has been sold. Lovely cat! Here’s the whole text and the dead link:
Oct, 1938: our Micheal [sic]
The love radiating from the phrase “our Michael” alone is enough to warm our hearts.
The photographer and story are unclear. The source of this vintage photo is an old eBay listing, but the link isn’t active:
Welcome to the final CatSaturday of the month: Saturday, May 30, 2026, shabbos for Jewish cats, and National Mint Julep Day, an excellent drink when you use good bourbon and plenty of crushed mint. From Wikipedia (note the reference to Williamsburg, Virginia):
The mint julep originated in the southern United States, probably during the eighteenth century. The earliest known mentions come from 1770 and include a satirical play by Robert Munford, The Candidate (where a drunkard character “Mr. Julip” appears); and “A Short Poem on Hunting” (which describes julep as a concoction “Which doctors storm at, and which some adore”), published in the WilliamsburgVirginia Gazette. Further evidence of mint julep as a prescription drink can be found in 1784 Medical communications: “sickness at the stomach, with frequent retching, and, at times, difficulty of swallowing. I then prescribed her an emetic, some opening powders, and a mint julep.”
Here’s one with the caption, “A mint julep made with Henry Clay’s original recipe at the Round Robin Bar. According to bartender and historian Jim Hewes, the cocktail was originally served in a crystal glass because it represented a more upper-class beverage.”
Readers are welcome to mark notable events, births, or deaths on this day by consulting the May 30 Wikipedia page.
A faculty member ordered cookies for the undergraduates at their research symposium, and some of them were meant to display Botany Pond, which the undergrads apparently love. They saved one cookie for me, and here it is. I ate it this morning with coffee, but I hated to ingest such a work of art:
Da Nooz:
*Well, it looks as if the war with Iran isn’t over yet. The news yesterday was all abuzz that a deal had been reached, and Trump was set to approve it. But, as always, that was wrong. Nothing was announced. From the BBC:
US President Donald Trump had a meeting with top aides on Friday to make a “final determination” about a framework for extending the ceasefire with Iran, but it concluded without clarity on the next steps.
He said Iran must agree to never have a nuclear weapon or bomb, that the Strait of Hormuz be reopened for “unrestricted shipping traffic, in both directions”, and that any mines in the waterway are “destroyed”.
The meeting was held in the White House’s Situation Room, used for dealing with major crises. Iran earlier said it was not negotiating on its nuclear programme – which it insists is wholly for civilian purposes.
On Thursday, the two countries had agreed a framework of a deal – known as a memorandum of understanding – pending the approval of Trump and Iran’s leadership, according to US officials.
The deal would reportedly extend the ceasefire for 60 days and launch talks on the future of Iran’s nuclear programme.
“President Trump will only make a deal that is good for America and satisfies his red lines. Iran can never possess a nuclear weapon,” a White House official told CBS News, the BBC’s US news partner.
Since the ceasefire came into effect on 8 April, Trump has repeatedly suggested the US and Iran are close to a deal and negotiations are progressing, but so far there have been no substantive results.
In a social media post earlier on Friday, Trump said he was prepared to lift the US naval blockade of the Strait of Hormuz, allowing ships caught in the waterway to “start the process of ‘heading home!'”
He also insisted that Iran allow the US to remove and destroy its enriched uranium.
“No money will be exchanged, until further notice,” he said. “Other items, of far less importance, have been agreed to.”
Later, a White House official confirmed to the BBC that the meeting in the Situation Room had concluded. The official provided no further details.
Of course the “Iran will never possess a nuclear weapon” stipulation holds only for Trump’s presidency. And even now who can trust Iran to keep that pledge? Their whole history of evasion and cheating says otherwise.
Michigan Gov. Gretchen Whitmer (D), who has been widely viewed as a potential Democratic presidential candidate,said Thursday that she won’t be seeking her party’s nomination in 2028.
Hours later, she said otherwise.
Whitmer is term-limited next year after winning two gubernatorial elections in her key battleground state, and pundits have regularly identified her as part of Democrats’ crowded potential presidential field.
In an interview with Fox 2 Detroit on Thursday morning, she said: “There will be a robust group of people running for president. … I will not be one of them in 2028. I can tell you that.”
But later in the day, at an annual gathering of Michigan’s top civic and business leaders, she said she had spoken too soon.
“I never thought I would run for governor, so I guess I should know better,” she said during a panel discussion, later adding: “Never say never.”
Whitmer rose to the national spotlight during the coronavirus pandemic, when she pushed back on President Donald Trump’s efforts to antagonize her as “that woman from Michigan.”
She led a push to codify abortion rights in the state constitution in 2022, when Michigan Democrats won control of all three branches of state government and then used that “trifecta” to repeal a law that makes it harder for workers to unionize.
Whitmer drew some criticism for a 2025 speech in which she found some common ground with Trump but continued to stoke speculation that she could be preparing a run.
This year, she was one of several potential candidates who traveled to the Munich Security Conference, which does not typically attract U.S. governors, to lay out alternatives to Trump’s foreign policy.
I would vote for Whitmer in a heartbeat against any Republican candidate I know of, though I know some readers aren’t fond of her. But she’d be better than “progeressives” like Harris and Newsom, though these two are now are trying to “de-progressivize” themselves. I’m pretty sure that Harris won’t be the Democratic candidate because of both her election loss and her inability to speak coherently, but everything is still up for grabs.
The Supreme Court on Thursday threw out a Mississippi man’s conviction and death sentence. By a vote of 5-4, the court in Pitchford v. Cain agreed with Terry Pitchford that the judge at his 2006 trial had not properly analyzed whether the prosecutor in Pitchford’s case violated the Constitution’s ban on racial discrimination in jury selection.
Justice Brett Kavanaugh wrote for the majority, in a nine-page opinion joined by Chief Justice John Roberts and Justices Sonia Sotomayor, Elena Kagan, and Ketanji Brown Jackson. Quoting a 2019 opinion in which the court threw out the conviction of Mississippi inmate Curtis Flowers in a case that involved the same prosecutor, Kavanaugh acknowledged that “‘America’s trial judges operate at the front lines of American justice’ and ‘the job of enforcing’” the Supreme Court’s 1986 decision in Batson v. Kentucky, holding that the use of peremptory challenges (that is, challenges for any reason) to remove potential jurors based on race violates the Constitution, “‘rests first and foremost with trial judges.’” But in Pitchford’s case, Kavanaugh wrote, “the Mississippi trial court erroneously omitted” a key part of the Batson inquiry.
Justice Neil Gorsuch dissented, in a 10-page opinion joined by Justices Clarence Thomas, Samuel Alito, and Amy Coney Barrett. In his view, Kavanaugh’s “opinion errs on the law and the factual record alike.”
Pitchford, who was 18 at the time, was charged with murder for his role in the 2004 shooting death of a shopkeeper. A 16-year-old, Eric Bullins, fired the shots that actually killed Reuben Britt; he pleaded guilty and was sentenced to 20 years in prison.
Notice that two conservatives joined with the three liberal judges in this decision, which makes it unusual. But I think it’s a good decision because they are following the Constitution, which is their job. You can see the decision here. In the NYT, Yale Law School graduate Avital Fried agreed with the decision in an op-ed called, “College admissions are race blind. Jury selection is not.” Two bits (you won’t like the op-ed if you think affirmative action is essential to ensure “equity”):
The court recently ruled out the consideration of race in other contexts, like college admissions (as decided in Students for Fair Admissions v. Harvard) and voting rights (as decided in Louisiana v. Callais). The court has explained the shift toward a race-blind approach in those contexts as a way to reduce discrimination. To be sure, there are reasons to question this new approach in a racialized society like ours. But if that is the court’s stance, it should be applied to jury selection, too, where the stakes can be much higher and the consideration of race can be even more clearly linked to discrimination.
. . . The court’s decision on Thursday took a step in the right direction, upholding the current jury selection standard. But more needs to be done to align discrimination protections in this area with those in college admissions — both governed by the constitutional promise of equal protection under the law. The court has read that promise to protect high schoolers applying to elite colleges, and the very same promise serves as the bedrock of criminal trial rights. No one has a right to be admitted to Harvard, just as no one has a right to be seated on a jury. Still, every person has a right not to be denied a spot at Harvard or a seat on a jury because of his or her race.
If anything, the stakes are higher in a criminal trial than in college admissions. Discrimination in jury selection undermines people’s right to a fair trial when their life or liberty is on the line. Surely, high schoolers applying to elite universities should not get moreprotection than those facing the deprivation of life or liberty. Mr. Pitchford’s legal saga began when he was the same age as students around the country applying to college. Furthermore, racially biased strikes prevent members of the public from participating in an important civic duty. Just as the right to vote is carefully guarded, the right to be considered to serve on a jury is worthy of extra protection.
I have no beef with this decision, and am happy that two conservatives voted with three liberal.
*As always, I’ll steal a few items from Nellie Bowles weekly snark-and-humor column at the Free Press, called this week, “TGIF: The Donald Trump $250 bill.” Sadly, the real author is Nick Gillespie, a Free Press editor and libertarian.
Speaking of assisted dying:
→ Tim Hortons with a side of death: A Canadian doctor, James MacLean, approved medical aid in dying (MAID) for a 45-year-old man after briefly assessing him outside the popular coffee-and-donuts chain Tim Hortons, named for a beloved hockey player whose death in a car crash shocked fans. After determining that the man had inflammatory bowel disease and depression, Dr. MacLean then personally drove the man to a morgue where the MAID was administered in an industrial unit filled with other human cadavers. In another case, reports The National Post, “MacLean failed to administer one of three drugs used in assisted deaths—one that paralyzes the body’s muscles, including the muscles involved in breathing. The patient resumed spontaneously breathing again after initially being pronounced dead, and after MacLean had already left the home.”
Even—or especially—for supporters of MAID (I’m one), this sort of malpractice must be thoroughly investigated and punished.
If that’s the way MAID is actually practiced in Canada, it needs much more severe scrutiny, and the doctor needs his license pulled.
→ When you see only one set of footprints in the sand, that’s when Israel carried you:
→ Let’s check in on RFK Jr.: “Cheryl cheerleads the removal of a pair of Black Racers from Dr Oz’s patio.” Of course she does! I’m fond of saying we’re living in a Philip K. Dick novel as “shorthand for just how fucking weird our world is, and how much weirder it continues to get on a daily basis. What writer could have created Hunter Biden, or Lauren Boebert, or Elon Musk? The idea that Arnold [Schwarzenegger] would emerge as a major political player is strange—until you get to Trump.” Or RFK Jr.
Nobody but nobody is as good as Nellie at writing TGIF!
Like many on Thursday’s stage for theScripps National Spelling Bee finals, Shrey Parikh was a returning competitor. But his appearance this year wasn’t guaranteed.
He ranked 89th in 2022 and third in 2024. He seemed poised to take yet another flight from his hometown of Rancho Cucamonga, California,to the nation’s capital to contend for the Scripps Cup. Then he misspelled a word in his middle school’s bee last year. He was disqualified before nationals — or regionals — even began.
The word was calipers.
“Last year, I was really dejected and just very upset,” Shrey said. “It didn’t even sink in until the next day. I had a really tough time.”
Now, he’s got it down: “C-A-L-I-P-E-R-S,” he said for good measure on Thursday evening from the Scripps stage at DAR Constitution Hall after the competition ended.
In his last year of eligibility, the 14-year-old finally earned what he has coveted for years: the towering floral Scripps cup and a $50,000 cash prize. He beat out 246 other contenders. From the stage where he had just claimed his title as national champion, Shrey compared his feelings with his loss early last year.
“It’s like two ends of a spectrum,” he said. “Right now, I’m probably the happiest I’ve ever been.”
Shrey had a buzzworthy run in this year’s bee, which knocked out four of nine finalists in one round and ended in the competition’s third-ever spell-off tiebreaker. In several intense rounds of spelling during the finals, Shrey bested words like Bhubaneswar, Pluchea, hwyl, Metohija and Philepitta, before moving to the spell-off, where he spelled a record 32 words correctly in 90 seconds.
Shrey’s championship word — the last word he spelled correctly in the spell-off — was bromocriptine.
Ishaan Gupta, the runner up, spelled 25 words correctly.
*If you look at Wikipedia’s list of national spelling bee winners, you’ll see that Indians or Indian Americans have had a lock in the championship for about 18 years. (They do allow international competitors, so I can’t tell if the winners are citizens, but who cares?: it’s still amazing.) Shrey, who practices spelling for five hours a day, was in his last year of eligibility. His prize was a big trophy and $50,000.
Here’s a video of the competition and the winner (they can’t write down anything); note that it is mostly minority students of Asian origin who reached the top. The spelling part ends at 4:38, so you can stop there.
Here are the finalists in a screenshot from the video above:
You can take your own spelling bee quiz here (I haven’t yet done it).
Meanwhile in Dobrzyn, Editor Hili is keeping Andrzej in line:
Andrzej: What are we running in “Letters” tomorrow?
Hili: Something short, because yesterday the readers complained that you’re making them read too much.
In Polish:
Ja: Co dajemy jutro w „Listach”
Hili: Coś krótkiego, bo wczoraj czytelnicy narzekali, że każesz im za dużo czytać.
. . . and Andrzej posted this photo on his public FB page:
From Masih, who’s down on AOC for the Congresswoman’s apparent glorification of oppression:
“My body, my choice.” Except when a Muslim mayor says cover up. Then it’s “my body for votes.”
Since yesterday, when I criticized AOC, I have been under attack by her fellow feminists and colleagues calling me Islamophobic. Really? I have no fear of my beautiful mother, who… pic.twitter.com/Y4rC5PtsJP
Here’s the speech and appearance of AOC that Masih criticized. I have to say that here AOC makes me cringe. Donning a hijab, indeed! It’s either hypocrisy, pandering, or AOC is a covert Islamist.
Hello @AOC, while you smiled in a hijab at a New York event, I was in Federal Court facing the 4th hitman hired by the Islamic Republic to assassinate me, for campaigning for Iranian women to have the same freedom you performed for a photo op. Will you come to court with me in… pic.twitter.com/25mEGcdQ9d
One from my feed; the English translation of the Japanese is this: “A performance titled ‘Stairway to Success’… It steals your gaze without you realizing it.” Ah, life!
These three Dutch Jewish girls, with the youngest only three years old, were gassed as soon as they arrived in Auschwitz. Their mother was also gassed.
In the dim light of a late fly-out, to the tune of cicadas, Nayang’s wrinkle-lipped bats leave their cave…just as they have probably done every night for thousands of years…🦇#bats #Thailand #wildlife
I’m starting to get some new batches of wildlife photos, and I encourage readers to submit their good photos for consideration.
Today’s installment features the photos of UC Davis ecologist Susan Harrison, who recently went birding not too far from Chicago:
Birding in the Upper Midwest
Minnesota and Wisconsin may not be at the top of everyone’s list of nature travel destinations, but do they have darned nice birding? You betcha! On a late May work trip to Minneapolis, it was my good fortune to visit some of the Upper Midwest’s riparian forests, wetlands, and restored prairies during spring migration. Friendly people and well-tended parks and nature reserves helped make it delightful.
Rarer small birds that were new (a.k.a. “lifers”) for me….
Kirtland’s Warbler (Setophaga kirtlandii), a specialized inhabitant of young Jack Pine (Pinus banksiana) forests, only recently removed from the endangered species list:
Louisiana Waterthrush (Parkesia motacilla), a warbler that lives on the banks of crystal-clear headwater streams in forests:
LeConte’s Sparrow (Ammospiza leconteii), a secretive marsh dweller that sings in the dark and scurries around on the ground:
Henslow’s Sparrow (Centronyx henslowii), a stealthy bird of the region’s much-diminished grasslands (historical note: it was named by John James Audubon in honor of Darwin’s mentor John Stevens Henslow):
