Math News and Discussions

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Association for Computing Machinery and Institute of Mathematical Statistics Release First Issues of ACM/IMS Journal of Data Science
March 27, 2024

Introduction:

(Eurekalert) ACM, the Association for Computing machinery, and IMS, the Institute of Mathematical Statistics, have announced the publication of the first issues of the ACM/IMS Journal of Data Science (JDS), a new peer-reviewed publication. The scope of the journal is multi-disciplinary and broad, spanning statistics, machine learning, computer systems, and the societal implications of data science. JDS accepts original papers as well as novel surveys that summarize and organize critical subject areas. The ACM/IMS Journal of Data Science is a Gold Open Access publication, permanently and freely available online for anyone, anywhere to read.

Read more of the Eurekalert website here: https://www.eurekalert.org/news-releases/1039305

For the JDS website: https://jds.acm.org/

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New Mathematical Proof Helps to Solve Equations with Random Components
June 24, 2024

Introduction:

(Eurekalert) Whether it’s physical phenomena, share prices or climate models – many dynamic processes in our world can be described mathematically with the aid of partial differential equations. Thanks to stochastics – an area of mathematics which deals with probabilities – this is even possible when randomness plays a role in these processes. Something researchers have been working on for some decades now are so-called stochastic partial differential equations. Working together with other researchers, Dr. Markus Tempelmayr at the Cluster of Excellence Mathematics Münster at the University of Münster has found a method which helps to solve a certain class of such equations. The results have been published in the journal Inventiones Mathematicae.

The basis for their work is a theory by Prof. Martin Hairer, recipient of the Fields Medal, developed in 2014 with international colleagues. It is seen as a great breakthrough in the research field of singular stochastic partial differential equations. “Up to then,” Markus Tempelmayr explains, “it was something of a mystery how to solve these equations. The new theory has provided a complete ‘toolbox’, so to speak, on how such equations can be tackled.”

The problem, Tempelmayr continues, is that the theory is relatively complex, with the result that applying the ‘toolbox’ and adapting it to other situations is sometimes difficult. “So, in our work, we looked at aspects of the ‘toolbox’ from a different perspective and found and proved a method which can be used more easily and flexibly.” The study, in which Markus Tempelmayr was involved as a doctoral student under Prof. Felix Otto at the Max Planck Institute for Mathematics in the Sciences, published in 2021 as a pre-print. Since then, several research groups have successfully applied this alternative approach in their research work.

Read more here: https://www.eurekalert.org/news-releases/1049153

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Physicists Accidentally Found a New Way to Represent Pi
by Clare Watson
June 22, 2024

Introduction:

(Science Alert) Our favorite mathematical constant, pi (π), describing the ratio between a circle's circumference and its diameter, has taken on new meaning.

The new representation was borne out of the twists and turns of string theory, and two physicists' attempts to better describe particle collisions.

"Our efforts, initially, were never to find a way to look at pi," says Aninda Sinha of the Indian Institute of Science (IISc) who co-authored the new work with fellow IISc theoretical physicist Arnab Priya Saha.

"All we were doing was studying high-energy physics in quantum theory and trying to develop a model with fewer and more accurate parameters to understand how particles interact. We were excited when we got a new way to look at pi."

Being a mathematical constant, the value of pi hasn't changed, however irrational a number it is; over time we've simply gotten more exact renderings of its precise value, achieving 105 trillion figures at the latest count.

Read more here: https://www.sciencealert.com/mathemati ... resent-pi

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Mathematicians Just Discovered a Whole New Class Of Shape
by Kate Spalding
September 13, 2024

Introduction:

(IFL Science) As smart as we as a species are, Mother Nature almost always seems to have us beat. It’s true for things like brain surgery and robotics; it’s true for the race to swerve the heat death of the planet; and, apparently, it’s also true for advanced math.

“A central problem of geometry is the tiling of space with simple structures,” begins a new paper, published this week by researchers at the University of Oxford and reporting the discovery of a brand-new class of shapes named soft cells.

“The classical solutions, such as triangles, squares, and hexagons in the plane and cubes and other polyhedra in three-dimensional space are built with sharp corners and flat faces,” the authors write. “However, many tilings in Nature are characterized by shapes with curved edges, nonflat faces, and few, if any, sharp corners.”

Basically, the problem is this: how do we best completely fill a space with shapes or objects? When you set this question to humans, we instinctively go for sharp-cornered shapes – squares, triangles, hexagons, those kinds of things. It makes sense – after all, try to fill a space with circles, and you will necessarily end up with some empty bits, regardless of how small or intricately you pack them.

Conclusion:

“The lack of sharp corners and their soft, highly curved geometry makes soft cells ideal candidate models for biological structures which evolved under full or partial constraint to fill space,” they conclude.

Read more of the Eurekalert article here: https://www.iflscience.com/mathematici ... ape-75938

For results of the study as published in Pnas Nexus: https://academic.oup.com/pnasnexus/arti ... ogin=false

[firestar464]

High-Dimensional Sudoku Puzzle Proves Mathematicians Wrong about Long-Standing Geometry Problem

https://archive.ph/gKAeJ

[firestar464]

This Elegant Math Problem Helps You Find the Best Choice for Hiring, House-Hunting and Even Love

https://archive.ph/nKxNE

(Note that it doesn't really work for love; someone may turn you down LOL)

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'Impossible' Proofs of Pythagoras' Theorem Published by High School Students
by Tessa Koumoundouros
October 29, 2024

Introduction:

(Science Alert) What began as a bonus question in a high school math contest has resulted in a staggering 10 new ways to prove the ancient mathematical rule of Pythagoras' theorem.

It's long been claimed impossible to use trigonometry to prove what is effectively a theorem that's fundamental to trigonometry. This falls into the logical fallacy of circular thinking by trying to prove an idea with the idea itself.

"There are no trigonometric proofs because all the fundamental formulae of trigonometry are themselves based upon the truth of the Pythagorean theorem," mathematician Elisha Loomis had written in 1927.

But two US high school classmates, Ne'Kiya Jackson and Calcea Johnson, achieved the 'impossible' during their final year of high school in 2023.
Now they've published those results along with a further nine proofs.

Read more of the Eurekalert article here: https://www.sciencealert.com/impossibl ... -students

For a technical presentation of the proofs as published in The American Mathematical Monthly : https://www.tandfonline.com/doi/full/10 ... 0#d1e1821