Category Archives: Mathematics

An Update on Shinichi Mochizuki, Inter-Universal Teichmüller Theory, and the ABC Conjecture

‘The occasion was a conference on the work of Shinichi Mochizuki, a brilliant mathematician at Kyoto University who in August 2012 released four papers that were both difficult to understand and impossible to ignore. He called the work “inter-universal Teichmüller … Continue reading

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A metric for sets of trajectories that is practical and mathematically consistent

‘Metrics on the space of sets of trajectories are important for scientists in the field of computer vision, machine learning, robotics and general artificial intelligence. Yet existing notions of closeness are either mathematically inconsistent or of limited practical use. In … Continue reading

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From Quanta Magazine: ‘Outsiders’ Crack 50-Year-Old Math Problem

‘In 2008, Daniel Spielman told his Yale University colleague Gil Kalai about a computer science problem he was working on, concerning how to “sparsify” a network so that it has fewer connections between nodes but still preserves the essential features … Continue reading

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Fun With Math: How To Make A Divergent Infinite Series Converge by Kevin Knudson

“Fun With Math: How To Make A Divergent Infinite Series Converge” is an interesting article about how to make the harmonic series converge by systematically discarding terms. Shockingly, the article appeared in Forbes. ‘I was having dinner with a visiting … Continue reading

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From Math Stack Exchange: How to choose a proper contour for a contour integral?

One of the great difficulties with contour integration is choosing an appropriate contour. Like integration itself, there are few rules and choosing the right contour is a matter of intuition, experience, and trial and error. A member of math stack … Continue reading

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The vector algebra war: A historical perspective

‘There are a wide variety of different vector formalisms currently utilized in science. For example, Gibbs three-vectors, spacetime four-vectors, complex spinors for quantum mechanics, quaternions used for rigid body rotations and Clifford multivectors. With such a range of vector formalisms … Continue reading

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A Computational Introduction to Number Theory and Algebra by Victor Shoup

A Computational Introduction to Number Theory and Algebra ‘A book introducing basic concepts from computational number theory and algebra, including all the necessary mathematical background. The book (now in its second edition) is published by Cambridge University Press. It can … Continue reading

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