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AlphaGeometry
AlphaGeometry is an artificial intelligence (AI) program that can solve hard problems in Euclidean geometry. The system comprises a data-driven large language model (LLM) and a rule-based symbolic engine (''Deductive Database'' ''Arithmetic Reasoning)''. It was developed by DeepMind, a subsidiary of Google. The program solved 25 geometry problems out of 30 from the International Mathematical Olympiad (IMO) under competition time limits—a performance almost as good as the average human gold medallist. For comparison, the previous AI program, called Wu's method, managed to solve only 10 problems. DeepMind published a paper about AlphaGeometry in the peer-reviewed journal ''Nature'' on 17 January 2024. AlphaGeometry was featured in ''MIT Technology Review'' on the same day. Traditional geometry programs are symbolic engines that rely exclusively on human-coded rules to generate rigorous proofs, which makes them lack flexibility in unusual situations. AlphaGeometry combines such ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
DeepMind
DeepMind Technologies Limited, trading as Google DeepMind or simply DeepMind, is a British–American artificial intelligence research laboratory which serves as a subsidiary of Alphabet Inc. Founded in the UK in 2010, it was acquired by Google in 2014 and merged with Google AI's Google Brain division to become Google DeepMind in April 2023. The company is headquartered in London, with research centres in the United States, Canada, France, Germany, and Switzerland. DeepMind introduced neural Turing machines (neural networks that can access external memory like a conventional Turing machine), resulting in a computer that loosely resembles short-term memory in the human brain. DeepMind has created neural network models to play video games and board games. It made headlines in 2016 after its AlphaGo program beat a human professional Go player Lee Sedol, a world champion, in a five-game match, which was the subject of a documentary film. A more general program, AlphaZer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Artificial Intelligence
Artificial intelligence (AI) is the capability of computer, computational systems to perform tasks typically associated with human intelligence, such as learning, reasoning, problem-solving, perception, and decision-making. It is a field of research in computer science that develops and studies methods and software that enable machines to machine perception, perceive their environment and use machine learning, learning and intelligence to take actions that maximize their chances of achieving defined goals. High-profile applications of AI include advanced web search engines (e.g., Google Search); recommendation systems (used by YouTube, Amazon (company), Amazon, and Netflix); virtual assistants (e.g., Google Assistant, Siri, and Amazon Alexa, Alexa); autonomous vehicles (e.g., Waymo); Generative artificial intelligence, generative and Computational creativity, creative tools (e.g., ChatGPT and AI art); and Superintelligence, superhuman play and analysis in strategy games (e.g., ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
AI Software
Artificial intelligence (AI) is the capability of computational systems to perform tasks typically associated with human intelligence, such as learning, reasoning, problem-solving, perception, and decision-making. It is a field of research in computer science that develops and studies methods and software that enable machines to perceive their environment and use learning and intelligence to take actions that maximize their chances of achieving defined goals. High-profile applications of AI include advanced web search engines (e.g., Google Search); recommendation systems (used by YouTube, Amazon, and Netflix); virtual assistants (e.g., Google Assistant, Siri, and Alexa); autonomous vehicles (e.g., Waymo); generative and creative tools (e.g., ChatGPT and AI art); and superhuman play and analysis in strategy games (e.g., chess and Go). However, many AI applications are not perceived as AI: "A lot of cutting edge AI has filtered into general applications, often without b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclidean Geometry
Euclidean geometry is a mathematical system attributed to ancient Greek mathematics, Greek mathematician Euclid, which he described in his textbook on geometry, ''Euclid's Elements, Elements''. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. One of those is the parallel postulate which relates to parallel lines on a Euclidean plane. Although many of Euclid's results had been stated earlier,. Euclid was the first to organize these propositions into a logic, logical system in which each result is ''mathematical proof, proved'' from axioms and previously proved theorems. The ''Elements'' begins with plane geometry, still taught in secondary school (high school) as the first axiomatic system and the first examples of mathematical proofs. It goes on to the solid geometry of three dimensions. Much of the ''Elements'' states results of what are now called algebra and number theory ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Google
Google LLC (, ) is an American multinational corporation and technology company focusing on online advertising, search engine technology, cloud computing, computer software, quantum computing, e-commerce, consumer electronics, and artificial intelligence (AI). It has been referred to as "the most powerful company in the world" by the BBC and is one of the world's List of most valuable brands, most valuable brands. Google's parent company, Alphabet Inc., is one of the five Big Tech companies alongside Amazon (company), Amazon, Apple Inc., Apple, Meta Platforms, Meta, and Microsoft. Google was founded on September 4, 1998, by American computer scientists Larry Page and Sergey Brin. Together, they own about 14% of its publicly listed shares and control 56% of its stockholder voting power through super-voting stock. The company went public company, public via an initial public offering (IPO) in 2004. In 2015, Google was reorganized as a wholly owned subsidiary of Alphabet Inc. Go ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Mathematical Olympiad
The International Mathematical Olympiad (IMO) is a mathematical olympiad for pre-university students, and is the oldest of the International Science Olympiads. It is widely regarded as the most prestigious mathematical competition in the world. The first IMO was held in Romania in 1959. It has since been held annually, except in 1980. More than 100 countries participate. Each country sends a team of up to six students, plus one team leader, one deputy leader, and observers. Awards are given to approximately the top-scoring 50% of the individual contestants. Teams are not officially recognized—all scores are given only to individual contestants, but team scoring is unofficially compared more than individual scores. Question type The content ranges from extremely difficult algebra and pre-calculus problems to problems in branches of mathematics not conventionally covered in secondary or high school and often not at university level either, such as projective and complex geo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wu's Method
Wenjun Wu's method is an algorithm for solving multivariate polynomial equations introduced in the late 1970s by the Chinese mathematician Wen-Tsun Wu. This method is based on the mathematical concept of characteristic set introduced in the late 1940s by J.F. Ritt. It is fully independent of the Gröbner basis method, introduced by Bruno Buchberger (1965), even if Gröbner bases may be used to compute characteristic sets. Wu's method is powerful for mechanical theorem proving in elementary geometry, and provides a complete decision process for certain classes of problem. It has been used in research in his laboratory (KLMM, Key Laboratory of Mathematics Mechanization in Chinese Academy of Science) and around the world. The main trends of research on Wu's method concern systems of polynomial equations of positive dimension and differential algebra where Ritt's results have been made effective. Wu's method has been applied in various scientific fields, like biology, computer v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nature (journal)
''Nature'' is a British weekly scientific journal founded and based in London, England. As a multidisciplinary publication, ''Nature'' features Peer review, peer-reviewed research from a variety of academic disciplines, mainly in science and technology. It has core editorial offices across the United States, continental Europe, and Asia under the international scientific publishing company Springer Nature. ''Nature'' was one of the world's most cited scientific journals by the Science Edition of the 2022 ''Journal Citation Reports'' (with an ascribed impact factor of 50.5), making it one of the world's most-read and most prestigious academic journals. , it claimed an online readership of about three million unique readers per month. Founded in the autumn of 1869, ''Nature'' was first circulated by Norman Lockyer and Alexander MacMillan (publisher), Alexander MacMillan as a public forum for scientific innovations. The mid-20th century facilitated an editorial expansion for the j ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MIT Technology Review
''MIT Technology Review'' is a bimonthly magazine wholly owned by the Massachusetts Institute of Technology. It was founded in 1899 as ''The Technology Review'', and was re-launched without "''The''" in its name on April 23, 1998, under then publisher R. Bruce Journey. In September 2005, it was changed, under its then editor-in-chief and publisher, Jason Pontin, to a form resembling the historical magazine. Before the 1998 re-launch, the editor stated that "nothing will be left of the old magazine except the name." It was therefore necessary to distinguish between the modern and the historical ''Technology Review''. The historical magazine had been published by the MIT Alumni Association, was more closely aligned with the interests of MIT alumni, and had a more intellectual tone and much smaller public circulation. The magazine, billed from 1998 to 2005 as "MIT's Magazine of Innovation", and from 2005 onwards as simply "published by MIT", focused on new technology and how it is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symbolic Artificial Intelligence
Symbolic may refer to: * Symbol, something that represents an idea, a process, or a physical entity Mathematics, logic, and computing * Symbolic computation, a scientific area concerned with computing with mathematical formulas * Symbolic dynamics, a method for modeling dynamical systems by a discrete space consisting of infinite sequences of abstract symbols * Symbolic execution, the analysis of computer programs by tracking symbolic rather than actual values * Symbolic link, a special type of file in a computer memory storage system * Symbolic logic, the use of symbols for logical operations in logic and mathematics Music * Symbolic (Death album), ''Symbolic'' (Death album), a 1995 album by the band Death * Symbolic (Voodoo Glow Skulls album), ''Symbolic'' (Voodoo Glow Skulls album), a 2000 album by the band Voodoo Glow Skulls Social sciences * Symbolic anthropology, the study of cultural symbols and how those symbols can be interpreted to better understand a particular society ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rule-based System
In computer science, a rule-based system is a computer system in which domain-specific knowledge is represented in the form of rules and general-purpose reasoning is used to solve problems in the domain. Two different kinds of rule-based systems emerged within the field of artificial intelligence in the 1970s: * Production systems, which use ''if-then rules'' to derive ''actions'' from ''conditions''. * Logic programming systems, which use ''conclusion if conditions rules'' to derive ''conclusions'' from ''conditions''. The differences and relationships between these two kinds of rule-based system has been a major source of misunderstanding and confusion. Both kinds of rule-based systems use either forward or backward chaining, in contrast with imperative programs, which execute commands listed sequentially. However, logic programming systems have a logical interpretation, whereas production systems do not. Production system rules A classic example of a production rule-b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Large Language Model
A large language model (LLM) is a language model trained with self-supervised machine learning on a vast amount of text, designed for natural language processing tasks, especially language generation. The largest and most capable LLMs are generative pretrained transformers (GPTs), which are largely used in generative chatbots such as ChatGPT or Gemini. LLMs can be fine-tuned for specific tasks or guided by prompt engineering. These models acquire predictive power regarding syntax, semantics, and ontologies inherent in human language corpora, but they also inherit inaccuracies and biases present in the data they are trained in. History Before the emergence of transformer-based models in 2017, some language models were considered large relative to the computational and data constraints of their time. In the early 1990s, IBM's statistical models pioneered word alignment techniques for machine translation, laying the groundwork for corpus-based language modeling. A sm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
