Innovative research utilizing machine learning to analyze atomic pieces of geometry has marked a major advancement in mathematics, potentially revolutionizing the field by speeding up the identification and understanding of complex geometric shapes and patterns.
New research has leveraged machine learningMachine learning is a subset of artificial intelligence (AI) that deals with the development of algorithms and statistical models that enable computers to learn from data and make predictions or decisions without being explicitly programmed to do so. Machine learning is used to identify patterns in data, classify data into different categories, or make predictions about future events. It can be categorized into three main types of learning: supervised, unsupervised and reinforcement learning.” data-gt-translate-attributes=”[{“attribute”:”data-cmtooltip”, “format”:”html”}]”>machine learning techniques to identify the properties of atomic pieces of geometry. This groundbreaking effort holds the potential to propel the advancement of novel findings in the field of mathematics.
Mathematicians from the University of NottinghamThe University of Nottingham is a public research university located in Nottingham, England. It was founded in 1881 and is one of the oldest and most prestigious universities in the country. The University of Nottingham has a wide range of academic programs and disciplines, including the humanities, social sciences, natural sciences, engineering, and medicine. It is known for its strong research and has a number of research centers and institutes focused on various fields, including environmental science, energy, and health. It is a member of the Russell Group, a group of leading research-intensive universities in the UK.” data-gt-translate-attributes=”[{“attribute”:”data-cmtooltip”, “format”:”html”}]”>University of Nottingham and Imperial College LondonEstablished on July 8, 1907, by Royal Charter, Imperial College London is a public research university in London with a focus on science, engineering, medicine, and business. Its main campus is located in South Kensington, and it has an innovation campus in White City, a research field station at Silwood Park, and teaching hospitals throughout London. Its full legal name is the Imperial College of Science, Technology and Medicine.” data-gt-translate-attributes=”[{“attribute”:”data-cmtooltip”, “format”:”html”}]”>Imperial College London have, for the first time, used machine learning to expand and accelerate work identifying ‘atomic shapes’ that form the basic pieces of geometry in higher dimensions. Their findings have been published in Nature Communications<em>Nature Communications</em> is a peer-reviewed, open-access, multidisciplinary, scientific journal published by Nature Portfolio. It covers the natural sciences, including physics, biology, chemistry, medicine, and earth sciences. It began publishing in 2010 and has editorial offices in London, Berlin, New York City, and Shanghai. ” data-gt-translate-attributes=”[{“attribute”:”data-cmtooltip”, “format”:”html”}]”>Nature Communications.
Developing a ‘Periodic Table’ for Geometric Shapes
The research group started their work to create a Periodic Table for shapes several years ago. The atomic pieces are called Fano varieties. The team associates a sequence of numbers, called quantum periods, to each shape, giving a ‘barcode’ or ‘fingerprint’ that describes the shape. Their recent breakthrough uses a new machine learning methodology to sift very quickly through these barcodes, identifying shapes and their properties such as the dimension of each shape.
Insights from the Research Team
Alexander Kasprzyk is an Associate Professor in Geometry in the School of Mathematical Sciences at the University of Nottingham and was one of the authors on the paper. He explains: “For mathematicians, the key step is working out what the pattern is in a given problem. This can be very difficult, and some mathematical theories can take years to discover.”
Professor Tom Coates from the Department of Mathematics at Imperial College London and co-author on the paper said, “This is where Artificial Intelligence could really revolutionize Mathematics as we have shown that machine learning is a powerful tool for spotting patterns in complex domains like algebra and geometry.”
Sara Veneziale, co-author and a PhD student in the team, continues: “We’re really excited about the fact that machine learning can be used in Pure Mathematics. This will accelerate new insights across the field.”
Reference: “Machine learning the dimension of a Fano variety” by Tom Coates, Alexander M. Kasprzyk and Sara Veneziale, 8 September 2023, Nature Communications.
DOI: 10.1038/s41467-023-41157-1
Source: SciTechDaily
