solved

Spain seems to have solved the problem of aid for the purchase of electric cars. It only took seven years of chaos

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The aid to buy an electric car is chaos. They should stop being so soon. Very soon, in fact. Or, at least, that is the (umpteenth) promise that the Government has made in this regard. He announced it in the Council of Ministers, confirming that the presentation of the bases to receive the Auto+ Plan is just around the corner. This is what we know. What has been announced. He Auto+ Plan It should be up and running in the next few days or, at the latest, a few weeks. That is what has been announced in the press conference of the Council of Ministers where the first details have been given of how aid for the purchase of new completely electric vehicles should be unblocked. In the statement before the media, however, no more details have been clarified than those that were offered in February 2026 when the project was already late compared to the promises. That is to say: the aid will take into account the cost of the vehicle, its place of manufacture and the origin of its batteries. What did we know? Last February, The Government confirmed that aid for the purchase of electric cars They will be delivered as follows: Category Maximum aid amount Vehicle type Percentage received based on price Manufacturing Tourism (M1) 4,500 euros Electric: 50% of the aid (2,250 euros) Plug-in and electric hybrid with extended autonomy: 25% of the aid (1,125 euros) Maximum of 45,000 euros before taxes: Up to 35,000 euros: 25% of the maximum aid amount (1,125 euros) Between 35,001 and 45,000 euros: 15% of the maximum amount of aid (675 euros) Vehicles whose assembly and final completion prior to marketing has been carried out in an EU industrial facility will be allocated: 15% of the maximum aid amount (675 euros) Additionally, if a part of the battery manufacturing process (at least must include the assembly of the battery packs): additional 10% of the maximum aid amount (450 euros euros) Vehicle (N1) 5,000 euros Electric: 50% of the aid (2,500 euros) Plug-in and electric hybrid with extended autonomy: 25% of the aid (1,250 euros) No maximum limit: All vehicles receive 25% of the maximum aid amount (1,250 euros) Vehicles whose assembly and final completion prior to marketing has been carried out in an EU industrial facility will be allocated: 15% of the maximum aid amount (750 euros) Additionally, if a part of the battery manufacturing process (at least it must include the assembly of the battery packs): additional 10% of the maximum aid amount (500 euros) Moped (L3e, L4e and L5e) 1,100 euros Electric: 50% of the aid (550 euros) Plug-in and electric hybrid with extended autonomy: 25% of the aid (275 euros) Maximum of 10,000 euros before taxes: All vehicles receive 25% of the maximum aid amount (275 euros) Vehicles whose assembly and final completion prior to marketing has been carried out in an EU industrial facility will be allocated: 15% of the maximum aid amount (165 euros) Additionally, if a part of the battery manufacturing process (at least it must include the assembly of the battery packs): additional 10% of the maximum aid amount (110 euros) Quadricycle (L6e and L7e) 1,500 euros Electric: 50% of the aid (750 euros) Plug-in and electric hybrid with extended autonomy: 25% of the aid (375 euros) No maximum limit: All vehicles receive 25% of the maximum aid amount (375 euros) Vehicles whose assembly and final completion prior to marketing has been carried out in an EU industrial facility will be allocated: 15% of the maximum aid amount (225 euros) Additionally, if a part of the battery manufacturing process (at least it must include the assembly of the battery packs): additional 10% of the maximum aid amount (150 euros) In 2025 it has already been promised that these aids would be direct at the time of purchase. That is, the customer would leave the dealership without the obligation to advance the aid and waiting to receive the money in their bank account. The claim is recurring since 2019 when the first MOVES Plan was approved but that promise disappeared with the extension of the MOVES III Plan and it was said that it would be active with the application of the Auto + Plan. The deadline for this Auto+ Plan to come into force was January 1, 2026. However, weeks before it began to work, The dealers already indicated that they were not willing to advance the aid. Not, at least, if they had no guarantee of receiving the money within a reasonable period of time. So, who is going to provide the aid? It is something that is yet to be confirmed and that we will not know for sure until the aid bases are officially published, which should happen in the coming days. In Xataka we have contacted Ganvam (National Association of Vehicle, Repair and Spare Parts Sellers) who claim to have no confirmation of how this aid will be delivered. From Faconauto (Federation of Automotive Dealer Associations) yes, they have assured us that the aid can be obtained at the time of purchase but that the more specific details will arrive when the bases are presented. A loan that was a matter of faith. The intention, therefore, is that the customer can finally leave the dealership being very clear about the price of the car. The concessionaires’ employers assure us that there is no signed commitment of the time that the State will have to deliver said aid and that this is something that we will only know when the bases for the aid are published. Until now, manufacturers have been advancing help with an interest-free loan for 12 or 18 months (depending on the brand) in the hope that the client would receive the money before the bank received the payment of that fee, which can reach up to 4,500 euros. That is to say, it could be the case that the client ran out the deadline … Read more

We have been trying to optimize cooling for centuries. My grandfather from Toledo solved the heat with the simplest invention: a door split in two

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He looks at me and says: “broken doors.” In his country house, my grandfather’s door opens in half: bottom leaf, top leaf, each with its own hinge. Every time I see it I think of cowboy movies, the logo of saloon from some after-dinner western. I imagined: “of course, for the cat.” Nothing to see. history class. The idea of ​​the split door is not only from La Mancha or Toledo, it is the same principle as the Dutch doors or stable doors from four centuries ago. According to the definition itself, the first dutch doors They date from the mid-17th century, around period 1640-1650. From here they became a practical solution in farms and rural houses in the Netherlands and the United Kingdom, in order to let air and light in while keeping out animals, dust and some of the cold. The chronology itself can be found in Dutch paintings of the time, such as ‘Young Woman at a Dutch Door’, from 1645 and attributed to Samuel van Hoogstraten, a painter in Rembrandt’s workshop. Its use became popular in the American colonial era and its fame decreased towards the end of the 18th century, in favor of more robust, secure and single-leaf doors. A tunnel of cold and cleanliness. At that time, the word air conditioning did not exist, but there was a concern for hygiene: when you open only the upper half, the door works like a large window, releasing pollution from cooking smoke, which, being less dense, always accumulates at the top. And thus a small renewal current was created with the lower leaf closed. If the house had another opening on the opposite façade, the effect was amplified: cross ventilation is generated that brings in cooler air on one side while hot air leaves on the other. A simple but very effective formula if activated first thing in the morning or in the late afternoon, when the sun sets. And in winter? Well, the same door allows the opposite: opening only the lower part for a few minutes to ventilate without the entire pocket of hot air stuck to the ceiling escaping, reducing thermal losses in houses without modern insulation and where the heat was produced from braziersglories (under the floor) or low chimneys. In winter you open the bottom part to ventilate without losing the warmth that gets trapped on top. In summer, quite the opposite: you open the upper part so that the hot air can escape while the ground floor remains in darkness. If you light a fire in the kitchen, just open the top so that the smoke comes out through natural convection —chimney effect pure and hard—while the lower leaf continues to act as a barrier against the cold that comes from outside, usually the corral or the orchard. Thick walls, slow summers. The split door works because it works in tandem with another ancient technology: fat walls. So thick that they do not allow the electromagnetic radio waves that make WiFi to work. In the traditional architecture of the Meseta it is not uncommon to find enclosures more than fifty centimeters thick, chambers made of stone, rammed earth or solid brick, with a thermal inertia similar to that of a cave. The physics behind it couldn’t be simpler: the more mass the wall has, the longer it takes the outside heat to pass through it. Meanwhile, the interior remains relatively cool, as happens in any church where the sun takes hours to show itself or sometimes not even that. The same wall, in winter, absorbs part of the heat from braziers and stoves and slowly releases it when night falls, reducing thermal fluctuations in homes without radiators. What we call today “passive comfort management” is this very thing. And without IoT sensors or apps. Grandparents know it all. Silos: fresh but dry. The third lesson is taught to us silos and traditional barns. To store grain, a dry and cold microclimate must be created, in order to stop fungi, bacteria and insects that can rot the grain. When the grain is wet, the dough breathes, generates heat and creates pockets where the temperature rises and moisture condenses; If there is no ventilation, the pile becomes a breeding ground that can ruin tons of harvest. The solution is as simple as creating aeration ramps at the base and airlocks – small windows – along the walls that allow air to travel through the bulk, equalizing temperatures and removing steam upwards. It is the chimney effect but on the contrary: if you leave the ventilation openings open, the hot outside air enters through these ducts, rises through the mass of grain and heats it from within, forcing the openings to be sealed well once the cereal is dry and cold. Domestic science, with convection c. This whole repertoire of split doors, thick walls, and silos with eyes works because it takes advantage of three basic ideas of fluid physics: hot air rises, cold air falls, and air moves from areas of higher pressure to areas of lower pressure. End. The cross ventilation —that is, opening opposite openings so that air crosses the home—relies on pressure differences between facades and the orientation of the wind, while the chimney effect uses vertical corridors (patios, stairs, door openings) so that hot air rises and sucks in cooler air from below. In research On traditional patio houses, it has been measured how two patios with different temperatures activate a convection current that keeps the main rooms within comfortable ranges, without a single air conditioning machine. Each and every passive ventilation strategy involves some cooling, because “convection helps dissipate the heat accumulated inside as long as the openings and volumes are well thought out.” In the end, my grandfather’s split door didn’t hack anything, it was just properly installed. Two hundred years ago there were no engineers INTA in San Pablo de los Montes or in Quintanar de la Orden, but there were people with heat … Read more

There was a time when having a thermometer in the car was a luxury. This is how this ingenious invention solved it in the rearview mirror

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Today we have basic elements in our cars that have remained almost in the same place for decades. For example: the thermometer. For many years we have been able to know what temperature it is outside from the comfort of our car (although sometimes we wonder if the sensor works as it should). However, long before this element was incorporated into the instrument panel or the central screen of our car, some manufacturers opted for another place: under the driver’s side mirror. And at a time when analogue predominated, there was no other choice. The luxury America of the seventies The analog thermometer in the exterior mirror It was an invention born in the United States, in the context of the great American luxury cars of the seventies. A time when the most prestigious brands in the country competed to offer the most extravagant equipment possible, from Cartier watches integrated into the dashboard to garage opening systems or autonomy indicators. Click on the image to go to the post The mechanism was simple as well as ingenious. And just as they collect On the Curbside Classic forum, where owners and enthusiasts have debated this type of vehicle accessories for years, the thermometer worked using a spiral spring made of a material sensitive to changes in temperature (normally two metals with very different thermal expansion coefficients, such as brass or iron-nickel alloys). One end of the spring was fixed to the inside of the mirror housing; the other, to the small outer drum. As it expanded or contracted with heat or cold, the spring rotated the drum, which displayed the corresponding temperature on a graduated scale. There were no cables or electronics. It was pure precision mechanics. Additionally, some manufacturers included lighting built into the fixture, either through a light bulb or fiber optic which came from the dashboard (like in some Cadillacs). This last method was better, since it did not generate heat and did not alter the thermometer reading. Cadillac first, Lincoln later The brand that first offered this peculiarity was Cadillac, the jewel in the crown of General Motors. According to they count In The Autopian, Cadillacs equipped these thermometers in the side mirror around 1976, even before its direct rival Lincoln. The Cadillac Seville, the brand’s flagship model at that period, was one of those that included this accessory in its equipment, which was also available in other models in the range such as the Eldorado, the DeVille or the Fleetwood. Thermometer in a Lincoln. Image: Vanguard Motor Sales (Instagram) From Hagerty Media, in an article about the 1976 Cadillac Fleetwood Brougham, they say that the thermometer in the side mirror was an option available in that year’s catalog at a price of $18, which placed it among the most affordable extras within a menu of options that included everything from cruise control ($104) to the alarm system ($114) or the radio cassette ($239). The Buick Park Avenue, GM’s other big bet in the premium segment, also carried it from its early years as an equipment package to differentiate itself from the rest. As it appears on the equipment sheetthe original Park Avenue from 1975 already included the mirror with a thermometer along with other elements such as air conditioning and automatic rear leveling in the suspension. For its part, according to account In the middle, Lincoln, Ford’s luxury division, incorporated the illuminated thermometer into its models starting in 1978. A luxury that is difficult to find today Lincoln rearview mirror with built-in thermometer and wiring for automatic mirror control. Image: eBay Just like express the middle the middle, today it is extraordinarily difficult to find these mirrors in good condition. A mirror with thermometer for a 1988 Lincoln Town Car can reach between $140 and $660 on second-hand platforms such as eBay depending on the condition of the part, while one intended for the 1976-1979 Cadillac Seville can exceed $800. The Lincoln thermometer of the eighties already incorporated the double scale Fahrenheit and Celsius, something that the models of the late seventies did not have, as they only showed the temperature on the Fahrenheit scale. However, Cadillac started getting rid of its analog thermometerssince at the beginning of the 80s they already included more advanced temperature systems in their vehicles where the outside temperature was also displayed in digital format. The leap to digital The arrival of increasingly advanced electronic systems made these thermometers obsolete. In the first half of the 1980s, manufacturers they began to integrate digital screens on the dashboards that showed, among other data, the outside temperature. It was the era of “high-tech”, and digital had enormous appeal for the luxury buyer. The first car with digital instrumentation was the Aston Martin Lagondapresented as a prototype in 1976, although its cathode ray tube technology was too expensive for the mass public (imagine how expensive, if buying an Aston Martin wasn’t exactly cheap in itself). It was the arrival of liquid crystal LCD screens, and in particular the technology TN LCDcheaper and lighter, the one that democratized digital panels in cars during the first half of the eighties. From that moment on, show the outside temperature on a display inside the passenger compartment. It went from being a novelty to an increasingly common featurefirst in premium cars and, over the years, in increasingly accessible segments. In the mid-nineties, it was already a relatively common element in mid-high range cars. And if you have ever wondered where the sensor that measures the temperature and that is reflected on your car’s screen is located, usually It’s on the front bumperaway from the heat of the engine. Seen in perspective, the thermometer in the side mirror was a product of its time, but seeing it today, even in images, gives it a glimpse of very picturesque mechanical elegance. Cover image | The Autopian (eBay) In Xataka | Eddie Hall had a Bentley and many millions in the bank: he used both to set the most unlikely … Read more

Something strange happened inside the Earth in 2011 and 27 years of data have not solved the mystery

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In 2011, scientists observed an unexpected change in the flow of molten iron and nickel that makes up the earth core external. While its surface flow normally moves westward, it was detected to be moving just eastward. It was something totally unusual and mysterious. As a result of this observation, a study was launched, the results of which have recently been published. The objective was to know the reasons, but now there are only a few certainties and still many doubts. 27 years of observations. In this study 27 years of behavior of the Earth’s core were retrospectively analyzed, between 1997 and 2025. The core cannot be directly observed. However, its behavior directly influences that of the Earth’s magnetic field. Therefore, fluctuations in one can be detected in the other using satellite observations. It was seen that while the Earth’s outer core moves normally westward, there was a portion of it that went from a weak westward flow in 2010 to a much stronger eastward flow in 2012. It remained that way until 2020 and now appears to be starting to weaken again. Three options. When this change in movement was detected in 2011, it was thought that it could be due to three reasons. On the one hand, it could be a one-off fluctuation. On the other hand, it is possible that it is part of a periodic oscillation. And finally, it could be due to a way of establishing a balance in the circulation of the core. The only thing we see at the moment with the satellite observations is that the change was progressive. The behavioral modification began in 2010 and was already very clear in 2012. In 2011, when it was observed, it was in full transition. Other simultaneous observations. When analyzing the data from that period, it was seen that, coinciding with this change of direction, there were also some seismic signals that agree with the dates. Even geomagnetic shocks have been detected that correspond to a turbulent activity in the earth’s core. It’s not a whirlpool. This change of direction has not occurred throughout the core. For a start, the earth’s core consists of two parts: the internal and the external. The internal one is subjected to so much pressure that the metals are in a solid state despite the high temperatures. On the other hand, on the outside they are in a liquid state and, therefore, in motion. Even so, it wasn’t the entire outer core that changed its movement either. It corresponds to a specific region, located under the Pacific Ocean. It could be seen as a whirlpool, but these scientists have concluded that it is not, since the movement is part of a larger, wavy structure. Something like if an entire section of this part of the core suddenly began to move against expectations. Why is it important. The movement of the molten metal in the core generates electrical currents, which in turn give rise to a geomagnetic field that extends into space. Therefore, thanks to the movement of the Earth’s core we have an entire magnetic shield around the Earth that protects our atmosphere from the erosion caused by particles from the solar winds. For this nucleus to change its movement is not dangerous. We are not going to run out of atmosphere, because the core is still there. However, understanding its fluctuations can help us also understand the fluctuations of the magnetic field. This not only protects the atmosphere from erosion. It also helps us keep away a good part of the particles that could affect our telecommunications systems. Therefore, understanding how this shield works can help us prevent those more extreme events that do cause some technological havoc. That’s why, while this study has given us a lot of interesting data, it’s still not enough. We must continue monitoring the Earth’s core, what caused this anomaly of 2011. Image | THAT In Xataka | The Webb and Hubble telescopes simultaneously observed Jupiter’s auroras. The problem is that they didn’t see the same thing

The giant jugs of Laos have long baffled science. A “death jar” has solved the riddle

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The heart of Southeast Asia and scattered throughout the mountains of Xieng Khouang province in Laos, rest thousands of monumental stone vessels. Some of these reach three meters in height and weigh several tons, and that is why this place received the name ‘Plain of Jars’. However, this landscape has been a great mystery for all the experts because it is not known who carved them, nor how they moved them nor what they were for. Resolving. Now, a new archaeological study seems to have finally found the key piece of the puzzle, revealing a mortuary tradition much more complex and macabre than previously thought. The discovery of a huge “death jar” has confirmed that these stone colossi were not isolated monuments, but the protagonists of a sophisticated multigenerational funerary ritual. A secret. The key to this puzzle is based precisely on the analysis of a single, gigantic vessel that hid inside no more and no less than the bone remains of at least 37 different people. But the most interesting thing of all is that this “overcrowding” is not the product of a hasty mass grave or a sudden catastrophe, since the study shows that we are dealing with a practice known as secondary burial. How they did it. This practice, the truth is, is very far from our current customs, since instead of burying the deceased directly, the ancient culture that inhabited the area allowed the bodies to decompose first. Once cleaned of meat, the bones were transferred and deposited inside these monumental jars, being a process quite similar to the one that continues with Spanish royalty in the Royal Pantheon of Escorial. But the presence of the remains of so many people in a single jar suggests that these were reopened and reused over several generations, functioning as authentic family or community pantheons. Ritual recycling. This article does not come out of nowhere, but already in 2023 investigations at “site 1” of the plain had found signs of secondary burials around the stones, but this new discovery consolidates the hypothesis that the jars themselves were main containers of this mortuary tradition. The most fascinating thing about this research is the time lag that the dating has revealed since scientists have discovered that the history of the Plain of Jars is made up of overlapping layers. This shows that the human remains analyzed date from between the 9th and 13th centuries, but the gigantic stone jars are, according to geological and archaeological estimates, much older. What does it mean? Basically, the landscape was the subject of a profound “ritual recycling.” The medieval inhabitants of Laos did not carve the jugs; They came across a pre-existing, mysterious and monumental megalithic landscape, and decided to appropriate it for their own funerary rituals. In other words, the site was not built for a single function or at a single moment, but rather had an unusually long lifespan, being resignified by different cultures over the centuries. Images | Wikipedia In Xataka | We still don’t know where Tartessos was, but we do know where we are going to solve the enigma: in Badajoz

The banks didn’t want anything to do with oil. Wall Street has solved it with the 2008 mortgage strategy

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Oil and gas producers in the United States are turning to the financial magic of Wall Street to fuel their acquisitions in a frenetic race for growth. To achieve this, they are packaging thousands of pots into investment vehicles and selling stakes to American investors, replicating the exact same model that has long been used for mortgages, auto loans and other sources of securitized income. Away from the spotlight, the number of these operations has grown rapidly in recent years. Industry experts consulted by Financial Times They estimate that the total amount of debt issued through this format already ranges between 20,000 and 30,000 million dollars. It is a fundamentally opaque market, where most transactions are closed privately. Historically, independent oil and gas producers financed its operations through loans reserve-based (RBL) and high-yield debt. However, the situation has changed drastically. Some commercial banks have reduced their exposure to the extractive sector to meet their sustainability strategies under environmental, social and governance (ESG) policies, or in response to public concern over climate change. Added to this is the fear of traditional investors of “stranded assets” and the general uncertainty about the long-term viability of the sector in the midst of the energy transition. In addition, rising interest rates have raised costs, making high-yield debt too expensive or inaccessible for many producers. To survive, companies They have found an alternative way: They transfer their mature wells, known as proven, developed and producing (PDP) reserves, to a newly created Special Purpose Entity (SPE). This entity operates independently and is structured to be “bankruptcy-remote”, ensuring that the transferred assets are completely separate from the balance sheet of the producing company and safe in the event of its bankruptcy. Attracting conservative money By isolating these high-quality assets, the bonds issued by the SPE manage to achieve an “investment grade” rating. This seal of quality attracts a new class of investors who would normally avoid oil risk: pension funds, insurance companies and large asset managers looking for structured financial products with stable returns. For the oil companies, business is great. The securitization allows them to obtain advance rates (advance rates) of between 55% and 75% of the value of the reserves, figures significantly higher than those available in traditional RBL loans. To convince credit rating agencies, the secret lies in diversification and insurance. On the one hand, thousands of assets are grouped together; for example, Raisa Energy closed an operation combining more than 3,000 wells operated by more than 50 companies in more than 20 counties. On the other hand, long-term hedges are contracted to protect investors from oil fluctuations, reaching up to 85% of the entity’s production for a period of five to seven years. The “time bomb” and the cracks in private credit But financial engineering sometimes hides structural cracks. Brandon Davis, founder of energy intelligence company AFE Leaks, describes in FT These price hedges act as a “ticking time bomb” in case other production costs increase. If the price of oil rises, the company’s income is capped because the difference goes to the hedging counterparty (usually a bank). However, if at the same time there is inflation in operating costs, such as field services or water treatment, the profit margin backing the bonds could be seriously eroded. The cracks in this engineering are not an isolated case in the energy sector, but a symptom of a greater malaise in the opaque world of private credit on Wall Street, where patience (and money) is beginning to run out. This risk is framed at a time of growing tension for the entire private credit ecosystem on Wall Street. Investors are starting to demand their money back. In Cliffwater’s $33 billion fund, clients requested to withdraw 14% of their capital in a single quarter, but the firm said it only I would pay around 50% of those requests, forcing the other half to wait. If the panic spreads, traditional banks will not escape unscathed either. Lending by US banks to non-depository financial institutions, which includes private credit, reached 1.2 trillion dollars in the middle of last year, almost tripling its share compared to a decade ago. Furthermore, as with oil wells, the securitization market as a whole is extremely sensitive to external regulatory or macroeconomic shocks. A clear example occurred recently in another sector: Mpower Financing had to postpone the sale of almost $250 million in bonds backed by loans to international students. The cause was investors’ fear of the new restrictive visa policies of the Donald Trump administration. If regulatory changes or geopolitical crises hit the energy sector unexpectedly, oil securitization could face a similar collapse in demand. The danger of forgetting the nature of the business Wall Street has packaged a high-risk industry into a tame-looking product, but geology and the global market are difficult to tame. “The trick has always been to convince the rating agencies that measures have been put in place to mitigate the risk,” warns Olivier Darmounieconomist specialized in credit markets at HEC Paris. “But that’s the inherent thing about oil and gas, it’s an inherently volatile business.” Darmouni points out the ultimate risk: “If something goes wrong, the main problem will be that oil and gas will run out of capital” if producers start defaulting on bond payments. As long as the money keeps flowing, the machine will not stop. But as Laura Parrott warnshead of private fixed income at Nuveen, the market is experiencing a lot of effervescence. In scenarios of such investment fever, he concludes, “people are going to be trapped.” Image | Photo by David Vives on Unsplash Xataka | Climate change is no longer profitable: WallStreet and large investors abandon green policies

A young man has solved a mathematical problem that lasted 60 years in 80 minutes with ChatGPT. That’s the least interesting thing about the story.

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He is 23 years old, his name is Liam Price and he has no advanced mathematical training. Even so, a few days ago he opened the Erdös problem websitepicked one at random and pasted it into ChatGPT. I didn’t know the history of the problem or who had tried it before. What he received back seemed like a good solution, and after consulting with a friend who was studying mathematics, the two realized they might be on to something special. A few hours later Terence Tao, one of the most renowned mathematicians in the world, confirmed that problem #1196 of Erdös, a conjecture about primitive sets of integers that had not been solved since 1966, had a solution. I had found her GPT-5.4 Pro in just 80 minutes. Not like that. This problem analyzed a question about the behavior of a particular mathematical sum on primitive sets, that is, sets of integers where none divides the other, when those numbers become very large. Jared Lichtman, a Stanford mathematician, had spent years on the problem and had made partial progress, but he and those who had tried before were starting from the same starting point that seemed like the right path. A novel idea. GPT-5.4 used another starting point. He stayed in the airmetic terrain and used a special function called von Mangoldt functiona classic tool of number theory known for its connections to prime numbers and Riemann zeta function. No one had thought about that approach to the problem, and as Lichtman explained when talking about the OpenAI model solution, “The LLM took a completely different route.” The achievement is real, but with nuances. Litchman praised the proposed solution by GPT-5.4, but there is one detail that has been omitted in many comments on this event: the raw output of ChatGPT was, in the words of this mathematician, “pretty poor.” This solution made it necessary for several experts to interpret it, detail it and extract from it the underlying idea that allowed the conjecture to be solved. Price didn’t know he had the solution until his friend read it, and he wasn’t sure until Tao confirmed it. The official repository of AI contributions to Erdös problemsmaintained by Tao himself on GitHub, classify the result as a solution generated in human-AI collaboration, not as a solution developed solely by AI. The distinction is important. A previous scandal. A few weeks ago Sebastien Bubeck, a researcher at OpenAI, posted on X that GPT-5 had “solved” several Erdös problems. That publication exceeded 100,000 views, but the mathematical community and also that surrounding the AI ​​industry criticized that statement. Demis Hassabis, CEO of DeepMind, called that statement “shameful.” What had actually happened is that the model I had found solutions to already solved problems on the web. Bubeck finished deleting the original tweet and tried to back down, but all this raised doubts about the validity of the application of AI to solve mathematical problems. AI and the mathematical success rate. Terence Tao and Nat Sothanaphan maintain the aforementioned record of all AI contributions to Erdös problems on GitHub. Each of the entries in that list or table is classified with a traffic light: green for complete solution, yellow for partial progress, and red for failure. In the category of completely AI-generated solutions with no known prior literature there are three green, fourteen yellow, and eight red traffic lights. However, the repository itself adds a unique comment: those who try to use AI to solve these problems and fail do not usually report it, so it is likely that AI has been applied “silently” to a large number of these problems without success, and those attempts do not appear in any table. There is a clear bias here because only successes generate headlines. Trying to measure what matters. In February 2026, eleven mathematicians created the initiative “First Proof“. In it they included ten mathematical problems that arose naturally in their research projects. For each one they included encrypted answers uploaded to a verification site, and they gave the AI ​​systems a week to try to solve those problems that had never appeared in any training data set. Preliminary results indicate that today AI models cannot overcome that barrier autonomously, and what happens is that there are still limits to what AI can really contribute in mathematics. But then, is there a revolution or not? Terence Tao offered a clear explanation as to why GPT-5.4 had succeeded where others had failed for 60 years. What had happened was what he described as a collective blockage of the mathematical community, because everyone started from the same origin because it was “the natural one”, the one marked by tradition. The AI ​​didn’t know that was the “correct” way to start, and that ignorance turned out to be an advantage. It’s not that the AI ​​was smarter, it’s that it had no biases about how to approach the problem. Now it remains to be seen if this novel way of trying to solve problems in unorthodox ways works. This will confirm whether what happened with Erdös’s problem number 1196 was an isolated case or whether a 23-year-old boy has managed to change our vision of how to tackle mathematical problems. Image | Universal Pictures In Xataka | There is a mathematically perfect way to cut a ham and cheese sandwich and it has been discussed since 1938.

Iceland has solved it in the middle of the desert

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Trapping carbon dioxide emissions and literally turning them into stone seems like an invention straight out of the blue. Futuramawhere in the future everything is recycled. The problem is that this trick of underground alchemy hid a terrifying small print: his exorbitant thirst. To get carbon to mineralize underground, the system needs to swallow absurd amounts of liquid, specifically between 20 and 50 times more water than the mass of CO₂ we are trying to store. However, a new industrial-scale study published in the magazine Nature just rewritten the rules of the game. An international team, with researchers from Iceland, Saudi Arabia and Italy, has shown in the western Saudi desert that it is possible to petrify CO₂ without wasting a single drop of external fresh water. Salvation under the sands of Saudi Arabia. As the authors of the research detail, this area is a real challenge: it is full of large facilities that emit a lot of CO₂, such as refineries and desalination plants, but it lacks the underground saline aquifers or sedimentary traps that are traditionally used to inject carbon. Salvation was under his feet. About 24 kilometers from the Jizan Economic Complex and Refinery, geologists took advantage of an immense bed of highly fractured volcanic rocks (basalts) that have been there for between 21 and 30 million years. There they tested an ingenious system for recirculating subsoil fluids. The gigantic “soda” trick. To carry out the experiment, the engineers used two main wells, separated by just 130 meters: one functions as a “production” well (extracts water) and the other as an “injection” well. The process is a closed circuit and isolated from the atmosphere so that oxygen does not enter or gas escape. They extract the water that already lives in the depths, circulate it through pipes and, 150 meters underground, inject pure CO₂ into it in the form of bubbles until it completely dissolves. According to the project scientists, dissolving the gas in water has two brutal chemical and mechanical advantages: It gets heavy: CO₂-laden water is denser than regular still water, so it creates a non-buoyant fluid, greatly limiting the risk of the gas migrating to the surface and back into the atmosphere. It becomes acidic: This liquid is acidic and greatly accelerates the dissolution of the silicate minerals present in the basaltic rock. As the rock dissolves, it releases metals that provide the cations needed to form stable minerals, such as calcite. A question of geopolitical survival. The data from this pilot is a resounding success. The team injected 131 tons of CO₂ into the subsoil. After monitoring the area with trackers, they discovered that approximately 70% of all that injected carbon had been mineralized within ten months. Measurements showed that the concentration of dissolved inorganic carbon in the returning water had been reduced by 90% compared to what was initially injected. Reusing water from the reservoir itself offers substantial advantages. Not only do you forget about bringing external water, but you also reduce the risk of the pressure of fluids underground increasing dangerously. Furthermore, by injecting water that has the same composition as the original underground reserve, the risk of compatibility problems, such as losses of permeability in the reservoir, is reduced. The current dimension. As we recently analyzed in Xataka In the wake of military escalation in the region, the real Achilles heel of the Arabian Peninsula is not oil, but thirst. Countries like Saudi Arabia depend 70% on their desalination plants to survive. In a scenario where the supply of fresh water is a strategic vulnerability and a matter of biological survival, allocating massive volumes of water to bury emissions was simply unfeasible. Therefore, this advance opens the door for the Middle East – where a large part of global oil production is also concentrated – to be able to use its basalt rocks to store carbon without sacrificing a vital resource. A providential accident. Sometimes setbacks are the best of tests. In September 2023, the submersible pump in the extraction well broke down. When the technicians brought it to the surface, they found its interior full of rock grains cemented by up to 14% calcite, as well as other minerals such as siderite and ankerite. The isotope analyzes made it clear: these solid cements were formed from the CO₂ injected during the pilot project. The gas had literally petrified in the very bowels of the machine. An “energy bargain”. As if that were not enough, we must add energy savings. As the research details, injecting CO₂ with this method requires a surface pressure of only 12 to 14 bars. That’s 8 to 16 times less pressure than conventional carbon capture plants require. Basically, CO₂-laden water is drawn into the system driven by gravity. Regarding its future potential, engineers calculate that the underground pores of this particular area (estimated between 24,000 and 43,000 m³) would have enough space to house between 22,000 and 40,000 tons of mineralized CO₂. Geology dictates: the limit of the stone. Every geological technology has its own physical limits. As experts explain Natureas water, CO₂ and basalt interact, the total volume of solid minerals increases. This means that the pore space is reduced and can end up blocking water flow paths in the long term. To get around this problem, the researchers propose that we may have to resort to fracturing the rock (fracking), an option still little explored in basaltic systems. What is clear is that this technological innovation is proposed as a great complement to conventional capture systems, not as an exclusive alternative, since in the end it is the geological conditions that rule. But thanks to this pioneering experiment, there is something we can take for granted: the lack of rivers or fresh aquifers is no longer an excuse for not returning our emissions to the subsoil and turning them into stone. Image | Eric Gaba and Nature Xataka | Neither oil nor gas: if a total war breaks out between the US … Read more

We have solved the problem of space junk by burning it. A SpaceX lithium trail just proved to be a terrible idea

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For decades, the aerospace industry has had a consensus solution to the problem of space junk: burn it. A fairly simple phenomenon that is based on the satellite reentry when it ends its useful life in the atmosphere so that it begins to suffer friction and completely disintegrates. But the reality is that we are facing a huge problemsince physics reminds us that matter is neither created nor destroyed. We have captured him. Science is realizing that we are not removing space junk, we are just vaporizing it into metallic aerosols that are changing the chemistry of our own sky. And the definitive clue to this problem was found on the night of February 19, 2025where a team of German researchers pointed a laser into the sky over Kühlungsborn. What they detected in this case at about 100 kilometers altitude, in the thermosphere, was something that should not be there, since there were large amounts of lithium. And it wasn’t there for no reason, since it just coincided hours before with the re-entry of a SpaceX Falcon 9 rocket which had disintegrated over the Atlantic between Ireland and the United Kingdom. Something new. The signal measured in this case was not very subtle, since was 10 times bigger to the usual concentration in that region, and this finding was collected in an article because it marks a great milestone: it is the first time that the metallic contamination released from a specific piece of space junk at the exact moment of burning has been observed “live” and from Earth. The metallic iceberg. The incident with this Falcon is not something isolated in our society, but is a symptom of the structural change we are experiencing. In 2023, a team of researchers already used different devices to be able analyze more than 50,000 aerosol particles in the stratospherewhich is the layer where our ozone layer resides, at about 15-30 km altitude. What did they see? Historically, the metals found in the stratosphere came from meteorites that entered our planet. But today it is estimated that 210 tons of aluminum per year in the atmosphere comes from the disintegration of satellites and rockets, compared to the 20 tons per year that vaporize naturally from meteors. But lithium is not the only metal in the atmosphere of our planet, since scientists have detected more than twenty elements, among which aluminum, copper, lead or silver stand out… This is something that does not fit with the normal composition of meteorites, but it does coincide with the materials that different aerospace companies use to create their rockets and satellites. There is no planning. The pace of launches has skyrocketed in recent years, and if today we are close to 10,000 objects orbiting the Earth, we have to know that only Starlink aspires to have more than 40,000 satellites in Earth orbit low. But the problem is that the useful life of these devices is short, so their inevitable fate is to end up vaporized over our heads. Its effects. Science here is quite clear that the effects of filling the stratosphere with these metals are currently unknown. But the projections suggest that we should not be calm because elements such as aluminum and copper are important catabolizers that can affect the delicate ozone layer. In addition to this, metallic particles can act as special condensation nuclei, altering the microphysics of polar stratospheric clouds. And if that were not enough, adding anthropogenic material to sulfuric acid aerosols changes their size and ability to scatter sunlight. Ironically, we are altering the reflectivity of the stratosphere, the same layer that some scientists want to use for climate geoengineering, without knowing what the consequences will be. The planetary limit. The models here suggest that, if the planned megaconstellations materialize, the fraction of stratospheric particles contaminated with aluminum from satellites will rise from the current 10% to around 50%. In other words, the load of metals in the stratosphere could grow by around 40% compared to natural levels. Here for years space agencies have assumed that disintegrating satellites was a completely harmless and clean practice. The example of the Falcon 9, which has validated the warnings of the scientific community, shows us that the Earth’s orbit and our atmosphere make up a connected ecosystem. In this way, launching tens of thousands of objects into space and then burning them on our own roof may be a solution to keep space clean, but we are dirtying the sky in return. In Xataka | Spain and Portugal have joined forces to launch satellites with a mission: to monitor catastrophes in real time

In 1986 a man parked on the wrong side of the gas station. That day he solved an embarrassing problem for all drivers

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The history of innovation It’s full of big names and epic breakupsbut also of silent advances born from minimal errors, from everyday mistakes that anyone could have made. Sometimes, a small mistake reveals a problem so common that no one had thought of it or knew how to formulate it, and it is enough to look at it differently to find a solution that ends up benefiting millions of people without it being barely noticed. In this case, one man saved millions of drivers from embarrassment. A universal problem. Maybe his name doesn’t sound familiar to you, but the story of Jim Moylan It is more important than it seems. The story begins with a scene as trivial as it is recognizable: a Ford engineer (Moylan) soaked by the rain, standing at a gas station, realizing that he has parked in the wrong side of the pump. Where anyone would have felt frustration or perhaps some embarrassment, he saw an everyday problem that could be solved elegantly, cheaply and definitively, and in a matter of minutes. wrote a memorandum proposing a small symbol on the instrument panel to indicate which side the tank was on, a simple idea born from personal experience and the conviction that eliminating that doubt would save time, inconvenience and, yes, small humiliations for millions of drivers. The path to a great idea. Moylan was not a media figure or a senior manager, but an engineer with a long and discreet career within the all-powerful Ford Motor Company, a man, yes, professionally obsessed. with instrument panels and with making them as clear and useful as possible. Thus, after sending his original proposal in 1986, the man did not think about it again, but the company did: the symbol he had scribbled on a page quickly went into development, it was approved without much resistance. and ended up integrating in the first models of the late eighties, demonstrating that in large organizations there was still room for a good idea, no matter how small and coming from whoever it was, to cross the hierarchy and become a reality. From Thunderbird to the entire world. Months passed until the first public appearance of the arrow came, an almost imperceptible moment, hidden in the instrument panel of a Ford Thunderbird 1989. It didn’t matter, its power lay precisely in that simplicity. It was so obvious and useful that the competition It didn’t take him long to copy itand in a very short time it went from being an internal Ford solution to becoming a de facto standard in the global automobile industry, and it did so to the point that today it appears in practically any car in the world, including electric ones, where it points to the side of the charging port with the same unbeatable logic. The inventor without a patent (or ego). Unlike other innovators, Moylan He never patented his idea nor did he ask for financial compensation or public recognition, content simply to see how his arrow worked and helped people. For decades, millions of drivers benefited from his invention without even knowing his name, while he silently watched as that little “walk of shame” at gas stations disappeared, getting closer sometimes to strangers to explain the usefulness of the symbol, but without ever mentioning that it had been his doing. Late recognition. I remembered a few weeks ago the wall street journal which was not until many years later, thanks to a chance investigation from a podcast and to the rescue of internal files, when Jim Moylan’s name came to light and he was publicly recognized as the author of one of the most discreet and universal innovations in the automobile. The man died without having sought famebut he left a legacy that lives on every time someone stops at a pump and, with a simple glance at the instrument panel, knows exactly where to stand, reminding us that sometimes true genius lies in solving the obvious in the simplest way possible. Image | Josh In Xataka | An engineer decided one day to put the BMW airplane engine in a car. The result was tremendous In Xataka | When an engineer wanted to cross Africa by car, he invented a wooden one. It would be the beginning of the end

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