Mathematicians needed 300 years to demonstrate Fermat’s last theorem. Computers have not achieved it

“I have found a really admirable demonstration, but the margin of the book is very small to put it.” It is what the 17th -century French mathematician Pierre de Fermat wrote when stating his His “last theorem”. Fermat’s problem took three decades to be found between the mathematician papers and three centuries until that admirable test was discovered. And yet the case is not entirely settled, only that the challenge is something different. Take it to a computer. He New challenge It is to make a computer to try the elusive theorem. That is the objective of a new project, FERMAT FORMALISINGled by Imperial College London. Fermat’s problem. Fermat’s last theorem “postulates that, if A, byc are natural numbers and not equal to zero, the an+bn = cn equation has no solution if n is greater than two. Formally demonstrating something is not as simple as trying it by rehearsal and error, and this demonstration, too complex for the “megish margin” of the Fermat’s notebook would be lost for centuries. The problem was resolved in 1994 by the British Andrew Wiles, who had begun to solve this puzzle with only 10 years. In 2016 Wiles was awarded the ABEL award, the award considered “The Nobel of Mathematics.” Almost one million pounds. Another 30 years after the resolution of the enigma and more than three centuries after the death of Fermat, a team of researchers, led by Kevin Buzzard, of Imperial College London, has put to work to take a different step, teach A computer to solve this problem. The new project It began at the end of 2024 and will last until 2029. It has a financing of just over 934,000 pounds and already begins to give some results, in the form of code fragments that are added to a Database in Github. What remains to be resolved.It can be contraintuitive, but this type of reasoning, which lead us to formally demonstrate mathematical theorems, are difficult to teach computers. Recently, Buzzard and other experts They explained the complexity of the matter to the French newspaper I monde. To begin with, we must take into account that the resolution of this theorem is complex, it is no accident that several generations of mathematics would turn the brains trying to find it. These mathematicians also had previous experience in the field of resolution of these types of problems. As Buzzard explained to the French newspaper, mathematicians have a base that allows them to “jump steps” when explaining the resolution to this problem. A computer, however, must start from scratch when building its own explanation for the matter. And all this, for what? “Fermat’s last theorem (…) has no applications, theoretical or practices, in the real world,” Buzzard pointed out A few months ago to the magazine New Scientist. So why so much effort to teach a computer to solve something we already resolved? The key here is not in the past but in the future. According to Explain the team at the head of the projectcomputers today can be used to attend mathematicians trying to solve problems such as demonstration of theorems, but there is an obstacle to materializing some forms of help. The problem, they point out, is that few mathematicians have focused on working with this software, so there are no tools that have the “definitions” used by mathematicians to solve these problems. Working on this problem should be used to create the necessary databases for solving similar problems in the future. In Xataka | We had more than a century trying to solve some mathematical problems. The AI ​​is starting to unravel Image | Diofanto’s arithmetic / Pierre de Fermat by Rolland Lefebvre

El Corte Inglés boundary offers leave OLED televisions, speakers, computers and much more

During this weekend, El Corte Inglés has launched its particular campaign Limit offerswhich will be available until next February 16 and is loaded with very good discounts on all types of products in the electronics category. From Samsung OLED televisions to MSI laptops. Samsung Oled S93D by 1,199 eurosa very complete 55 -inch television that has a good 43%discount. HP S5 524SW by 129 eurosa monitor with anti -reflective screen and with Eyesafe certification. Samsung Galaxy Buds Fe by 59 eurosvery good Bluetooth headphones that have dropped in price with the 46%discount. Marshall Acton III by 220.15 eurosa Bluetooth speaker with retro design and with a good audio power. MSI KATANA 15 by 1,399 eurosa gaming laptop with Intel processor and RXT 4060 graphics card. Samsung Oled S93D OLED televisions do not usually lower too much price, except for the occasional exception. During the boundary offers of El Corte Inglés, we can find a good discount on the Samsung Oled S93Dsince it stays for 1,199 euros instead of 2,099 euros. This television stands out, among other things, for its 55 -inch OLED OLED PANELfor their speakers that offer an audio power of 60W RMS and that are compatible with Dolby Atmos And because it comes with the voice assistant Alexa integrated. * Some price may have changed from the last review HP S5 524SW If you are looking for a good Monitor to work at homein the boundary offers of El Corte Inglés we can find the HP S5 524SW for only 129 euros instead of 169 euros. It is interesting both for the price and for everything that offers: 23.9 inches antirreflective IPSEyesafe certification, 100 Hz soda rate and Full HD resolution. * Some price may have changed from the last review Samsung Galaxy Buds Fe On the other hand, if what you are looking for is a good price in some Bluetooth headphones That they are comfortable and that offer a very good audio quality, the Samsung Galaxy Buds Fe They are now reduced by 59 euros instead of the usual 109 euros. They are comfortable, perfect for sports, have a good autonomy of up to 30 hours and have Active noise cancellationas well as transparency mode. * Some price may have changed from the last review Marshall Acton III In the boundary offers of El Corte Inglés there are also very good prices in Bluetooth speakers. One of the best offers is the model Marshall Acton IIIsince it stays for 220.15 euros instead of 299 euros. The most striking is its retro design inspired by the classic amplifiers, but we must also know that it offers a good 30W RMS audio power. * Some price may have changed from the last review MSI KATANA 15 There are even very good prices in gaming laptops. Some models with components to have a very good experience in video games (also in productivity) have received discounts of the most interesting, such as the case of MSI KATANA 15which has dropped from 1,799 euros to 1,399 euros. The MSI computer comes with a 15.6 -inch QHD screen, riding an Intel Core i7 13620h processor, has 32 GB of RAM and 1 TB of SSD, its graphics card is a NVIDIA GEFORCE RTX 4060 And it comes with Windows 11 Home. * Some price may have changed from the last review 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 | The English Court and Buying (header), Samsung, HP, Marshall, MSI In Xataka | Better televisions in quality Price: which to buy and seven recommended 4K 4K 4K In Xataka | Best laptops in quality price. Which to buy depending on the use and eight recommended models

The future of quantum computers depends on helium-3 from the Moon. There is already a plan to start bringing it in 2029

Helium is the second lightest and most abundant chemical element in the universe, if we stick to ordinary matter. It is only surpassed in this classification by hydrogen. This noble gas accounts for between 24 and 26% of the total mass of stars, which are also responsible for manufacturing it. fusing hydrogen nuclei inside through the reactions of nuclear fusion that they carry out naturally, and which we talk to you about in quite some depth in the article that we dedicate to the life of the stars. Still, most of the helium in the universe was not made by stars: it was produced by the Big Bang, which is why scientists refer to it as “primordial helium.” But the most curious thing is that, despite how abundant it is in the universe, it is scarce on Earth. Its great lightness caused most of the helium contained in the cloud of dust and gas from which our planet was formed to escape gravitational confinement. Be that as it may, the real protagonist of this article is not the normal helium that we have all heard about; It is helium-3, an isotope that may play a crucial role in nuclear fusion reactions that will possibly help us solve forever our energy problems. And also in other areas, such as, for example, in dilution cooling systems that use superconducting quantum computersas well as other emerging technologies. Interlune plans to test the extraction of lunar helium-3 in 2027 Most of the helium that we can find in the universe has taken the form of an isotope known as helium-4, which is characterized by having two protons and two neutrons in its nucleus. Although, as we have seen, most of it was lost during the formation of the Earth, this gas can also arise as a result of natural radioactive decay of heavier chemical elements, such as uranium, radium or thorium, which are relatively scarce on our planet. The only difference between helium-4 and helium-3 is that the latter isotope has one less neutron in its nucleus. That’s all. We know that helium-4 nuclei have two protons and two neutrons, so helium-3 nuclei will have two protons and a single neutron. It may seem like an irrelevant difference, but it is not. It is a very important difference because the physicochemical properties of the element vary as a consequence of their lower atomic mass. And, in the case of these two isotopes of helium, their behavior also changes from the point of view of quantum mechanics. The solar wind spreads helium-3 throughout the solar system and beyond, causing it to reach surrounding planets in relatively large quantities. The bad news is that if helium-4 is relatively scarce on Earth, helium-3 is even more so. Stars, like our Sun, produce it in large quantities as a result of nuclear fusion reactions between hydrogen nuclei that occur when they are in the main sequence stage during which they burn most of their fuel. Once created, the solar wind spreads helium-3 throughout the solar system and even beyond, causing it to reach surrounding planets in relatively large quantities. The reason why this gas hardly accumulates on Earth is that our planet has a double protective shield: the atmosphere and the Earth’s magnetic field. These two barriers represent a very effective defense against the solar wind and cosmic radiation, which reaches the atmosphere mainly in the form of protons and high-energy alpha particles. The Moon, unlike the Earth, has no atmosphere, so it lacks this protective shield. Additionally, its magnetic field is much weaker than Earth’s and is not dipolar. The terrestrial, on the other hand, can be approximated to a magnetic dipole, so the magnetic field lines are directed from the north pole to the south pole. All this causes the surface of the Moon to be much more exposed to cosmic rays and the solar wind than the surface of the Earth, causing very significant quantities of helium-3 transported by the solar wind to accumulate there, which is deposited in rocks and lunar dust, a few meters deep. Up to a million tons of regolith need to be processed to obtain a single kilogram of helium-3 The first challenge that humanity will have to solve to appropriate the helium-3 accumulated on the Moon is none other than the processing of lunar regolithwhich is the loose layer of soil and rock fragments that covers the surface of the satellite. Interlune, a company founded in Seattle (USA) in 2020, plans to extract the regolith and process it using compact harvesting robots that, according to this company, are very efficient. The problem is that lunar dust is very abrasive, and, in addition, up to a million tons of regolith must be processed to obtain a single kilogram of helium-3. Even so, this company plans to test the extraction of this isotope with a lunar mission in 2027, and in 2029 it intends to build a pilot plant on the Moon. It sounds good, but a priori these dates seem excessively optimistic. Additionally, it is still unclear how much it will cost to transport lunar helium-3 to Earth using space vehicles. Be that as it may, we can be sure that it will not be easy or cheap to do so. Image | Pixabay More information | Quantum Insider In Xataka | Graphene is ready to break into quantum computers: scientists plan to use it in a new type of qubit

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