May 2026 - Page 28 of 105

Separations between people over 50 are growing. And there are two words that explain it: gray divorce

May 23, 2026 by usatoday24

The term may be striking, but one thing must be recognized: it does not leave much room for misunderstanding. The “gray divorces” They are neither more nor less than that, separations carried out by couples with gray hair, spouses who are over 50 years old and often have been married for several decades. Until not long ago they were a relatively strange phenomenon; But as the population pyramid widened at its upper end and society changed, they have gained weight. So much, in fact, that there are already experts investigating its causes to understand them better. New times, new trends. Divorces with last name. There is nothing written about love. About heartbreak, either. There are those who end their marriages just a few years after saying “I do”, those who do so after decades and those who sign the divorce papers after the age of 60, when both spouses have gray hair. Sociologists and academics specialized in demographic phenomena have even given the latter a name: “gray divorces”. The term is not entirely new. In 2004 I used it and to the American Association of Retired Persons (AARP) and in 2012 researchers from the Bowling Green State University They even spoke of a “gray divorce revolution”, but since then it has attracted the attention of more and more experts. Today the expression is replicated in a good number of essaysincluding a extensive article published in 2024 in Sage Journal and that seeks to investigate its causes. A rising phenomenon. It takes reviewing some figures to understand that interest. In the US, the divorce rate among adults at least 50 years old has more than duplicate in a matter of two decades to the point that in 2010 almost 25% of separations could be considered “gray divorces”. Some experts have detected that their incidence has stabilized over the last decade or that they have even decreased after the pandemic, but still almost 40% of the people who decided to dissolve their marriages in the US in 2022 were still over 50 years old. Beyond the USA. The phenomenon is not exclusive to the US. The INE also leaves some brush strokes interesting about what is happening in Spain. For example, almost a third (31.8%) of divorces made official in 2024 were carried out by couples who had been married for at least two decades. Another key fact is that, although the highest number of separations occurs between spouses who are in their forties (40 to 49 years old), the average age at which they decide to follow different paths has not stopped growing in recent years until it is approaching 50. Among men it is already close to 49 years old. In general, the INE estimates that over the last three decades, senior divorces, between couples over 50, have skyrocketed by around 40%. Accented from 65 onwards. “Divorce in old age is increasing in the Western world, even in family-oriented societies like Israel, in which the most common family status for older adults, aged 60 or over, is to be in a long-term heterosexual marriage with adult children,” a group of researchers from the University of Haifa reflected a few months ago in an article focused precisely on the drift and causes of gray divorces. In their analysis, they also see a particularly marked increase among couples with members who are 65 or even older. Average age of spouses at divorce (YEARS) Women Men 2015 43.8 46.3 2016 44.2 46.7 2017 44.8 47.2 2018 45.2 47.6 2019 45.5 47.9 2020 45.6 48.2 2021 45.5 47.8 2022 45.9 48.4 2023 46.2 48.7 2024 46.6 49 And why do they separate? The big question. And there is no single answer. The first and obvious thing is that not only those who get divorced have changed; society itself has done it, increasingly older in regions like Europe or the US. Considering that the average age of Americans has gone growing gradually since the 1970s or that the population over 64 years of age hasn’t stopped to gain weight, it makes sense that there are also more and more divorces involving couples who have blown out all 50 candles. life expectancy has been stretched Furthermore, which broadens the life horizon of couples. “Your ability to enjoy has improved”. “In these societies, older adults enjoy relatively good health and functioning, and these conditions have improved their ability to enjoy life,” they add the Halifa researchers, who point both to the transformations of the population pyramid and at the cultural and social level. “Later-life divorce is increasing due to changes in marital and family structures and demographic trends.” Although that is the general framework, there are those who appreciate important nuances. After observing a slight drop in divorce rates among couples aged 50 to 60 from 2022, a study Recent research from Bowling Green State University raises an interesting reflection: gray divorces could be “largely” a phenomenon associated with couples Baby Boomersformed by spouses born around the middle of the 20th century. One process, two phases. During your studio Researchers at the University of Halifa discovered something else: they concluded that divorces that occur after the age of 50 or even in old age are usually the result of a “complex” and long process, lasting several years, during which two well-differentiated phases can be identified. “The first, continuous and prolonged, is that of staying together despite the distance. The second captures the moment of the final decision to separate, with a point of no return or inflection and several accelerating factors in the background.” The experts too have identified two large layers in divorces between older couples: the “interpersonal” and the “demographic”, such as increased life expectancy. Of the two, the most curious are the first, since – the researchers highlight – they do not differ much from the reasons that lead younger couples to break up: distancing, infidelities, health or financial problems, poor communication, behavioral changes or an imbalance of roles in the home. Second … Read more

In the year 958, King Sancho I of León was so fat that his court forced him to do something unprecedented: the first miracle diet.

May 23, 2026 by usatoday24

His reign was fleeting, troubled and controversial, but Sancho I of León It well deserves to go down in the books of national history. And it deserves it for two compelling reasons, never better said. The first is that if he was removed from the throne in 958, it was not because of a game of palace conspiracies and disputes between nobles. Or those weren’t the only reasons, at least. The trigger was his exorbitant bellya belly so prominent that it earned him the nickname ‘El Gordo’ and made his subjects doubt whether he was the most suitable person for the throne. The second is that he can boast of having completed perhaps the most successful (and earliest) “miracle diet” in Spain. We explain ourselves. When I was a child, in the 940s, there was little reason to think that Sancho could one day become a relevant character in the kingdom of León. His status as the third male child of Ramiro II relegated him to a secondary position, behind his Vermudo brothers (died 944) and Ordoño. And if the crib had not favored him, his health was not buoyant either: he was not a young man given to long rides or exercising. Theirs were rather the comforts of the palace, especially those that were served in fountains, well watered with oil. From Ramiro ‘the Great’ to Sancho ‘the Fat’ Miniature representing King Sancho I of León. At the table, Infante Sancho did not hold back. They say that it was given to anthological feastswith seven meals a day, sometimes consisting of 17 dishes, among which there was no shortage of stews with game meat. Perhaps history exaggerates and has deformed his figure, but it has left us at least one piece of information to give us an idea of how plump Sancho was and to what extent he developed morbid obesity: it is said that, already in his adult stage, he came to weigh 240 kilos. If his father had been nicknamed Ramiro ‘the Great’ —or ‘the Devil’, as his enemies referred to him—and his predecessor Alfonso “the Monk”Sancho was given a much less epic and much more descriptive nickname: ‘el Crassus’. Or directly ‘El Gordo’. However, it was one thing to be fond of lavish banquets and quite another to renounce the throne and settle for the delegated government of the county of Castile, a responsibility that had been assigned to him in 944. Once his father died and his older brother became Ordoño IIISancho organized a rebellion between 954 and 955 to expel him from power. The trick came to fruition. His attempt to overthrow him by force was a resounding failure, but in a surprising turn opportune for Sancho’s interests, Ordoño III died not long after, thus granting him the accession in 956 to the crown of a kingdom that was facing delicate moments due to internal tensions and Muslim incursions. His belly didn’t help either. It was bad to weigh 240 kilos, but worse to combine such weight with that of a crown that required being willing to be embedded in armor. As Professor Margarita Torres recalls in an article of the Royal Academy of History (RAH), in the 10th century a king was expected to will combine certain qualities: good judgment, balance, firmness… and the skills of a war leader. It would have been very difficult for Sancho I to appear on a horse on the battlefield, as well as fighting while brandishing a sword or even something as crucial for the crown as providing offspring. Such a condition undermined his image among the kingdom’s aristocracy, who ended up losing respect for him. Add to that the memory of Sancho’s failed coup against his brother Ordoño III and the decisions he made once seated on the throne, which led him, for example, to distance himself from his uncle, the influential Count Fernán Gonzálezand a perfect cocktail will emerge for the fall from grace of a novice monarch. Helping the king lose weight Just two years after being crowned in Compostela, ‘el Crassus’ lost his precious scepter, which passed in 958—by siege—to the infante Ordoño Alfonso. Sancho managed to save his skin and took refuge where he knew he would be safe: in Navarra, with his grandmother, Queen Todoan old woman more than 70 years. The story of Sancho I could have ended then. Fortunately, her maternal grandmother was a woman of means and decided to ask for help from the person who would have the least qualms about plotting against a Christian monarch: Abd al-Rahman IIIthe caliph of Córdoba, an interesting ally both for his position and his resources. At his service he had a renowned doctor, the Jewish scholar Hasday ibn Shapruta skilled, polyglot, cultured man who could help the king overcome his overweight. In exchange for the alliance with Abd al-Rahmanto which the Navarrese joined, the supporters of Sancho I agreed to hand over fortresses on the border. It was not a bad payment for a move that not long later, in April 959, would allow him to return triumphant to the capital of his kingdom while Ordoño IValias ‘el Malo’, was forced to flee and end up in Córdoba. The second and definitive stage of the reign of Sancho I began, which would last until his death in 966. The surprising thing is that—if we believe tradition—the Sancho who returned exultantly to León had little to do with the one who had fled some time ago to take refuge in his maternal grandmother’s castle. In fact, the nickname ‘Crassus’ had become too much for him. The reason? The strict “bikini operation” to which Shaprut had subjected him before his return to the throne, in Córdoba. The remedy was so effective that it is said that Sancho lost more than 100kg in a matter of a few weeks. Before embarking on following the diet of the wise Jew, it is better that you take note, however, of what you will need, … Read more

which cars can circulate and which rest on May 23

May 23, 2026 by usatoday24

A new Saturday Today No Circula day is launched this weekend, a measure coordinated by the Environment Secretariat of Mexico City (SEDEMA) whose objective is to mitigate pollution levels in the Valley of Mexico. Those who plan to travel in their private vehicles must carefully verify the last digit of their license plate and the verification hologram before going out on the street. It is worth remembering that this ordinance not only restricts mobility in the 16 municipalities of CDMX, but its obligation extends to various metropolitan municipalities of the State of Mexico. The program operates in: Atizapan of Zaragoza Coacalco de Berriozábal Cuautitlan Cuautitlán Izcalli Chalco Chicoloapan Chimalhuacan Ecatepec de Morelos Huixquilucan Ixtapaluca Peace Naucalpan de Juárez Nezahualcoyotl Nicolas Romero Tecámac Tlalnepantla de Baz Tultitlan Chalco Valley Also, remember that if your route passes through any of these locations, the Saturday No Circulation Day also applies. Which vehicles and license plates are affected by Hoy No Circula Saturday? The objective is to reduce the volume of cars in circulation to reduce polluting emissions; However, Saturday sessions operate under particular guidelines that complement the rules in force from Monday to Friday. Not all units must stop on the same weekend: the hologram, the completion of the license plate and whether Saturday corresponds to an even or odd week will determine which driver must leave their car parked and who has the option of transiting. Likewise, it is mandatory to consider that the Saturday Hoy No Circula does not remain active during the entire day. The hours of application go from 5:00 a.m. to 10:00 p.m., so outside of that period—during the night and early morning—the regulations do not limit road traffic, unless the authorities dictate an environmental contingency or another extraordinary measure with added restrictions. For the specific date of May 23, 2026it is established that as we are talking about the fourth Saturday of the month, it is the vehicles with hologram 1 and license plates whose ending is an even number that will have to suspend their activities and not circulate for the duration of the program. If your car has these characteristics, it will be mandatory to keep it motionless until the regulatory deadline ends after 10:00 p.m. In contrast, those cars that have a 0 and 00 hologram retain the authorization to move freely under the guidelines of Today No Circula Saturday. Meanwhile, the units identified with hologram 2 cannot circulate under any circumstances on Saturdays. Apart from the previous categories, it is necessary to take into account that there is a list of exempt vehicles that enjoy the benefit of circulating without being compromised by the restrictions current. These include: Electric, natural gas or hybrid technology vehicles Units registered with plates for people with disabilities All those intended for urban public transport services (including funeral services) Those dedicated to school or passenger transportation Those assigned to public security and/or civil protection Motorists who do not comply will face significant financial penalties. The fine for violating the program ranges from 20 to 30 times the Measurement and Update Unit (UMA), which is equivalent to approximately 1,924.40 pesos at the minimum and up to 2,886.60 pesos at the maximum. Along with the direct monetary impact, the potential retention of the unit in a warehouse and the setbacks linked to clearing the corresponding procedures with the authorities are contemplated. In short, if you plan to make trips in your car this Saturday through CDMX or through the suburban municipalities of the State of Mexico that are included in this regulation, it is advisable to carefully check before starting what hologram your vehicle has, what the ending of your license plate is and if the calendar shows an even or odd week. Photo | Sunira Moses In Xataka | The countries that pollute the most in the world, gathered in a detailed graph

the key is in tiny technology

May 23, 2026 by usatoday24

The promise of 6G It has been on the table for years, but there is a part of that story that is usually left out of the window. We’re not just talking about faster mobile phones, seamless video calls or almost instant downloads, but about something much more complex: getting huge amounts of data to travel through the air with great stability. That’s where technology meets its own ceiling. And a Japanese team just placed a tiny piece right in the center of that problem. 112Gbps. What the researchers have achieved is to send data wirelessly at 112 Gbps in the 560 GHz band. The demonstration was announced by Tokushima University and researchers from this university and Gifu University participated. The important fact is not only the speed, which is already enormous, but also the place where it has been achieved: above 420 GHz. According to the researchers, it is the first time that 100 Gbps class wireless communication has been demonstrated above 420 GHz. The 350 GHz wall. To understand why this result matters, we have to look at the problem that terahertz communications have been experiencing. Mobile networks have gained speed and capacity by increasing working frequencies, but this path becomes more complicated when entering extreme territories. Above 350 GHz, conventional electronic technologies face to lower output power and increased phase noise. In other words: it costs more to generate a strong, stable and useful signal to transmit data at high speed. The tiny piece is a microcomb. The word may sound strange, but the underlying idea is quite visual. A microcomb generates multiple regularly spaced optical frequency modes, like the tines of a comb. Tokushima University explains that this allows very high frequency optoelectronic signals to be obtained with a quality superior to that of conventional electronic approaches. In the configuration used by the team, an optical fiber is attached directly to the microresonator, which eliminates the need to perform extremely precise optical alignments as in conventional systems. The way forward. First, the microcomb allows the generation of a cleaner and more stable terahertz signal than that obtained with conventional electronics at those frequencies. Then modulation comes into play, which is the way of encoding the information within that signal so that it carries more data. The official source talks about high-order modulation techniques, such as QPSK and 16QAM. With QPSK, the system achieved 84 Gbps; with 16QAM, it reached 112 Gbps. It is not for tomorrow’s mobile. It is advisable to understand the scope of the advance before imagining phones directly connected to 560 GHz. The university itself speaks of a technological base for ultra-fast backhaul links and integrated photonic-wireless networks in 6G systems. Simply put, backhaul is the part of the infrastructure that connects base stations to the main network. That’s where very high-capacity wireless transmission can make sense: moving large volumes of data between fixed points. There is still a way to go. Researchers want to extract even more performance from these waves by reducing phase noise, developing more advanced antennas and increasing power output. The objective is clear: that speeds like these do not remain a one-time demonstration, but can be sustained at greater distances. There will be an important part of the reality test. What we’ve seen now is not a finished 6G network, but rather a piece of technology that helps show how a part of that network can be built. Images | Tokushima University In Xataka | Reddit was one of the last corners of the Internet free from burning. Now it’s starting to show worrying signs.

His pieces now support a million-dollar business.

May 23, 2026 by usatoday24

He Airbus A380 It was born to be many things at once: a demonstration of European industrial muscle, a response to the growth of air traffic and a different way of imagining great long-haul trips. For years we saw it as the double-decker that promised to change the economics of denser routes, but the market ended up moving in another direction. The interesting thing is that his story did not end with the closure of the production line in 2021. Now, some of its value is showing up where it was least expected: on planes that no longer fly. The explanation begins in a very specific tension in the market. In April 2025, VAS Aero Services noted that delays in deliveries of Boeing 777Xdelayed until at least 2026, were increasing dependence on the A380 to meet the demand for large long-haul aircraft. The company then estimated that there could be up to 175 units of the model in operation worldwide, a figure that helps understand the pressure on the inventory of certified used parts. The question is not just how many A380s remain in service, but how such a dedicated fleet is maintained when the aircraft is no longer in production and the supply chain increasingly relies on certified used material. The focus is on that market, where recovered parts can re-enter service after the corresponding processes. This detail changes the reading of the retired aircraft: it stops being only an asset at the end of its useful life and begins to function as a source of components for other operators. In a limited fleet, each recoverable item carries more weight. The business is also in the planes that no longer fly In practice, this economy of the retired A380 involves converting a complete aircraft into a parts catalogue. Airbus has selected the aforementioned VAS Aero Services to manage the disassembly and redistribution of certified used material from several units that are decommissioned. The plan announced by the company involves working together with Tarmac Aerosave in Tarbes, France, and placing the recovered parts in Europe to serve the market. EMEA. The firm, an independent subsidiary of Satairan Airbus Services company, acts here as a bridge between retiring aircraft and operators in need of spare parts. The VAS information does not put a total figure on the resulting catalogue, but it does point to especially relevant elements: the engines of these aircraft will be offered for rent and can also be used as a source of used parts in demand. Simple Flying adds two pieces of information that help understand the size of the business: a set of superjumbo landing gear weighs about 5,443 kg and can fetch several million dollars on the secondary market, while a Rolls-Royce Trent 900one of the engines used in the A380, can be sold in service condition for about 10 million dollars. As we can see, each retired aircraft becomes more than just scrap. The company itself expresses it in quite clear terms. Tommy Hughes, CEO of VAS, assures that they early identified the A380 platform as a “growth opportunity in the aftermarket” and that they continue to invest in A380 aircraft at the end of their useful life to make critical components available to the global market of large aircraft operators. In the same communication, the manager adds that the time has come for a program focused on retiring the A380 at the end of its life and “monetizing the residual value of its parts in serviceable condition.” The paradox is powerful because it returns the A380 to an unexpected place. The plane that was born to redefine great long-haul travel ended up being too big for many of the airlines that had to support it, but its retired units still retain value in an industry that needs keep existing fleet operational. We are not facing a complete vindication of the program, nor before a second youth without nuances. We are looking at something more concrete and perhaps more revealing: even one of Airbus’ biggest setbacks can continue to generate business when dismantled piece by piece. Images | Airbus | Engine Alliance In Xataka | Boeing is losing ground to Airbus on all fronts. Including Italy’s air tankers

Today the culmination of one of the most famous series in the history of Spain arrives on Prime Video in an ironic closing format

May 22, 2026 by usatoday24

When the series ‘Aída’ ended in June 2014 with four million viewers saying goodbye, no one seriously considered a sequel. A decade later, Paco León turns that reunion into metacinema with ‘There and back’which now premieres Prime Videoa film that functions as another chapter, but also as a question about what it means to revisit something that has not completely disappeared from collective memory. It is clear that the dizzying audience figures for ‘Aída’ belong to another era, when audience fragmentation was not as great as it is now. At one of its peaks, the series reached 33.2% share and 6,282,000 spectators. Throughout its nine years on screen, the series led the audience in its first two seasons; During the 2006-2007 season it was the most viewed Spanish fiction, and in the following season it not only maintained the leadership, but did so above foreign productions. ‘There and back’ arose as a commemoration of the tenth anniversary of the end of the series and twenty years of the original premiere. The filming featured almost the entire original cast (Carmen Machi, Mariano Peña, Miren Ibarguren, Eduardo Casanova, Pepe Viyuela, Melani Olivares, Canco Rodríguez and León himself), with the notable exception of Ana Polvorosa (Lore), who felt that she was not at her best to reprise her role. The twist that no one expected was the one that led the film to merge elements of fiction with metanarrative to show the recording process of an episode, mixing the original characters with the actors themselves giving life to themselves. The narrative axis is Carmen Machi’s resistance to returning to the character, and all this with abundant reflections on the nature and limits of humor, which the original series exceeded on numerous occasions. Can’t you make humor out of anything anymore? ‘Back and forth he does it… and he also wonders why. In Xataka | This Prime Video series ends after 7 years and 40 chapters, making history with an audience more divided than ever

has to dodge space junk and is leaving blind spots on the map

May 22, 2026 by usatoday24

Imagine that there was a satellite capable of detect fires shortly after the first spark. Even before calls to emergency services begin. Imagine now that the maps drawn thanks to that satellite suddenly begin to have unexpected gaps. Blind spots where fires can spread freely. It would be tragic, right? Without a doubt, although the truth is that it would not be. It is. This story is totally true and the worst thing is that the reason these blind spots exist is because the satellite has to move over and over again to avoid the space debris that experts have been warning us about for so long. The collateral damage of anti-debris maneuvers. NASA’s Aqua satellite has an instrument called MODIS, which has the ability to detect hot spots and smoke by measuring infrared radiation. These heat and smoke points are minimal, which is why it is used to detect fires from their earliest stages. Since its launch in 2002, NASA has been using it to create fire maps that allow emergency systems to move more quickly and concisely to the places where the fire is located. It’s not even its function; since, as its name indicates, it is a satellite centered on water. However, this side effect has helped save many lives and many acres of land. Unfortunately, every time he moves to avoid incoming space debris he has to let his guard down, with very worrying consequences. One of three. Aqua is one of the three satellites that make up the NASA Earth Observing System (EOS). The other two are Terra and Aura. Their names already give us a clue as to what their function is. Basically, they do a comprehensive survey of the Earth by land, water and air. Terra was first launched in 1999. It is responsible for analyzing the interactions between the atmosphere, land, snow, ice and oceans. It can, for example, detect the progress of deforestation. Then, in 2002, Aqua was launched. Its functions are the analysis of ocean evaporation, atmospheric water vapor, clouds, precipitation, soil moisture, ice and snow. In fact, its MODIS instrument was designed to analyze data related to the water cycle, but it turned out to be an ideal fire detector. Finally, in 2004 Aura was launched, which analyzes the chemistry of the atmosphere, the state of the ozone layer and air quality. The problem comes in 2005. Space debris has been growing in abundance in the last 20 years. Above all, there is a lot of debris in low Earth orbit, since there is a greater gravitational influence there and these are retained. Both Aqua, Terra and Aura are in that same orbit, to be able to carry out their work close to their objectives. Therefore, they are increasingly at risk of being hit by space debris. In fact, since 2005 is calculated who have had to deviate at least 32 times to avoid these impacts. The consequences. These detours prevent them from being able to properly carry out their functions, but they also cost a lot of extra fuel. All of these satellites are having a longer lifespan than expected. However, precisely because of these maneuvers they are using more fuel than expected, so they may stop working next year or the following year. More satellites. Luckily, there are more satellites in space dedicated to detecting fires. NASA itself has several. However, Aqua is one of those that has given the best results. Furthermore, now a call has been made about the risk to the three EOS satellites, but there are many more, from many space agencies and companies, that are in danger from space debris. And the worst thing is that this has only just begun. The European Space Agency (ESA) is following up of more than 50,000 pieces of space debris in orbit, but there are possibly many more. In fact, if we look at smaller objects, between 1 centimeter and 10 centimeters, the figure rises to 1.2 million detected objects. In 2005, 16,000 objects were being tracked, so the numbers have increased greatly. Kessler syndrome. One of the biggest risks from space debris is Kessler syndrome. This is a phenomenon which would occur when fragments of space debris impact satellites, breaking them and releasing more pieces that in turn become more space debris and continue impacting other satellites. It’s kind of like a domino effect. If this happens, the consequences can be many and none of them good. It may take a while for us to be aware of the magnitude of the problem. Therefore, the example of fire hunters is very illustrative. Without them, the planet is in serious danger. The consequences of an impact in space, or even maneuvers to avoid it, also have a full impact here on Earth. You have to do everything possible to avoid it.. Images | NASA/Matt Palmer (Unsplash) In Xataka | If the question is how to protect the mountain from fires, in Soria they have an ancient solution: luck of pines

A mathematical problem had been resisting experts for more than 80 years. An AI has surpassed them all

May 22, 2026 by usatoday24

In 1946 the Hungarian mathematician Paul Erdős asked a seemingly very simple question: if you place n points in the plane, how many pairs of points can be exactly at a distance 1 from each other? This dilemma is known as unit distance problem in the planeand has maintained many mathematicians who research in the field of geometry, immersed in its resolution for no less than eighty years. The classic strategy proposed by many of them to try to solve it was to resort to a square grid. They soon realized that the number of pairs at unit distance grows at least as n to the power of (1 + C/loglog(n)), where C is a positive constant that quantifies how much a particular construction can be better than a basic square grid. It’s a complicated idea, it’s true, but we can try to approach it in a slightly more intuitive way. A standard square grid produces approximately 2n pairs of points at unit distance. If we rescale it in an ingenious way by choosing the scale factor as a number that has many divisors (in number theory this property is known as a number with many small prime factors), you get more pairs of points to fall exactly at distance 1. The value of C measures precisely the efficiency of that choice. This is the key. An AI from OpenAI has achieved the first major breakthrough in 80 years As we are seeing, the question Erdős asked is very easy to state, but extraordinarily difficult to resolve. If we develop the classical approach a little further we will realize that since loglog(n) grows very slowly, the exponent approaches 0. This means that the square grid grows only slightly faster than n, but not enough to exceed n at a fixed rate. This milestone was achieved by a general-purpose inference model that OpenAI was testing internally. This is why for decades mathematicians predicted that the upper bound would be approximately n^(1+o(1)), that is, just slightly larger than n. Now we know that they were wrong, and the person who refuted this conjecture was not a particularly skilled current mathematician; this milestone has pointed it out a general purpose inference model which OpenAI was testing internally. and not one artificial intelligence (AI) specialized in mathematics. This model has provided an infinite family of examples that produce polynomial improvement. In fact, he has shown that it is possible to construct configurations of points with at least n^(1+δ) pairs at unit distance, where δ is a fixed value greater than 0 that does not disappear as n grows. When the AI delivered this result, OpenAI researchers asked a group of Princeton mathematicians to review it. And his conclusion was blunt. The AI was right. This is the first progress on the lower bound of the problem posed by Erdős in 80 years. And, curiously, the OpenAI model has achieved this by using advanced engineering tools. algebraic number theory for an apparently elementary geometry problem. Several renowned mathematicians, such as Fields Medal winner Tim Gowers or number theory expert Arul Shankar, have declared that the result that AI has delivered is an extraordinary achievement that could provide mathematicians with a bridge to explore other problems in the future. Image | Jeswin Thomas More information | OpenAI In Xataka | These two problems have baffled mathematicians for decades. A genius has solved them with a stroke of the pen

Türkiye seemed immune to the drop in birth rates. Now his Government is desperate because it does not know how to stop it

May 22, 2026 by usatoday24

In Türkiye 2025 was the “Year of the Family” and the decade ahead of us (2026-2035) will be that of “Family and Population”. It’s not a coincidence. Just like many other countries from Europe, Asia or America, the Turkish Government increasingly looks with greater concern its declining birth rates. Specifically there is two data that worry Recep Tayyip Erdoğan’s team: the number of births has been falling since 2014, which has dragged the fertility rate to its lowest level so far this century, far from what is necessary to keep the population stable. The problem is that neither the “Year of the Family” nor the rest of the measures deployed by Erdoğan seem to be running too much. What has happened? That Türkiye has not managed to avoid the demographic winter that hits other countries in the world, such as Japan, South Korea either much of Europe. It is not just that the birth rate is falling or that the country’s demographic engine is showing clear signs of having caught the flu. The most revealing are the ‘pro-birth’ initiatives and above all the statements of Erdoğan encouraging his fellow citizens to have more offspring, which shows that the issue is generating more and more suspicion in Turkish institutions. In March, the Turkish Minister of Family and Social Services, Mahinur Ozdemir Goktas, expressed it clearly (and dramatically) during an interview: for the Executive, demography has become “a question of survival.” “Our strongest strength is the family,” the leader stressed after recalling that in a matter of 27 years Turkey has experienced the same decline in birth rates that has taken nine decades in other nations. Number of births and total fertility rate, 2001-2025. What does the data say? The last ones, published This same week by the Turkish Statistical Institute (TUIK) they draw a very unflattering scenario. In 2025, 895,374 babies were born in Türkiye, a bad figure no matter how you look at it. To begin with, because it represents a drop of 4.78% compared to 2024 and the lowest figure in the entire historical series disclosed by TUIK, which dates back to 2001. As if that were not enough, it aggravates the decline in what is known as the ‘total fertility rate’, which has been moving away from the levels necessary for years to keep the population stable. Why are they important? Of all the TUIK indicators, the ‘total fertility rate’ is probably the one that worries Ankara the most. And it is logical. It basically shows the number of children that, on average, a woman is expected to have throughout her reproductive life (between 15 and 49 years old). In 2001 this indicator stood at 2.38 births. It was good data because it far exceeded the necessary rate (2.1) to keep the population stable without having to take into account other factors, such as immigration. The problem is that since 2014 that indicator has been receding steadily until it remained at 1.77 in 2020, 1.49 in 2024 and 1.42 last year. In fact, 2025 has been the ninth consecutive year in which Turkey falls below the ‘replacement rate’, which means that if Turkey does not want to lose population in the future it will probably need the arrival of foreigners. The crude birth rate has also plummeted in the last five years. Total fertility rate by province, 2025. Can it go further? Yes. He latest report of TUIK suggests that the trend is far from stopping. If in 2017 the organization registered 57 provinces with a fertility rate insufficient to keep the population stable, last year that list had already skyrocketed to 76 territories. What’s more, what has grown the most is the number of provinces with the worst birth rates. If in 2017 there were only four with a fertility rate of less than 1.5, last year 59 provinces were in that situation. What’s more, in all of Türkiye there were only five regions where the replacement rate reached (or exceeded) 2.1. In general, Turkish women not only have fewer children, they also have them later. The average age of mothers in the country at the time of giving birth has skyrocketed in recent years, going from 26.7 in 2001 to 29.4 in 2025. There are a dozen provinces in which, on average, women do not have their first child until they are almost 30 years old. In Artvin or Istanbul, in fact, the average age for new mothers is 29 years old. What does the Government think? Türkiye’s fertility rate may have been declining for years, but still stays above of the EU average (1.34) and of course in countries like Italy, Poland, Lithuania, Spain or Mala, where this indicator does not even reach 1.2. Despite this, Erdoğan has elevated demography almost to a state issue. In fact, he has not hesitated to cross out “disaster” the country’s low birth rates and “betrayal” of fertility control. “Why not have at least four children, or five?”, recently reflected the Turkish leader, leader of the conservative AK Parti, who on other occasions has already warned that the nation is seeing its average age increase (around 34 years old) and the weight of the elderly population. What have they done about it? Beyond political discourse, its Executive has promoted different pro-natal measures. In April Parliament supported extending maternity leave eight to 16 weeks and last year Erdoğan himself advertisement that the Executive would increase its financial aid to families that have children, with the payment of 5,000 liras after the birth of the first-born. “We are also implementing financial aid per child of 1,500 liras per month for the second child and 5,000 liras per month for the third and subsequent children,” advanced. The big question is whether these measures will have an effect and will encourage Turkish births. What do people think? That’s what he tried to find out a few days ago The New York Timesthat interviewed to several Turks to find out if they would … Read more

Airbus had a single center in the world to convert commercial aircraft into military tankers. Now another one will open in Seville

May 22, 2026 by usatoday24

Airbus has chosen Seville to install its second global conversion center for the A330 MRTT, the best-selling tanker and military transport aircraft on the market outside the United States. The San Pablo plant will thus become the twin of the Getafe plant, until now the only one in the world capable of transforming A330 commercial aircraft into its multirole military version. We made the announcement during the opening of the ADM Sevilla 2026 fair and the facilities are expected to be operational at the end of 2027. Why it matters. The A330 MRTT is experiencing a sweet moment, as it accumulates some 91 orders from 19 countries and controls 90% of the world market share, excluding the United States. The war in ukrainethe escalation of military spending in Europe and the growing need for tanker aircraft to extend the air forces’ operating margin have triggered demand for a model that until now was assembled at a rate limited by its single-plant capacity. Add Seville will allow you to go from five to seven annual conversions and thus take some work off the Getafe plant. In detail. The conversion process is usually a rather complex task for European aerospace engineering. Civilian A330s leave the Toulouse chain and they are transferred to the conversion center, where for about nine months military systems, in-flight refueling equipment, specific avionics, communications and interior configurations adapted to each client are integrated, until they are ready for aerial refueling missions, troop transport, strategic cargo or medical evacuations. The plant in Seville will also assume maintenance, repair and modernization (MRO) tasks for aircraft already in service. Airbus will take advantage of the current hangars in San Pablo and optimize them to work with two aircraft at a time, imitating Getafe’s way of workingwhere usually one is converted while the other receives maintenance tasks. Figures. The new line will generate around 200 direct jobswhich will be added to the 2,000 professionals already working in São Paulo, and about 600 additional positions in the auxiliary industry. In Andalusia, Airbus is responsible for around 3,500 people between the San Pablo, Tablada (Seville) and Cádiz plants, and more than 14,000 throughout Spain. Why Seville. The president of Airbus in Spain, Francisco Javier Sánchez Segura, pointed ABC that the reasons were based above all on the technical knowledge accumulated in the A400M and C295 programs, the existing infrastructure (San Pablo is the only Airbus factory with two final assembly lines) and the operational proximity with Getafe, which will act as strategic coordinator of the entire program. A technological leap. Until now, Airbus Defense and Space’s activity in Seville revolved around the assembly and maintenance of the A400M and the C295, both military transport aircraft. Sanchez Segura underlined The Seville center will replicate the cutting-edge technologies developed in Getafe, including the intensive use of augmented reality applied to the assembly and inspection of systems. Andalusia, in the focus of aviation. For the Junta de Andalucía, the announcement fits into its strategy to place the community in one of the three most important European points, along with Toulouse and Hamburg. The acting Minister of Industry, Jorge Paradela, recalled that the region already has several important investments, such as the arrival of the Swiss company Pilatus to manufacture private and military training aircraft, and the Ryanair projectvalued at 500 million euros, to internalize the repair of aeronautical engines in Andalusia, with 600 direct jobs planned. The acting Minister of Economy, Carolina España, rated the Airbus announcement is “magnificent news”, also highlighting that exports from the Andalusian aerospace sector have grown by 86% so far in 2026. The other side. The ADM Seville fair, where the advertisement was presented, also attracted protests. The STOP Arms Fair Platform, which brings together social groups, unions, environmentalists and pacifists, gathered at the gates of FIBES to denounce “the institutional support” for the defense industry and the presence of companies that, according to these organizations, have links to human rights violations in armed conflicts such as the one in Gaza. What’s coming now. Airbus has about two years of works, personnel training and technological adaptation ahead before San Pablo delivers its first converted aircraft. If the planned pace is met, Seville and Getafe will end up operating in a coordinated manner to satisfy a larger customer base in a context that does not seem to be going to let up. According to Sánchez SeguraAerópolis depends on around 70% of Airbus’ workload, and this for the Seville plant means consolidating in a field that until now was foreign to it. Cover image | Air and Space Army In Xataka | The war in Iran is doing something that not even Ryanair imagined: making 20 euro flights a relic of the past

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