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

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

https://archive.ph/gKAeJ

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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

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Mathematicians Use Topology to Study the Shape of the World and Everything In It
by John Etnyre
February 26, 2025

Introduction:

(The Conversation) When you look at your surrounding environment, it might seem like you’re living on a flat plane. After all, this is why you can navigate a new city using a map: a flat piece of paper that represents all the places around you. This is likely why some people in the past believed the earth to be flat. But most people now know that is far from the truth.

You live on the surface of a giant sphere, like a beach ball the size of the Earth with a few bumps added. The surface of the sphere and the plane are two possible 2D spaces, meaning you can walk in two directions: north and south or east and west.

What other possible spaces might you be living on? That is, what other spaces around you are 2D? For example, the surface of a giant doughnut is another 2D space.

Through a field called geometric topology, mathematicians like me study all possible spaces in all dimensions. Whether trying to design secure sensor networks, mine data or use origami to deploy satellites, the underlying language and ideas are likely to be that of topology.

Read more here: https://theconversation.com/whats-the- ... t-235635

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It's sad that they had to write "most people" instead of "everyone"

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200-year-old "algebra wall" shattered with a bold new approach
https://newatlas.com/science/algebras-oldest-problem/

New research details an intriguing new way to solve "unsolvable" algebra problems that go beyond the fourth degree – something that has generally been deemed impossible using traditional methods for two centuries, until now.

Mathematician Norman Wildberger, an Honorary Professor at Australia's University of New South Wales, and computer scientist Dean Rubine have thrown out the rulebook and presented a new way to solve polynomial equations that go beyond x to the power of four – something that has only been resolved with "approximate solutions." While this won't mean a whole lot to school students in math class, accuracy in answering higher-order polynomial problems could have huge implications in the fields of science and technology.

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Prime Numbers, the Building Blocks of Mathematics, Have Fascinated for Centuries − Now Technology is Revolutionizing the Search for Them
by Jeremiah Bartz
May 30 , 2025

Introduction:

(The Conversation) A shard of smooth bone etched with irregular marks dating back 20,000 years puzzled archaeologists until they noticed something unique – the etchings, lines like tally marks, may have represented prime numbers. Similarly, a clay tablet from 1800 B.C.E. inscribed with Babylonian numbers describes a number system built on prime numbers.

As the Ishango bone, the Plimpton 322 tablet and other artifacts throughout history display, prime numbers have fascinated and captivated people throughout history. Today, prime numbers and their properties are studied in number theory, a branch of mathematics and active area of research today.

A history of prime numbers

Informally, a positive counting number larger than one is prime if that number of dots can be arranged only into a rectangular array with one column or one row. For example, 11 is a prime number since 11 dots form only rectangular arrays of sizes 1 by 11 and 11 by 1. Conversely, 12 is not prime since you can use 12 dots to make an array of 3 by 4 dots, with multiple rows and multiple columns. Math textbooks define a prime number as a whole number greater than one whose only positive divisors are only 1 and itself.

Math historian Peter S. Rudman suggests that Greek mathematicians were likely the first to understand the concept of prime numbers, around 500 B.C.E.

The linked article (see below) also includes a discussion of very large prime numbers.

Read more here: https://theconversation.com/prime-numb ... m-249223

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SciAm- Math Breakthroughs from Behind Bars

https://archive.ph/o06Md

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Probability Theorem Gets Quantum Makeover After 250 Years
August 28, 2025

Introduction:

(Eurekalert) How likely you think something is to happen depends on what you already believe about the circumstances. That is the simple concept behind Bayes’ rule, an approach to calculating probabilities, first proposed in 1763. Now, an international team of researchers has shown how Bayes’ rule operates in the quantum world.

“I would say it is a breakthrough in mathematical physics,” said Professor Valerio Scarani, Deputy Director and Principal Investigator at the Centre for Quantum Technologies, and member of the team. His co-authors on the work published on 28 August 2025 in Physical Review Letters are Assistant Professor Ge Bai at the Hong Kong University of Science and Technology in China, and Professor Francesco Buscemi at Nagoya University in Japan.

Additional extract:

Consider a case in which a person tests positive for flu. They may have suspected they were sick, but this new information would change how they think about their health. Bayes’ rule provides a method to calculate the probability of flu conditioned not only on the test result and the chances of the test giving a wrong answer, but also on the individual’s initial beliefs.

Bayes’ rule interprets probabilities as expressing degrees of belief in an event. This has been long debated, since some statisticians think that probabilities should be “objective” and not based on beliefs. However, in situations where beliefs are involved, Bayes’ rule is accepted as a guide for reasoning. This is why it has found widespread use from medical diagnosis and weather prediction to data science and machine learning.
Principle of minimum change

When calculating probabilities with Bayes’ rule, the principle of minimum change is obeyed. Mathematically, the principle of minimum change minimises the distance between the joint probability distributions of the initial and updated belief. Intuitively, this is the idea that for any new piece of information, beliefs are updated in the smallest possible way that is compatible with the new facts. In the case of the flu test, for example, a negative test would not imply that the person is healthy, but rather that they are less likely to have the flu.

Read more of the Eurekalert articel here: https://www.eurekalert.org/news-releases/1096395

Abstract

(Physical Review Letters)
Bayes’ rule, which is routinely used to update beliefs based on new evidence, can be derived from a principle of minimum change. This principle states that updated beliefs must be consistent with new data, while deviating minimally from the prior belief. Here, we introduce a quantum analog of the minimum change principle and use it to derive a quantum Bayes’ rule by minimizing the change between two quantum input-output processes, not just their marginals. This is analogous to the classical case, where Bayes’ rule is obtained by minimizing several distances between the joint input-output distributions. When the change maximizes the fidelity, the quantum minimum change principle has a unique solution, and the resulting quantum Bayes’ rule recovers the Petz transpose map in many cases.

Source of abstract: https://journals.aps.org/prl/abstract/ ... 5n4p-bxhm

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