Author: IMC

Mathematician Shinichi Mochizuki’s Inter-universal Teichmüller theory has attracted controversy since it was published in 2012, with no one able to agree whether it is true. Now, a $1 million prize is being launched to settle the matter.

The Inter-Universal Geometry Center (IUGC) is overseeing the prize

Zen University

A prize of $1 million is being offered to anyone who can either prove or disprove an impenetrable mathematical theory, the veracity of which has been debated for over a decade.

Inter-universal Teichmüller theory (IUT) was created by Shinichi Mochizuki at Kyoto University, Japan, in a bid to solve a long-standing problem called the ABC conjecture, which focuses on the simple equation a + b = c. It suggests that if a and b are made up of large powers of prime numbers, then c isn’t usually divisible by large powers of primes.

In 2012, Mochizuki published a series of papers, running to more than 500 pages, that appeared to be a serious attempt at tackling the problem, but his dense and unusual style baffled many experts.

His apparent proof struggled to find acceptance and attracted criticism from some of the world’s most prominent mathematicians, including two who claimed in 2018 to have found a “serious, unfixable gap” in the work. Despite this, the paper was formally published in 2020, in a journal edited by Mochizuki himself. It was reported by Nature that he had nothing to do with the journal’s decision.

Since then, the theory has remained in mathematical limbo, with some people believing it to be true, but others disagreeing. Many mathematicians contacted for this story, including Mochizuki, either didn’t respond or declined to comment on the matter.

Now, the founder of Japanese telecoms and media company Dwango, Nobuo Kawakami, hopes to settle the issue by launching a cash prize for a paper that can prove – or disprove – the theory.

Two prizes are on offer. The first will see between $20,000 and $100,000 awarded annually, for the next 10 years, to the author of the best paper on IUT and related fields. The second – worth $1 million – is reserved for the mathematician who can write a paper that “shows an inherent flaw in the theory”, according to a press release.

Dwango didn’t respond to a request for interview, but during a press conference Kawakami said he hoped that his “modest reward will help increase the number of mathematicians who decide to get involved in IUT theory”.

To be eligible for the prizes, papers will need to be published in a peer-reviewed journal selected from a list compiled by the prize organisers, according to a report in The Asahi Shimbun newspaper, and Kawakami will choose the winner.

The competition is being run by the Inter-Universal Geometry Center (IUGC), which has been founded by Kawakami specifically to promote IUT, says Fumiharu Kato, director of the IUGC.

Kato says that Kawakami isn’t a mathematician, but sees IUT as a momentous part of the history of mathematics and believes that the cash prize is a “good investment” if it can finally clear up the controversy one way or the other.

“For me, IUT theory is logically simple. Of course, I mean, technically very, very hard. But logically it’s simple,” says Kato, who estimates that fewer than 10 people in the world comprehend the concept.

Kato believes that the controversy stems from the fact that Mochizuki doesn’t want to promote his theory, talk to journalists or other mathematicians about it or present the idea in a more easily digestible format, believing his work speaks for itself. Kato says that his current and former students are also reticent to do the same because they see him “as a god” in mathematics and don’t want to go against his wishes.

Because of this, most mathematicians are “at a loss” for a way to understand IUT, says Kato, who concedes that, despite earlier optimism about the idea, it is possible that the theory will eventually be disproven.

Ivan Fesenko at the University of Nottingham, UK, who is also deputy director at the IUGC, has long been a supporter of Mochizuki. He told New Scientist that there is no doubt about the correctness of IUT and that it all hinges on a deep understanding of an existing field called anabelian geometry.

“All negative public statements about the validity of IUT have been made by people who do not have proven expertise in anabelian geometry and who have zero research track record in anabelian geometry,” he says. “The new $1m IUT Challenger Prize will challenge every mathematician who has ever publicly criticised IUT to produce a paper with full proofs and get it published in a good math journal.”

For more such insights, log into www.international-maths-challenge.com.

*Credit for article given to Matthew Sparkes*

A new study into classroom practices, led by Dr. Steve Murphy, has found extensive research fails to uncover how teachers can remedy poor student engagement and perform well in math.

More than 3,000 research papers were reviewed over the course of the study, but only 26 contained detailed steps for teachers to improve both student engagement and results in math. The review is published in the journal Teaching and Teacher Education.

Dr. Murphy said the scarcity of research involving young childrenwas concerning.

“Children’s engagement in math begins to decline from the beginning of primary school while their mathematical identity begins to solidify,” Dr. Murphy said.

“We need more research that investigates achievement and engagement together to give teachers good advice on how to engage students in mathematics and perform well.

“La Trobe has developed a model for research that can achieve this.”

While teachers play an important role in making decisions that impact the learning environment, Dr. Murphy said parents are also highly influential in children’s math education journeys.

“We often hear parents say, ‘It’s OK, I was never good at math,’ but they’d never say that to their child about reading or writing,” Dr. Murphy said.

La Trobe’s School of Education is determined to improve mathematical outcomes for students, arguing it’s an important school subject that is highly applicable in today’s technologically rich society.

Previous research led by Dr. Murphy published in Educational Studies in Mathematics found many parents were unfamiliar with the modern ways of teaching math and lacked self-confidence to independently assist their children learning math during the COVID-19 pandemic.

“The implication for parents is that you don’t need to be a great mathematician to support your children in math, you just need to be willing to learn a little about how schools teach math today,” Dr. Murphy said.

“It’s not all bad news for educators and parents. Parents don’t need to teach math; they just need to support what their children’s teacher is doing.

“Keeping positive, being encouraging and interested in their children’s math learning goes a long way.”

For more such insights, log into our website https://international-maths-challenge.com

Credit of the article to be given La Trobe Universit

By rapidly analysing large amounts of data and making accurate predictions, artificial intelligence (AI) tools could help to answer many long-standing research questions. For instance, they could help to identify new materials to fabricate electronics or the patterns in brain activity associated with specific human behaviours.

One area in which AI has so far been rarely applied is number theory, a branch of mathematics focusing on the study of integers and arithmetic functions. Most research questions in this field are solved by human mathematicians, often years or decades after their initial introduction.

Researchers at the Israel Institute of Technology (Technion) recently set out to explore the possibility of tackling long-standing problems in number theory using state-of-the-art computational models.

In a recent paper, published in the Proceedings of the National Academy of Sciences, they demonstrated that such a computational approach can support the work of mathematicians, helping them to make new exciting discoveries.

“Computer algorithms are increasingly dominant in scientific research, a practice now broadly called ‘AI for Science,'” Rotem Elimelech and Ido Kaminer, authors of the paper, told Phys.org.

“However, in fields like number theory, advances are often attributed to creativity or human intuition. In these fields, questions can remain unresolved for hundreds of years, and while finding an answer can be as simple as discovering the correct formula, there is no clear path for doing so.”

Elimelech, Kaminer and their colleagues have been exploring the possibility that computer algorithms could automate or augment mathematical intuition. This inspired them to establish the Ramanujan Machine research group, a new collaborative effort aimed at developing algorithms to accelerate mathematical research.

Their research group for this study also included Ofir David, Carlos de la Cruz Mengual, Rotem Kalisch, Wolfram Berndt, Michael Shalyt, Mark Silberstein, and Yaron Hadad.

“On a philosophical level, our work explores the interplay between algorithms and mathematicians,” Elimelech and Kaminer explained. “Our new paper indeed shows that algorithms can provide the necessary data to inspire creative insights, leading to discoveries of new formulas and new connections between mathematical constants.”

The first objective of the recent study by Elimelech, Kaminer and their colleagues was to make new discoveries about mathematical constants. While working toward this goal, they also set out to test and promote alternative approaches for conducting research in pure mathematics.

“The ‘conservative matrix field’ is a structure analogous to the conservative vector field that every math or physics student learns about in first year of undergrad,” Elimelech and Kaminer explained. “In a conservative vector field, such as the electric field created by a charged particle, we can calculate the change in potential using line integrals.

“Similarly, in conservative matrix fields, we define a potential over a discrete space and calculate it through matrix multiplications rather than using line integrals. Traveling between two points is equivalent to calculating the change in the potential and it involves a series of matrix multiplications.”

In contrast with the conservative vector field, the so-called conservative matrix field is a new discovery. An important advantage of this structure is that it can generalize the formulas of each mathematical constant, generating infinitely many new formulas of the same kind.

“The way by which the conservative matrix field creates a formula is by traveling between two points (or actually, traveling from one point all the way to infinity inside its discrete space),” Elimelech and Kaminer said. “Finding non-trivial matrix fields that are also conservative is challenging.”

As part of their study, Elimelech, Kaminer and their colleagues used large-scale distributed computing, which entails the use of multiple interconnected nodes working together to solve complex problems. This approach allowed them to discover new rational sequences that converge to fundamental constants (i.e., formulas for these constants).

“Each sequence represents a path hidden in the conservative matrix field,” Elimelech and Kaminer explained. “From the variety of such paths, we reverse-engineered the conservative matrix field. Our algorithms were distributed using BOINC, an infrastructure for volunteer computing. We are grateful to the contribution by hundreds of users worldwide who donated computation time over the past two and a half years, making this discovery possible.”

The recent work by the research team at the Technion demonstrates that mathematicians can benefit more broadly from the use of computational tools and algorithms to provide them with a “virtual lab.” Such labs provide an opportunity to try ideas experimentally in a computer, resembling the real experiments available in physics and in other fields of science. Specifically, algorithms can carry out mathematical experiments providing formulas that can be used to formulate new mathematical hypotheses.

“Such hypotheses, or conjectures, are what drives mathematical research forward,” Elimelech and Kaminer said. “The more examples supporting a hypothesis, the stronger it becomes, increasing the likelihood to be correct. Algorithms can also discover anomalies, pointing to phenomena that are the building-blocks for new hypotheses. Such discoveries would not be possible without large-scale mathematical experiments that use distributed computing.”

Another interesting aspect of this recent study is that it demonstrates the advantages of building communities to tackle problems. In fact, the researchers published their code online from their project’s early days and relied on contributions by a large network of volunteers.

“Our study shows that scientific research can be conducted without exclusive access to supercomputers, taking a substantial step toward the democratization of scientific research,” Elimelech and Kaminer said. “We regularly post unproven hypotheses generated by our algorithms, challenging other math enthusiasts to try proving these hypotheses, which when validated are posted on our project website. This happened on several occasions so far. One of the community contributors, Wolfgang Berndt, got so involved that he is now part of our core team and a co-author on the paper.”

The collaborative and open nature of this study allowed Elimelech, Kaminer and the rest of the team to establish new collaborations with other mathematicians worldwide. In addition, their work attracted the interest of some children and young people, showing them how algorithms and mathematics can be combined in fascinating ways.

In their next studies, the researchers plan to further develop the theory of conservative matrix fields. These matrix fields are a highly powerful tool for generating irrationality proofs for fundamental constants, which Elimelech, Kaminer and the team plan to continue experimenting with.

“Our current aim is to address questions regarding the irrationality of famous constants whose irrationality is unknown, sometimes remaining an open question for over a hundred years, like in the case of the Catalan constant,” Elimelech and Kaminer said.

“Another example is the Riemann zeta function, central in number theory, with its zeros at the heart of the Riemann hypothesis, which is perhaps the most important unsolved problem in pure mathematics. There are many open questions about the values of this function, including the irrationality of its values. Specifically, whether ζ(5) is irrational is an open question that attracts the efforts of great mathematicians.”

The ultimate goal of this team of researchers is to successfully use their experimental mathematics approach to prove the irrationality of one of these constants. In the future, they also hope to systematically apply their approach to a broader range of problems in mathematics and physics. Their physics-inspired hands-on research style arises from the interdisciplinary nature of the team, which combines people specialized in CS, EE, math, and physics.

“Our Ramanujan Machine group can help other researchers create search algorithms for their important problems and then use distributed computing to search over large spaces that cannot be attempted otherwise,” Elimelech and Kaminer added. “Each such algorithm, if successful, will help point to new phenomena and eventually new hypotheses in mathematics, helping to choose promising research directions. We are now considering pushing forward this strategy by setting up a virtual user facility for experimental mathematics,” inspired by the long history and impact of user facilities for experimental physics.

For more insights like this, visit our website at www.international-maths-challenge.com.

Credit of the article given to Ingrid Fadelli , Phys.org

For Michel Talagrand, who won the Abel mathematics prize on Wednesday, math provided a fun life free from all constraints—and an escape from the eye problems he suffered as a child.

“Math, the more you do it, the easier it gets,” the 72-year-old said in an interview with AFP.

He is the fifth French Abel winner since the award was created by Norway’s government in 2003 to compensate for the lack of a Nobel prize in mathematics.

Talagrand’s career in functional analysis and probability theorysaw him tame some of the incredibly complicated limits of random behaviour.

But the mathematician said he had just been “studying very simple things by understanding them absolutely thoroughly.”

Talagrand said he was stunned when told by the Norwegian Academy of Science and Letters that he had won the Abel prize.

“I did not react—I literally didn’t think for at least five seconds,” he said, adding that he was very happy for his wife and two children.

Fear of going blind

When he was young, Talagrand only turned to math “out of necessity,” he said.

By the age of 15, he had endured multiple retinal detachments and “lived in terror of going blind”.

Unable to run around with friends in Lyon, Talagrand immersed himself in his studies.

His father had a math degree and so he followed the same path. He said he was a “mediocre” student in other areas.

Talagrand was particularly poor at spelling, and still lashes out at what he calls its “arbitrary rules”.

Especially in comparison to math, which has “an order in which you do well if you are sensitive to it,” he said.

In 1974, Talagrand was recruited by the French National Centre for Scientific Research (CNRS), before getting a Ph.D. at Paris VI University.

He spent a decade studying functional analysis before finding his “thing”: probability.

It was then that Talagrand developed his influential theory about “Gaussian processes,” which made it possible to study some random phenomena.

Australian mathematician Matt Parker said that Talagrand had helped tame these “complicated random processes”.

Physicists had previously developed theories on the limits of how randomness behaves, but Talagrand was able to use mathematics to prove these limits, Parker said on the Abel Prize website.

‘Monstrously complicated’

“In a sense, things are as simple as could be—whereas mathematical objects can be monstrously complicated,” Talagrand said.

His work deepening the understanding of random phenomena “has become essential in today’s world,” the CNRS said, citing algorithms which are “the basis of our weather forecasts and our major linguistic models”.

Rather than creating a “brutal transformation”, Talagrand considers his discoveries as a collective work he compared to “the construction of a cathedral in which everyone lays a stone”.

He noted that French mathematics had been doing well an elite level, notching up both Abel prizes and Fields medals—the other equivalent to a math Nobel, which is only awarded to mathematicians under 40.

“But the situation is far less brilliant in schools,” where young people are increasingly less attracted to the discipline, he lamented.

The new Abel winner admitted that math can be daunting at first, but re-emphasized his belief that it gets easier the more you do it.

He advised aspiring mathematicians not to worry about failure.

“You can fail to solve a problem 10 times—but that doesn’t matter if you succeed on the 11th try,” he said.

It can also be hard work.

“All my life I worked to the point of exhaustion—but I had such fun!” he said.

“With math, you have all the resources within yourself. You work without any constraints, free from concerns about money or bosses,” he added.

“It’s marvelous.”

Talagrand will receive his prize, including a 7.5-million-kroner ($705,000) check, in Oslo on May 21.

For more such insights, log into our website https://international-maths-challenge.com

Credit of the article given to Juliette Collen

A George Washington University research team has created a novel formula that demonstrates how, why, and when hate speech spreads throughout social media. The researchers put forth a first-principles dynamical theory that explores a new realm of physics in order to represent the shockwave effect created by bigoted content across online communities.

This effect is evident in lightly moderated websites, such as 4Chan, and highly regulated social platforms like Facebook. Furthermore, hate speech ripples through online communities in a pattern that non-hateful content typically does not follow.

The new theory considers recently gained knowledge on the pivotal role of in-built communities in the growth of online extremism. The formula weighs the competing forces of fusion and fission, accounting for the spontaneous emergence of in-built communities through the absorption of other communities and interested individuals (fusion) and the disciplinary measures moderators take against users and groups that violate a given platform’s rules (fission).

Researchers hope the formula can serve as a tool for moderators to project the shockwave-like spread of hateful content and develop methods to delay, divert, and prevent it from spiraling out of control. The novel theory could also be applied beyond social mediaplatforms and online message boards, potentially powering moderation strategies on blockchain platforms, generative AI, and the metaverse.

“This study presents the missing science of how harms thrive online and, hence, how they can be overcome,” Neil Johnson, professor of physics at the George Washington University and co-author of the study, said. “This missing science is a new form of shockwave physics.”

For more such insights, log into our website https://international-maths-challenge.com

Credit of the article given to George Washington University

When President Ronald Reagan proclaimed the first National Math Awareness Week in April 1986, one of the problems he cited was that too few students were devoted to the study of math.

“Despite the increasing importance of mathematics to the progress of our economy and society, enrollment in mathematics programs has been declining at all levels of the American educational system,” Reagan wrote in his proclamation.

Nearly 40 years later, the problem that Reagan lamented during the first National Math Awareness Week—which has since evolved to become “Mathematics and Statistics Awareness Month”—not only remains but has gotten worse.

Whereas 1.63%, or about 16,000, of the nearly 1 million bachelor’s degrees awarded in the U.S. in the 1985–1986 school year went to math majors, in 2020, just 1.4%, or about 27,000, of the 1.9 million bachelor’s degrees were awarded in the field of math—a small but significant decrease in the proportion.

Post-pandemic data suggests the number of students majoring in math in the U.S. is likely to decrease in the future.

A key factor is the dramatic decline in math learning that took place during the lockdown. For instance, whereas 34% of eighth graders were proficient in math in 2019, test data shows the percentage dropped to 26% after the pandemic.

These declines will undoubtedly affect how much math U.S. students can do at the college level. For instance, in 2022, only 31% of graduating high school seniors were ready for college-level math—down from 39% in 2019.

These declines will also affect how many U.S. students are able to take advantage of the growing number of high-paying math occupations, such as data scientists and actuaries. Employment in math occupations is projected to increase by 29% in the period from 2021 to 2031.

About 30,600 math jobs are expected to open up per year from growth and replacement needs. That exceeds the 27,000 or so math graduates being produced each year—and not all math degree holders go into math fields. Shortages will also arise in several other areas, since math is a gateway to many STEM fields.

For all of these reasons and more, as a mathematician who thinks deeply about the importance of math and what it means to our world—and even to our existence as human beings—I believe this year, and probably for the foreseeable future, educators, policymakers and employers need to take Mathematics and Statistics Awareness Month more seriously than ever before.

Struggles with mastery

Subpar math achievement has been endemic in the U.S. for a long time.

Data from the National Assessment of Educational Progress shows that no more than 26% of 12th graders have been rated proficient in math since 2005.

The pandemic disproportionately affected racially and economically disadvantaged groups. During the lockdown, these groups had less access to the internet and quiet studying spaces than their peers. So securing Wi-Fi and places to study are key parts of the battle to improve math learning.

Some people believe math teaching techniques need to be revamped, as they were through the Common Core, a new set of educational standards that stressed alternative ways to solve math problems. Others want a return to more traditional methods. Advocates also argue there is a need for colleges to produce better-prepared teachers.

Other observers believe the problem lies with the “fixed mindset” many students have—where failure leads to the conviction that they can’t do math—and say the solution is to foster a “growth” mindset—by which failure spurs students to try harder.

Although all these factors are relevant, none address what in my opinion is a root cause of math underachievement: our nation’s ambivalent relationship with mathematics.

Low visibility

Many observers worry about how U.S. children fare in international rankings, even though math anxiety makes many adults in the U.S. steer clear of the subject themselves.

Mathematics is not like art or music, which people regularly enjoy all over the country by visiting museums or attending concerts. It’s true that there is a National Museum of Mathematics in New York, and some science centers in the U.S. devote exhibit space to mathematics, but these can be geographically inaccessible for many.

A 2020 study on media portrayals of math found an overall “invisibility of mathematics” in popular culture. Other findings were that math is presented as being irrelevant to the real world and of little interest to most people, while mathematicians are stereotyped to be singular geniuses or socially inept nerds, and white and male.

Math is tough and typically takes much discipline and perseverance to succeed in. It also calls for a cumulative learning approach—you need to master lessons at each level because you’re going to need them later.

While research in neuroscience shows almost everyone’s brain is equipped to take up the challenge, many students balk at putting in the effort when they don’t score well on tests. The myth that math is just about procedures and memorization can make it easier for students to give up. So can negative opinions about math ability conveyed by peers and parents, such as declarations of not being “a math person.”

A positive experience

Here’s the good news. A 2017 Pew poll found that despite the bad rap the subject gets, 58% of U.S. adults enjoyed their school math classes. It’s members of this legion who would make excellent recruits to help promote April’s math awareness. The initial charge is simple: Think of something you liked about math—a topic, a puzzle, a fun fact—and go over it with someone. It could be a child, a student, or just one of the many adults who have left school with a negative view of math.

Can something that sounds so simplistic make a difference? Based on my years of experience as a mathematician, I believe it can—if nothing else, for the person you talk to. The goal is to stimulate curiosity and convey that mathematics is much more about exhilarating ideas that inform our universe than it is about the school homework-type calculations so many dread.

Raising math awareness is a first step toward making sure people possess the basic math skills required not only for employment, but also to understand math-related issues—such as gerrymandering or climate change—well enough to be an informed and participating citizen. However, it’s not something that can be done in one month.

Given the decline in both math scores and the percentage of students studying math, it may take many years before America realizes the stronger relationship with math that President Reagan’s proclamation called for during the first National Math Awareness Week in 1986.

For more such insights, log into our website https://international-maths-challenge.com

Credit of the article given to Manil Suri, The Conversation

Studies by applied mathematicians at the University of Surrey are helping to identify ways of reducing how much liquids slosh around inside tanks.

Baffles slow down the movement of fluid by diverting its flow. The research found that two or three porous baffles dividing a tank calms sloshing better than a single separator, but the returns diminish as more baffles are added. The paper is published in the Journal of Engineering Mathematics.

The findings and improved understanding into how external movement impacts the way liquids slosh could help mathematicians and engineers design better tankers to transport liquids on land or at sea.

The findings could also be used in tuned liquid dampers, which reduce the sway of skyscrapers in earthquakes and high winds.

Dr. Matthew Turner, a mathematician at the University of Surrey and expert in fluid dynamics who conducted the research using mathematical modeling, said, “Sloshing liquids can impact safety and efficiency. For example, if a tanker transporting liquids via road stopped suddenly, extreme movement of liquid inside the tanker could move the vehicle forwards, and unstable fuel loads in a space rocket could be catastrophic. Porous baffles inserted within a tank can help stabilize loads and reduce sloshing. Our research helps clarify how many it’s worth using.”

Jane Nicholson, EPSRC’s director of research base, said, “This fundamental research demonstrates the potential impact of math research, as a result of our mathematical sciences small grants investment. It is motivated by real-world applications to ensure the safer and more efficient transportation of liquids and will bring new solutions in a wide range of sectors.”

Next Dr. Turner wants to investigate whether actively varying how porous the baffles are could offer further benefits, “A mechanism which controls the rate of flow through the baffle could help us optimize designs. It could also be helpful when designing wave energy converters.”

For more such insights, log into our website https://international-maths-challenge.com

Credit of the article to be given UK Research and Innovation

There’s a strange trend in mathematics education in England. Math is the most popular subject at A-level since overtaking English in 2014. It’s taken by around 85,000 and 90,000 students a year.

But many universities—particularly lower-tariff institutions, which accept students with lower A-level grades—are recruiting far fewer students for math degrees. There’s been a 50% drop in numbers of math students at the lowest tariff universities over the five years between 2017 and 2021. As a result, some universities are struggling to keep their mathematics departments open.

The total number of students studying math has remained largely static over the last decade. Prestigious Russell Group universities which require top A-level grades have increased their numbers of math students.

This trend in degree-level mathematics education is worrying. It restricts the accessibility of math degrees, especially to students from poorer backgrounds who are most likely to study at universities close to where they live. It perpetuates the myth that only those people who are unusually gifted at mathematics should study it—and that high-level math skills are not necessary for everyone else.

Research carried out in 2019 by King’s College London and Ipsos found that half of the working age population had the numeracy skills expected of a child at primary school. Just as worrying was that despite this, 43% of those polled said “they would not like to improve their numeracy skills.” Nearly a quarter (23%) stated that “they couldn’t see how it would benefit them.”

Mathematics has been fundamental in recent technological developments such as quantum computing, information security and artificial intelligence. A pipeline of more mathematics graduates from more diverse backgrounds will be essential if the UK is to remain a science and technology powerhouse into the future.

But math is also vital to a huge range of careers, including in business and government. In March 2024, campaign group Protect Pure Math held a summit to bring together experts from industry, academia and government to discuss concerns about poor math skills and the continuing importance of high-quality mathematics education.

Prior to the summit, the London Mathematical Society commissioned a survey of over 500 businesses to gauge their concerns about the potential lack of future graduates with strong mathematical skills.

They found that 72% of businesses agree they would benefit from more math graduates entering the workforce. And 75% would worry if UK universities shrunk or closed their math departments.

A 2023 report on MPs’ staff found that skills in Stem subjects (science, technology, engineering and mathematics) were particularly hard to find among those who worked in Westminster. As many as 90% of those who had taken an undergraduate degree had studied humanities or social sciences. While these subject backgrounds are valuable, the lack of specialized math skills is stark.

Limited options

The mathematics department at Oxford Brookes has closed and other universities have seen recruitment reductions or other cuts. The resulting math deserts will remove the opportunity for students to gain a high-quality mathematics education in their local area. Universities should do their best to keep these departments open.

This might be possible if the way that degrees are set up changes. For many degree courses in countries such as the US and Australia, students are able to take a broad selection of subjects, from science and math subjects through to the humanities. Each are taught in their respective academic departments. This allows students to gain advanced knowledge and see how each field feeds into others.

This is scarcely possible in the UK, where students must choose a specialist and narrow degree program at aged 18.

Another possible solution would be to put core mathematics modules in degree disciplines that rely so heavily on it—such as engineering, economics, chemistry, physics, biology and computer science—and have them taught by specialist mathematicians. This would help keep mathematics departments open, while also ensuring that general mathematical literacy improves in the UK.

The relevance of mathematics and its vast range applications would be abundantly clear, better equipping every student with the necessary mathematical skills the workforce needs.

For more such insights, log into our website https://international-maths-challenge.com

Credit of the article given to Neil Saunders, The Conversation

In a new study published in The Journal of Finance and Data Science, a researcher from the International School of Business at HAN University of Applied Sciences in the Netherlands introduced the topological tail dependence theory—a new methodology for predicting stock market volatility in times of turbulence.

“The research bridges the gap between the abstract field of topology and the practical world of finance. What’s truly exciting is that this merger has provided us with a powerful tool to better understand and predict stock market behaviour during turbulent times,” said Hugo Gobato Souto, sole author of the study.

Through empirical tests, Souto demonstrated that the incorporation of persistent homology (PH) information significantly enhances the accuracy of non-linear and neural network models in forecasting stock market volatility during turbulent periods.

“These findings signal a significant shift in the world of financial forecasting, offering more reliable tools for investors, financial institutions and economists,” added Souto.

Notably, the approach sidesteps the barrier of dimensionality, making it particularly useful for detecting complex correlations and nonlinear patterns that often elude conventional methods.

“It was fascinating to observe the consistent improvements in forecasting accuracy, particularly during the 2020 crisis,” said Souto.

The findings are not confined to one specific type of model. It spans across various models, from linear to non-linear, and even advanced neural network models. These findings open the door to improved financial forecasting across the board.

“The findings confirm the theory’s validity and encourage the scientific community to delve deeper into this exciting new intersection of mathematics and finance,” concluded Souto.

For more such insights, log into our website https://international-maths-challenge.com

Credit of the article given to KeAi Communications Co.

P is not NP? That is the question

One of the biggest open problems in mathematics may be solved within the next decade, according to a poll of computer scientists. A solution to the so-called P versus NP problem is worth $1 million and could have a profound effect on computing, and perhaps even the entire world.

The problem is a question about how long algorithms take to run and whether some hard mathematical problems are actually easy to solve.

P and NP both represent groups of mathematical problems, but it isn’t known if these groups are actually identical.

P, which stands for polynomial time, consists of problems that can be solved by an algorithm in a relatively short time. NP, which stands for nondeterministic polynomial time, comprises the problems that are easy to check if you have the right answer given a potential candidate, although actually finding an answer in the first place might be difficult.

NP problems include a number of important real-world tasks, such as the travelling salesman problem, which involves finding a route between a list of cities that is shorter than a certain limit. Given such a route, you can easily check if it fits the limit, but finding one might be more difficult.

Equal or not

The P versus NP problem asks whether these two collections of problems are actually the same. If they are, and P = NP, the implications are potentially world-changing, because it could become much easier to solve these tasks. If they aren’t, and P doesn’t equal NP, or P ≠ NP, a proof would still answer fundamental questions about the nature of computation.

The problem was first stated in 1971 and has since become one of the most important open questions in mathematics – anyone who can find the answer either way will receive $1 million from the Clay Mathematics Institute in Cambridge, Massachusetts.

William Gasarch, a computer scientist at the University of Maryland in College Park, conducts polls of his fellow researchers to gauge the current state of the problem. His first poll, in 2002, found that just 61 per cent of respondents thought P ≠ NP. In 2012, that rose to 83 per cent, and now in 2019 it has slightly increased to 88 per cent. Support for P = NP has also risen, however, from 9 per cent in 2002 to 12 per cent in 2019, because the 2002 poll had a large number of “don’t knows”.

Confidence that we might soon have an answer is also rising. In 2002, just 5 per cent thought the problem would be resolved in the next decade, falling to 1 per cent in 2012, but now the figure sits at 22 per cent. “This is very surprising since there has not been any progress on it,” says Gasarch. “If anything, I think that as the problem remains open longer, it seems harder.” More broadly, 66 per cent believe it will be solved before the end of the century.

There was little agreement on the kind of mathematics that would ultimately be used to solve the problem, although a number of respondents suggested that artificial intelligence, not humans, could play a significant role.

“I can see this happening to some extent, but the new idea needed will, I think, come from a human,” says Gasarch. “I hope so, not for any reason of philosophy, but just because if a computer did it we might know that (say) P ≠ NP, but not really know why.”

Neil Immerman at the University of Massachusetts Amherst thinks that this kind of polling is interesting, but ultimately can’t tell us much about the P versus NP problem.

“As this poll demonstrates, there is no consensus on how this problem will be eventually solved,” he says. “For that reason, it is hard to measure the progress we have made since 1971 when the question was first stated.”

For more such insights, log into www.international-maths-challenge.com.

*Credit for article given to Jacob Aron*