Monday, 25 September 2023
New research has used machine learning to find the properties of atomic pieces of geometry, in pioneering work that could drive the development of new results in mathematics.
Mathematicians from the University of Nottingham and 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.
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 associate 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.
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.
This is where Artificial Intelligence could really revolutionise 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.”
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More information is available from Dr Alexander Kasprzyk on a.m.kasprzyk@nottingham.ac.uk
Notes to editors:
About the University of Nottingham
Ranked 32 in Europe and 16th in the UK by the QS World University Rankings: Europe 2024, the University of Nottingham is a founding member of the Russell Group of research-intensive universities. Studying at the University of Nottingham is a life-changing experience, and we pride ourselves on unlocking the potential of our students. We have a pioneering spirit, expressed in the vision of our founder Sir Jesse Boot, which has seen us lead the way in establishing campuses in China and Malaysia - part of a globally connected network of education, research and industrial engagement.
Nottingham was crowned Sports University of the Year by The Times and Sunday Times Good University Guide 2024 – the third time it has been given the honour since 2018 – and by the Daily Mail University Guide 2024.
The university is among the best universities in the UK for the strength of our research, positioned seventh for research power in the UK according to REF 2021. The birthplace of discoveries such as MRI and ibuprofen, our innovations transform lives and tackle global problems such as sustainable food supplies, ending modern slavery, developing greener transport, and reducing reliance on fossil fuels.
The university is a major employer and industry partner - locally and globally - and our graduates are the second most targeted by the UK's top employers, according to The Graduate Market in 2022 report by High Fliers Research.
We lead the Universities for Nottingham initiative, in partnership with Nottingham Trent University, a pioneering collaboration between the city’s two world-class institutions to improve levels of prosperity, opportunity, sustainability, health and wellbeing for residents in the city and region we are proud to call home.
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