helps

Fable 5 helps disprove a nearly century-old conjecture

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While Spain made history winning his second soccer World Cup on Sunday, a 34-year-old Harvard mathematician named Levent Alpöge asked Fable 5 for something interesting. Not that he tried to prove the Jacobi conjecture, but that he did the opposite: to refute it. Argentina kicked us while Spain played soccer and Ferrán of my life and my heart scored a historic goal. By the time it was all over, two things happened. The first, that Spain, we insist, was making history with its second star on the shirt. The second, that a conjecture that had not been proven for almost 90 years was definitively refuted thanks to the help of an AI. The aforementioned Jacobi conjecture suggests that a certain type of mathematical function could also work in reverse. It was formulated by Ott-Heinrich Keller in 1939, and in 1998 the mathematician Stephen Smale included it in his famous list of unsolved mathematical problems that were a challenge for mathematicians of the 21st century. A discovery that leaves as many questions as answers Alpöge has not explained in detail how he managed to reach that result or what prompt he used, but in his tweet he indicated that part of the credit was due to his “close friend fable“, the Anthropic model. Abhishek Sahafrom Queen Mary University of London, explained that the very way of facing the problem was unexpected. The conjecture seemed intuitively correct, but no one was trying to refute it, but rather prove it. Chris Bowman-Scargillfrom the University of York, pointed out something that he considers very important: it is one thing to find counterexamples that overturn conjectures and quite another to construct entire branches of mathematicswhich still requires human creativity. He gave as an example Fermat’s last theorem, solved by Andrew Wiles in 1994, and which forced him to develop dozens of pages with new and fascinating mathematical theories. Several experts have already validated this refutation, something that was relatively easy to do. For Saha, AI advances in mathematics had already surprised —they did it with one of the problems recently—, but this went further: “It is probably the most important conjecture in which AI has played a relevant role so far in mathematics,” he said. There is however some open questions: This particular counterexample refutes the conjecture with three variables, but a version with only two variables could be true. One thing is certain: mathematicians are taking advantage of this tool to help them in their work. The most famous in the world does it, of course. Ivan Fesenkofrom Westlake University in China, was talking about this when he stated that AI models are becoming more and more capable: “Right now, AI can already produce math graduates. In a year, it will produce math PhDs. And then the question arises: Do we really need that many mathematicians if AI can do these things so well?” It is a disturbing question, of course. Image | Vitaly Gariev In Xataka | A mathematical problem had been resisting experts for more than 80 years. An AI has surpassed them all

We have been told that drinking water on an empty stomach helps you lose weight. Scientific evidence says otherwise

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The Internet and social networks are full of supposedly easy tricks that promise almost miraculous results with a minimum effort for our body. One of these tricks is a habit that many people do as if it were a ritual: drinking a large glass of water, “yes or yes”, as soon as we get out of bed in the morning. This simple gesture promises to ‘wake up’ the intestines, activate the metabolism and promote weight loss. It’s a myth. What we hear on social networks is not always true, since we must face a large number of myths that have no scientific support behind them. And right now the best scientific evidence does not support this idea, Although it is true that drinking water increases our energy production. Thermogenesis. To understand where this widespread myth comes from, we must analyze the term “water-induced thermogenesis”, that is, the ability of our body to begin producing energy after drinking a glass of water. Here is a classic study In the medical literature it was observed that the consumption of 500 ml of water managed to increase the metabolic rate by around 30% during a period of 30 to 40 minutes. But although this percentage may seem incredible, the reality is that the acceleration of the metabolism translated into a total expenditure of 24 kilocalories. That is to say, its effect was so small that short-term weight loss was hardly going to be noticed due to this. It has been verified. Subsequent research in the fields of endocrinology and nutrition has attempted to replicate these data in different contexts. We have one of the examples in a clinical trial that evaluated the physiological effects in overweight or obese people, where an increase in energy expenditure of 24% was found for 60 minutes after ingesting 500 ml of water. But again it was seen that this slight temporary metabolic rebound does not imply a fat loss that is relevant in itself. On the scale. If now, instead of staying in the laboratory, we go to the real effect that this habit has on patients, we find that the narrative of water on an empty stomach as a slimming remedy loses much of its support, since the scientific evidence on weight loss attributable to water consumption is, in general terms, limited and of low to moderate quality. And the studies that have been done, despite pointing to weight loss, have a follow-up that is too short and a methodology that prevents giving a firm conclusion about applying this recommendation. The power of water. That dismantling the myth of a glass of water on an empty stomach is anticlimactic does not mean that hydration has no value in a weight control strategy. And the evidence suggests that drinking water helps to lose weight indirectly, since the mere fact of modifying the diet to go from a high consumption of sugary soft drinks or industrial juices to drinking water eliminates hundreds of calories a day with little effort. In addition, various trials suggest that drinking water before meals makes us feel full much sooner, which will reduce the amount of calories that we end up eating and, therefore, advancing a little further in the diet. Images | engin akyurt In Xataka | We believed that with Ozempic, people who lost weight exercised more. we believed wrong

We thought that sleeping was only good for rest. It actually helps us build new muscle.

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We spend a third of our lives sleeping, and although to some people it may seem a waste of time because literally while we sleep we are not ‘producing’, the reality is quite different. And it’s not just about resting, but our brain hides a real neural “switch” that, during sleep, dictates whether our body will build muscle, burn fat or, on the contrary, enter a state of metabolic emergency. What was seen. Joint research from the University of California and Stanford University, published in September 2025 in the prestigious magazine cell, managed to map this mechanism. The researchers identified a specific neuronal circuit in the hypothalamus composed of two fundamental players: the GHRH neuron, which acts as the “accelerator” of growth hormone, and somatostatin, which functions as the “brake.” Its balance is essential to regulate how much growth hormone is released during sleep. And it is not something that should be left in the background or only for children who are growing, but this hormone is essential to be able to build muscle, break down fat or even regulate glucose. In the first half of the night. Not all moments of the night are worth the same, since approximately 70% of daily growth hormone secretion occurs during the first cycle of deep sleep, also known as the N3 phase. In this way, if we shorten our hours in bed and miss that key rest, deep quality sleep is not achieved and the desired peak of growth hormone does not occur. What this directly leads to is accumulating fat and losing muscle tissue. The hunger. The muscle is not the only one affected, but our diet also suffers chemical sabotage. Here research has shown that little sleep drastically alters our appetite-regulating hormones. A large meta-analysis published in the journal Obesity Reviewsthat analyzed 21 studies with 2,250 participants, pointed out that short sleep causes leptin, which is the hormone that sends the signal of satiety, to decrease by 18%, while ghrelin, the hormone that triggers hunger, increases by 28%. This makes us have a greater appetite and prefer to consume more calories if we do not sleep enough hours. The metabolic risk. The impact of not sleeping goes far beyond hunger and the scale, since at a metabolic level, sleep restriction reduces insulin sensitivitywhich directly increases the risk of developing type 2 diabetes. More and more data. If you still had doubts about the benefits of sleeping correctly, we already know that having a good sleep allows us to be more productive and better integrate the different knowledge that we learn in our brain. But to this is now also added the ability to ‘create’ new muscle, making the smartest decision to be sleeping, although for some it is not very productive. Images | Slaapwijsheid.nl Anastase Maragos In Xataka | Hitting the gym every week is great, but it all depends on what you do right after you leave the gym.

The Navy mapped Cádiz by hand 230 years ago with sickening precision. Today it helps us to see how it has changed

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We tend to think of geography as a static canvas, unchanged by the passage of our short lives; however, when cartographic science It allows us to look into a window several centuries old, the reality is very different. And it is very different because the coast moves and changes, having in Spain a great example in the Bay of Cadizwhich has undergone a fascinating metamorphosis in recent centuries, and the secret to understanding it lies in a technical and scientific prodigy dated 1789. How it looks. We do not have (at the moment) a time machine to go back in our history, but we do have historical documents that do almost the same effect. One of the last analyzed has been the map of the port of Cádiz, a nautical chart which documents in obsessive detail what this region was like more than 230 years ago. A ‘Google Maps’. To understand the value of this document, you must travel to the period between 1783 and 1788. In the midst of the Enlightenment, the need to control the vital Atlantic routes required leaving behind approximate maps and embracing scientific rigor to be much more exact. Here was the brigadier of the Royal Navy Vicente Tofiño de San Miguel, then director of the Marine Guard Academies, who orchestrated the spectacular Maritime Atlas of Spain. The map of Cádiz, which is one of the 47 plates that make up this atlas, is a masterpiece of hydrographic engineering of the time. Outlined by the cartographer Felipe Bauzá and engraved by Fernando Selma, this 56.5 x 87 cm map mounted on canvas shows the cartography of the coast from Rota to the Sancti Petri river with a scale of 1:30,000. What makes it special. It is not only its aesthetics, but the data it contains by integrating precise toponyms, the exact location of the historic salt mines, military arsenals and even detailed bathymetric data mediated in “Castilian fathoms”. And with this basis, and after comparing it with the reality of the present, we can know how a piece of land has changed over time. The threat of sedimentation. Since 1726, the accumulation of sediments was a headache for maritime traffic in Cádiz as it is today. The cartographic comparison shows how the currents and the mouths of the rivers have been filling in parts of the bay, altering the natural draft and forcing the reconfiguration of port areas throughout the 19th and 20th centuries. The historic salt flats. In 1789, the map shows a vast and intricate network of salt mines that dominated the landscape, a crucial economic driver at the time since the value of salt was very high. But this has remained in the past, since the urban expansion of municipalities like Puerto Real and industrialization has devoured these salt flats. The coastal profile. In this case, comparisons between the past and present show us how the coastline has advanced and receded. In this way, areas that were previously estuaries or marshes are now dry land or port infrastructure that we have reclaimed from the sea, demonstrating the intense mark that man leaves on the environment. Anyone can see it. Fortunately, this piece of technological history is no longer confined to inaccessible display cases, since the National Geographic Institute It is available for download in its map library with the aim that any researcher can access it and draw conclusions like the ones we see today. Images | Nerea Garcia IGN In Xataka | One of the most impressive bridges in Europe is in Cádiz, it has a removable section and the largest span in Spain

helps you work safer from wherever you are

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Although it’s not for everyone, I love being what is now known as a digital nomad. I’m not tied to an office or a desk: I can work wherever I want (as long as I have an Internet connection, of course). That freedom makes it easy for you, although I think it is worth taking certain precautions in terms of security. Nothing too complicated: specifically, use a VPN like this one from Surfshark. It’s worth it cost-benefit: It barely costs 1.99 euros per month if you take their two-year plan. Surfshark Starter Subscription – monthly The price could vary. We earn commission from these links More security on your devices for less than the cost of a coffee a month We have spoken to you many times about VPNsa type of tool that is very easy to use and that gives us an extra layer of security while browsing the Internet. There are free options, yes, but you have to be careful with the vast majority of them: They are not as safe as they promise. It makes no sense to use something to gain security and have it work against you. In that sense, it is worth investing in one of the best VPNs. Because? It is easy to understand with a practical example. You are traveling with your laptop and need to work for a while. You choose a cafe or coworking with its WiFi network, since it provides you with both a network and a place to sit. Nothing has to happen, but the reality is that you will not know the security of that network nor if there is someone trying to intercept data in it. That’s where it comes into play a VPN like Surfshark. With a click (because really, using a VPN is not much more mysterious), you will pass your traffic through an encrypted tunnel that will prevent anyone from intercepting your data. This way, you are protecting your data and, probably, also those of your clients. For this reason, it is worth investing a little in one that provides you with good service, that is secure, fast, and has plenty of servers to connect to. Let’s now talk about price. Surfshark is one of the VPNs that has the best quality-price ratio with the offer it has active right now: it costs 1.99 euros per month if we choose its 24-month plan. The simple calculation tells us that we will pay 53.73 euros for having 2 years of VPN, although in reality it is more: the company gives us three extra months, so in reality it will be 27 months in total. Does that seem little to you? By choosing the 1 or 2 year plan, you also get a whole year of Calm free, one of the best medication and relaxation apps out there. A very attractive price for a tool that, if you work everywhere, can be great for you. Some of the links in this article are affiliated and may provide a benefit to Xataka. In case of non-availability, offers may vary. Images | Joseph Frank on UnsplashSurfshark In Xataka | Why it is dangerous to connect to public Wi-Fi and what you should do to protect yourself In Xataka | Antivirus in Windows 11: what they are, differences between free and paid and the best for your PC

There is a graphic that explains the atrocity that has occurred in Grazalema. And it helps to understand why the people continue to be evicted.

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And that graph is Nahel Belgherzea meteorologist who covers extreme events throughout the world and who, despite being used to them, has described what has occurred in the mountains of Cádiz as “hydrologically absurd.” “Hydrologically absurd”? It is. Grazalema, according to available datahas received more than 2,000 mm of rain in the last 20 days alone. That is, more than a normal year of rain and we are at the beginning of February. It is not surprising that Spanish reservoirs accumulate 43,341 hm³ of water; that is, 5,634 hm³ more than last week. As of today, Spain is at an astonishing 77.34% of its total capacity. And, in fact, today, many reservoirs continue to drain before the arrival of more water. What do you see in the graph? The graph in question is very simple: it is the accumulated rainfall for the Grazalema station. On the Additionally, in gray, you can see the cumulates from other years. And, as you can see, the curve is almost vertical: it has rained unspeakably in a few days. Compared to normal years (when the river grows in spring and winter), there is now a totally enormous water boom. Something unprecedented. And, precisely that, is what is forcing CISC technicians to continue reviewing the Grazalema aquifer. While the City Council insists that the return of the residents will take place when a safe return can be “guaranteed”, researchers from the Geological and Mining Institute of Spain (IGME) they are still on the ground. The aquifer, a geological structure 18 square kilometers in size, has been put under enormous pressure and authorities are focused on ruling out the slightest risk of collapse before the town’s inhabitants can return. The Junta de Andalucía, in fact, has been warning for days that it can go for a long time. Image | Nahel Belgherze In Xataka | Desertification is devouring southern Spain: Extremadura and Murcia face a completely dry future

a sports nutritionist helps us understand what’s behind it

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We eat every day and, even so, many doubts continue to arise around food. How many eggs are too manyif coconut oil deserves its fame, if sweeteners are a safe alternative or if training on an empty stomach really helps you burn more fat. These are questions that are repeated in conversations, social networks and headlines, often accompanied by forceful answers that do not always leave room for nuances. In the last episode of the first season of ‘Science and apart‘, which you can see on our YouTube channel and listen also on Spotify and iVooxÁngela Blanco chats with Maria Blancosports nutritionist, to calmly and contextually address some of the most widespread ideas about nutrition, habits and performance. Food, habits and many certainties that are not so certain The conversation starts with a question that forces us to go beyond personal tastes. If you had to choose a single food that is complete from a nutritional point of view, the specialist does not hesitate to point out a very specific one: “The egg is a very complete food. It has almost all the vitamins, it has minerals, it has a complete aminogram, that is, the protein we need, it has all the amino acids, and if it were missing something it would be vitamin C, it would lack fiber, it would lack other things… but well, the egg is the most complete food that I would choose.” After valuing the egg as food, the conversation enters one of the most repeated doubts. Is there really a clear limit to its consumption? María Blanco’s response is based on scientific evidence and avoids alarmism: “In scientific evidence, the daily egg, one to three eggs, is totally healthy. Because then we could restrict or avoid other types of foods that can harm us much more than the egg.” The episode also focuses on how certain reputations are built around what we eat. When asked by our colleague about foods with a reputation for being healthy, María Blanco points directly to one of the most popular in recent years: “Coconut oil. Because we have a very rich oil, which is olive oil. and that we have a very good origin because we are here and it is first-hand. And it (coconut oil) is like with a lot of propaganda.” The conversation also stops at one of the most used sugar substitutes. When talking about saccharin, María Blanco avoids simplifications and focuses attention on another less visible aspect: “There may be changes when using not only saccharin, but also sweeteners, in the microbiota that we have inside our intestine, and that can affect other areas.” To understand why this possible impact matters, the interviewee stops to explain what we are talking about when we mention the microbiota: “The microbiota or the microbiome is the set of bacteria that are living with us in our intestine.” And it adds a key nuance about internal balance: when these bacteria are no longer in a situation of eubiosis and dysbiosis occurs, effects that go beyond the digestive system can appear. The conversation ends by delving into some of the most discussed habits. From the appeal of ultra-processed foods to the debate on fasting and exercising on an empty stomach, María Blanco insists that the body does not work with instantaneous mechanisms: “There is no turn onthere is no switch, which is directly ‘well now I change this liver thing and start burning the fat from the adipocytes.’” We address all of this in more depth in ‘Science and Apart’, which closes its first season with a very interesting episode. A conversation designed to better understand how we eat and to put context to doubts that have been on the table for some time, with the help of our interviewee. Images | Xataka In Xataka | The Earth is not calm, it just seems that way: a geologist explains why natural disasters continue to surprise us

This app helps you fake your dream vacation

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There are times when entering Instagram it means getting depressed; people living dream lives and us at home with our pajamas on. Don’t worry because there is a new app with which you can also join the wave of posturing, one that uses AI to generate fake images of a vacation that never existed. Who needs vacations when you can invent them? Endless summer. The app in question is called Endless Summer and was created by Laurent del Rey, one of the members of the Meta superintelligence teamjust as they say in TechCrunch. Its creator defines the app as “a simple photo booth application to generate fake snapshots of your vacation, for when you feel exhausted and need to manifest the quiet life you deserve.” Because of course, if you are exhausted from working, the best thing is to invent a life in which you don’t work and are happy, no one ever said. The price of posturing. The app is available free for iPhone and the first two photos are free, but creating a larger album of your fake vacation is going to cost you money. Specifically 3.99 euros for 30 images, 19.99 euros for 150 images and 39.99 euros for 300 images. The result is quite good and, except for the clothes, I recognize myself in the photos that Endless Summer has taken for me, but you can’t choose where you want the AI ​​to take you on vacation. In my case it has been to a fast food restaurant in Los Angeles and a cafeteria in Paris. I’ve been to Los Angeles and I haven’t left this burger joint. Nano Banana. It is the model that the app uses to generate images. He spices it up with his own prompts to achieve that analog look and different variations of the subject. Nano Banana can be used within Gemini, so you don’t need to spend anything to create your fake vacation photos, just give it a nice prompt. Superintelligence. As we said at the beginning, the creator of Endless Summer is part of the superintelligence team that Zuckerberg has been forming all summer at the stroke of a checkbook. The best AI talents gather at the Meta offices to obtain the AGI (or That’s what Zuckerberg wanted). The reality is that we do not know much about its progress, only that They recently launched Vibes, an app to explore AI videos that was eclipsed days later by Sora 2 by OpenAIand that one of its members has just released a very frivolous app without much sense… Images | Endless Summer In Xataka | Meta does not have the most advanced AI of all, but it does have something much more important: a business plan

The secret to continuing to accumulate LEGO sets is not to keep them. This rental service helps you with that.

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Any adult LEGO fan have run into a similar problem. It is enormously enjoyable to set up the sets, but once finished comes the drama: where do we place it? The lack of space in modern homes or the impossibility of collecting several sets due to the space they occupy has led to the creation of a business especially aimed at those who do not want to give up building new sets, but do not need to keep them. Brick Borrow rents LEGO sets… which are then returned. How it works. Brick Borrow offers users the possibility of renting iconic sets by paying a fixed fee, always for an unlimited time. The amount of the fee determines what can be rented as follows: Mystery Set (9.99 euros): Brick Borrow chooses which set to send. Only one set per month. Builder (14.99 euros): The customer chooses what they want from the Brick Borrow catalogue. Unlimited loans every month. Only one set at a time. There is an annual version with a small discount. Master (24.99 euros): Like Buider, but with two sets per month. There are dozens of available setsin a catalog that is constantly growing, and as expected, we can find some of the most iconic: Mario Kart, the Shire from ‘The Lord of the Rings’, the Temple of the Golden Idol from Indiana Jones, Snow White’s cabin, the Creeper from ‘Minecraft’, the house from ‘Up!’, the ship from ‘Jaws’, a Concorde, Hogwarts, the Infinity Gauntlet, a bonsai, Sonic’s first level, Darth Vader’s helmet and a long etcetera… The wonderful world of AFOLs. This is a service clearly aimed at adult LEGO fans (or AFOL: Adult Fans Of LEGO), a typology that ranges from rigorous collectors to creative builders who see LEGO as a form of artistic expression, and who often value the building experience as much or more than the result. Rental introduces an interesting dimension for them: it democratizes access to complex or expensive sets that are sometimes inaccessible to a large part of the community. Aspects that a child does not appreciate, such as completism or playing with rare sets, are thus more accessible to this type of adult fans. To ride. It is more than proven therapeutic value of play in adults. But in addition, services like Brick Borrow (there are others, especially in the US: NetBricks, Brick Library, Blockria, Brickdrop, Lend A Brick, Chorley Bricks and many more) allow us to focus on an aspect of LEGO that sometimes goes unnoticed: building rather than enjoying the finished set. The activity of assembling blocks works as a mental escape and relaxation, similar to meditative or creative practices. The concentration on small pieces and the satisfaction of seeing a structure take shape generates a binding pleasure that transcends simple fun. The economics of access. There is a global trendlinked to a market increasingly dominated by subscriptions and temporary access to goods, for people looking for andxexperiences without the burden of storage or constant spending. Brick Borrow is not a unique experiment: we have seen it before on platforms that rent luxury clothing either technology. It implies a more responsible use of the product, promoting the so-called economy of access and reuse, repair, recycling and waste reduction, unlike the traditional linear model of “use and throw away”. The products and materials thus maintain their value for as long as possible, minimizing the environmental impact and promoting sustainable consumption. In Xataka | I worked for eight years in a sex shop. This is how the sector has changed and this is how it has changed me

HP Store helps us request and manage this help of 1,000 euros to renew PC

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For self -employed and for companies, having a good computer system to work is key. Here we talk about everything, both hardware and software. This, as is obvious in any field, requires a budget and investment that is not always feasible. To do this a little easier there is digital kit And HP helps us to manage it in full. HP makes it easy for us to take advantage of the digital kit He Digital kitAs we say, he is there to lend a hand to the Spanish freelancers and SMEs of less than 3 employees. It is a program of subsidies of European funds that allows access to a new computer with an aid that goes up to 1,000 euros of amount. If the equipment exceeds this price, you would only have to pay the difference (in addition to VAT, which is paid in all cases). Accessing it is a relatively simple process, although perhaps Not so much manage it once the subsidy is granted. Right there enters HP Store. This store will advise and accompany the entire process and SMEs, from the request to the management of the digital kit. Besides, All this help is completely freeso it is a great option to facilitate the entire process. Logically, they will also put at our disposal a series of very varied equipment so that we can choose the one that best suits each one. It should be noted that the time is over to request the digital kit. This can be requested Until October 31 or until the funds are exhaustedsomething that is likely to happen before that date. For that reason, it is something that we should not leave for the last day. These are some of the HP Store equipment that can be requested with the digital kit The HP equipment catalog that is included in the digital kit is quite varied, but we just leave you a selection of some of the most prominent. HP elitebook 845 series (and series 865) g11 + ms office As the first option, we have this ELITERBO 845 g11 series. It is a laptop that stands out for being compact and quite easy to transport, ideal for work. Its processor is an AMD Ryzen 5 and, at the memory level, it meets well: it has 16 GB of RAM and an SSD of 512 GB. Its screen is 14 inches And it comes with Windows 11 Pro and the Microsoft Install Officeto. We also have the 865 series available, which in this case takes its screen to 16 inches. HP elitebook 640 g11 + ms office series We have another interesting option with this Book Elite 640 Series. It is a device similar to the previous one as far as memory is concerned, but makes a power leap thanks to its processor, that in this case it is an intel core ultra 5. It also has a 14 -inch screen, comes with Windows 11 Pro and also with the Microsoft Office. HP Proone 440 G9 + MS Office In the event that we are not interested in a laptop, you can perfectly fit us this All in One of HP. This, in addition to also having the operating system and the Microsoft Office, comes with a 23.8 -inch screen and an Intel Core i5 processor of 13. generation. Besides, It has 32 GB of RAM512 GB of SSD and includes both keyboard and HP mouse. HP ZBook Power G11 Ryzen 9 + MS Office As a last option, we have this ZBook Power G11a perfect option for the most demanding. In this case, the team comes with a Ryzen 9, 32 GB processor of RAM and a 1 TB SSD. The most remarkable thing is that, unlike teams above, Bring an independent graph that is from Nvidia (A RTX 2000). In this case, in addition to the digital kit, we would have to pay 885 euros plus VAT. Some of the links of this article are affiliated and can report a benefit to Xataka. In case of non -availability, offers may vary. Images | HP In Xataka | Better laptops in quality Price: which to buy based on the use and eight recommended models In Xataka | Best Ultrabooks: Which buy and 10 light laptops recommended from 600 to 1700 euros

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