What's Happening in Mathematics?
page 5 (newest)
An occasionally updated series of links to mathematical news — new applications,
new discoveries, problems, personalities, prizes...
new discoveries, problems, personalities, prizes...
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When the signal is a change in tunnel length one thousandth of the diameter of a proton, noise is a huge problem. Template searches find what you're looking for — even if it's not there. Everyone expects gravitational waves to exist... but did LIGO find any?
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On 12 September 2015 the Laser Interferometer Gravitational-Wave Observatory (LIGO) switched on its upgraded detectors. Two days later it made its first detection. The media reported one of the greatest scientific breakthroughs of the century and a Nobel prize followed. Now a group of physicists, who have done their own analysis of the data, are skeptical: “We believe that LIGO has failed to make a convincing case for the detection of any gravitational wave event.” New Scientist investigates...
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The 2017 Atlantic hurricane season caused $265 billion of damage. Christina Patricola and Michael Wehner use a supercomputer to analyse cyclones (aka hurricanes, typhoons) via high-accuracy mathematical climate models that include convection on small spatial scales. They conclude that man-made climate change increased the wind speed and total rainfall of hurricanes such as Katrina, Irma, and Maria by 15%-30%. Hurricanes as severe as Harvey will become twenty times more likely by 2100.
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After a ten-year search, Raimar Wulkenhaar and Erik Panzer have obtained an explicit solution to an equation in quantum field theory that everyone thought could be solved only numerically. The equation has applications to elementary particles.
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How it spreads, and how to test methods for defending against it
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Dorje Brody and David Meier model fake news as biased noise in communication channels. Their model predicts such things as the likelihood of flipping an election outcome if false stories are released with a given frequency. Meier says their work "highlights the importance of mathematical modelling in dealing with the challenges our society faces."
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The Councils of the IMA and the LMS have awarded the 2018 Christopher Zeeman Medal to Dr Hannah Fry of University College London for her contributions to the public understanding of the mathematical sciences. The Christopher Zeeman Medal was created and named in honour of Professor Sir Christopher Zeeman FRS, the first mathematician to deliver the Royal Institution Christmas Lectures.
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The Fields Medal is the most prestigious award in mathematics, despite its low monetary value. It is awarded every four years by the International Mathematical Union. The 2018 winners were Caucher Birkar, Alessio Figalli, Peter Scholze, and Akshay Venkatesh.
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Biologist and amateur mathematician Aubrey de Grey has made a big advance on the Hadwiger-Nelson problem, which dates from 1950. How many colours are needed to colour every point in the plane, with no two points unit distance apart having the same colour? Until recently it was known to be 4, 5, 6, or 7. De Grey has proved it's not 4.
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László Fejes Tóth's Zone Conjecture of 1973 states that if a unit sphere is covered by several zones, their total width is at least π. A zone of width w is the set of points withing spherical; distance w of a great circle. A proof was found in 2017 by Zilin Jiang and Alexandr Polyanskii.
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Discovery of the 50th Mersenne Prime
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On 3 January 2018 the GIMPS project found the largest known prime number, 2^(77,232,917)-1, with 23,249,425 decimal digits. Like most record primes, it's a Mersenne prime—a power of two, minus one. The mathematical significance of such discoveries is small, but record-breaking computations are a good way to test computers. To prove the point, the same GIMPS software earlier revealed a flaw in Intel's Skylake CPU.
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Claims it was 500 years earlier than we thought are now disputed
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According to a press release from the Bodleian Library, carbon dating shows that the ancient Indian Bakhshali manuscript contains the oldest known occurrence of the symbol 'zero', making its origins 500 years older than previously believed. Three samples were dated to 224-383 AD, 680-779 AD, and 885-993 AD; zero appears on the oldest. But Kim Plofker et al. [The Bakhshali Manuscript: A Response to the Bodleian Library's Radiocarbon Dating , History of Science in South Asia, 5 134-150] argue that the birch bark folios dated 224-383 AD and 680-779 AD were consecutive in the manuscript, written by the same hand, and contain consecutive parts of the same calculation. If so, zero is not 500 years older than we thought.
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Current cosmology maintains that the universe contains 4.9% ordinary matter, 26.8% dark matter and 68.3% dark energy. But dark matter has never been detected directly. Alternatives have been proposed (and largely ignored); this is a new one. Colin Rourke's A New Paradigm for the Universe formulates Mach's Principle mathematically and removes the need for dark matter. In the proposed theory there is no Big Bang and the universe is much older than current estimates. Available on the arXiv and Amazon.
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Guozhen Wang and Zhouli Xu have answered a long-standing question by proving that the 61-sphere has a unique smooth structure. The only other odd-dimensional spheres with this property have dimensions 1, 3, 5. Download preprint from arXiv or access published paper in the Annals of Mathematics (account needed).
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