Author: IMC

When asked to describe mathematics we often resort to metaphor rather than attempt to provide strict definitions. These pictures from high school math textbooks from the 1930s are an example of this tendancy.

The simple hierarchies of these images resolve the complicated relationship between mathematics and science by appealing to our desire for an organic unity among disciplines, giving mathematics a foundational role within the general concept of science. These images are appealing, but do not stand up to scrutiny.

The simple relationship between mathematics and science becomes complicated when mathematics is described, as it sometimes is, as a science itself. It’s definition as “the science of space and quantity” is further complicated by the caveat that it is an exact deductive science, unlike the usual inductive kind. Following this line of thinking further, mathematics is then described as a kind of meta-science, or a limit point to which science might aspire – science emptied of all of its empirical content, a science of pure thought. While some view mathematics as a foundation for science, others as a supra-science, the emerging field of experimental mathematics brings mathematics back into the empirical fold, reducing it (or elevating it) to a science like any other. So, mathematics can be seen as root, branch, or even the form of the tree itself.

Thinking about these things for even a short while evokes some sympathy with Bertrand Russell’s remark that “mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.”

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*Credit for article given to dan.mackinnon*

One hundred years ago, in the 1924 Paris Olympics, American Johnny Weissmuller won the men’s 100m freestyle with a time of 59 seconds. Nearly 100 years later, in the most recent Olympics, the delayed 2020 Games in Tokyo, Caeleb Dressel took home the same event with a time that was 12 seconds faster than Weissmuller’s.

Swimming times across the board have become much faster over the past century, a result of several factors, including innovations in training, recovery strategy, nutrition, and some equipment advances.

One component in the improvement in swimming performances over the years is the role of biomechanics—that is, how swimmers optimize their stroke, whether it’s the backstroke, breaststroke, butterfly, or freestyle.

Swimmers for decades have experimented with different techniques to gain an edge over their competitors. But in more recent years, the application of mathematics and science principles as well as the use of wearable sensor technology in training regimens has allowed some athletes to elevate their performances to new heights, including members of the University of Virginia’s swim team.

 

In a new research paper, a UVA professor who introduced these concepts and methods to the team and some of the swimmers who have embraced this novel approach to training lay out how the use of data is helping to transform how competitive swimmers become elite. The paper is published in The Mathematical Intelligencer journal.

‘Swimming in data’

Ken Ono thought his time working with swim teams was over. Ono—a UVA mathematics professor, professor of data science by courtesy, and STEM advisor to the University provost—had spent years working with competitive swimmers, first during his time at Emory University in Atlanta and then with other college teams, including Olympians, over the years.

However, he didn’t plan to continue that aspect of his work when he arrived at UVA in 2019. But after a meeting with Todd DeSorbo, who took over the UVA swim program in 2017, Ono soon found himself once again working closely with athletes, beginning his work as a consultant for the team during the 2020-21 season. The UVA women’s swim team would win their first of four consecutive national championships that year.

“One of the things that WElike quite a bit about this work is that swimming is crazy hard,” Ono said. “We were never meant to be swimmers, and it is both an athletic challenge as well as a scientific challenge—it has it all.”

Last fall, following a suggestion from DeSorbo, Ono offered a class that outlined the science-focused approach to improving swimming performances that had proven so successful at UVA, but he wanted to make sure there were no misconceptions about the seriousness of the material.

“We don’t want people thinking that it’s a cupcake course that’s offered for the swimmers,” Ono said.

So, Ono teamed up with UVA students Kate Douglass, August Lamb, and Will Tenpas, as well as MIT graduate student Jerry Lu, who had worked with Ono and the UVA swim team while an undergraduate at the University, to produce a paper that covered the key elements of the class and Ono’s work with swimmers.

Tenpas and Lamb both recently completed the residential master’s program at the School of Data Science as well as their careers as competitive collegiate swimmers. Douglass, who finished her UVA swim career in 2023 as one of the most decorated swimmers in NCAA history, is a graduate student in statistics at the University and is set to compete in the Paris Olympics after winning a bronze medal in the 2020 games.

The group drafted the paper, which they titled “Swimming in Data,” over the course of two months, and it was quickly accepted by The Mathematical Intelligencer. There, Ono said, it has become one of the most-read papers on a STEM subject since tracking began. In July, a version of the paper will also be published in Scientific American.

“It seems to have taken off,” Ono said.

The impact of digital twins

After outlining the evolution of swimming over the past 100 years, the paper explains how an understanding of math and physics, combined with the use of technology to acquire individual-level data, can help maximize performances.

Essential to understanding the scientific principles involved with the swimming stroke, the paper says, are Newton’s laws of motion. The laws—which cover inertia, the idea that acceleration depends on an object’s mass and the amount of force applied, and the principle that an action exerted by an object on another elicits an equal and opposite reaction—help simplify how one should think about the many biomechanical factors involved with swimming, according to Tenpas.

“There are all sorts of flexibility limitations. You have water moving at you, you have wakes, you have currents—it’s easy to kind of get paralyzed by the number of factors,” said Tenpas, who after four years at Duke, where he studied mechanical engineering, enrolled in UVA’s data science program and joined the swim team with a fifth year of eligibility.

“WEthink having Newton’s laws is nice as it gives you this baseline we can all agree on,” he added.

It’s a way to understand pool mechanics given the counterintuitive motion swimmers must use to propel themselves forward, according to Ono.

“The reason that we go to great extent to recall Newton’s laws of motion is so that we can break down the factors that matter when you test a swimmer,” he said.

To conduct these tests, Ono and his team use sensors that can be placed on swimmers’ wrists, ankles, or backs to gather acceleration data, measured as inertial measurement units. That information is then used to generate what are called digital twins, which precisely replicate a swimmer’s movements.

These twins reveal strengths and weaknesses, allowing Ono and the coaching staff to make recommendations on technique and strategy—such as how to reduce drag force, a swimmer’s true opponent—that will result in immediate improvement. In fact, through the analysis of data and the use of Newton’s laws, it is possible to make an accurate prediction about how much time a swimmer can save by making a given adjustment.

Lamb, who swam for UVA for five years while a computer science undergrad, then as a data science master’s student, likened digital twins to a feature in the popular Nintendo game Mario Kart where you can race against a ghost version of yourself.

“Being able to have this resource where you can test for one month and then spend a month or two making that adjustment and then test again and see what the difference is—it’s an incredibly valuable resource,” he said.

To understand the potential of digital twins, one need only look at the example of Douglass, one of the co-authors, who is cited in the paper.

A flaw was identified in her head position in the 200m breaststroke. Using her digital twin, Ono and the coaching staff were able to quantify how much time she could save per streamline glide by making a modification, given her obvious talent and aerobic capacity. She did, and the results were remarkable. In November 2020, when her technique was tested, the 200m breaststroke wasn’t even on her event list. Three years later, she held the American record.

‘Everyone’s doing it now’

Swimming will be front and center in the national consciousness this summer. First, the U.S. Olympic Team Trials will be held in Indianapolis in June, leading up to the Paris Olympics in July and August, where DeSorbo, UVA’s coach who embraced Ono’s data-driven strategic advice, will lead the women’s team.

Many aspiring swimmers will undoubtedly be watching over the coming weeks, wondering how they might realize their full athletic potential at whatever level that might be.

For those who have access to technology and data about their technique, Tenpas encourages young swimmers to take advantage.

He noted the significant amount of time a swimmer must put in to reach the highest levels of the sport, estimating that he had been swimming six times per week since he was 12 years old.

“If you’re going to put all of this work in, at least do it smart,” Tenpas said.

At the same time, Lamb urged young swimmers who may not yet have access to this technology to not lose faith in their potential to improve.

“While this is an incredibly useful tool to make improvements to your technique and to your stroke, it’s not the end all, be all,” he said.

“There are so many different ways to make improvements, and we’re hopeful that this will become more accessible as time goes on,” Lamb said of the data methods used at UVA.

As for where this is all going, with the rapidly expanding use and availability of data and wearable technology, Ono thinks his scientific approach to crafting swimming strategies will soon be the norm.

“We think five years from now, our story won’t be a story. It’ll be, “Oh, everyone’s doing it now,'” he said.

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

Credit of the article given to Cooper Allen, University of Virginia

 

Graphic novels can help make math and physics more accessible for students, parents or teachers in training. Metamorworks/iStock via Getty Images

Post-pandemic, some educators are trying to reengage students with technology – like videos, computer gaming or artificial intelligence, just to name a few. But integrating these approaches in the classroom can be an uphill battle. Teachers using these tools often struggle to retain students’ attention, competing with the latest social media phenomenon, and can feel limited by using short video clips to get concepts across.

Graphic novels – offering visual information married with text – provide a means to engage students without losing all of the rigor of textbooks. As two educators in math and physics, we have found graphic novels to be effective at teaching students of all ability levels. We’ve used graphic novels in our own classes, and we’ve also inspired and encouraged other teachers to use them. And we’re not alone: Other teachers are rejuvenating this analog medium with a high level of success.

In addition to covering a wide range of topics and audiences, graphic novels can explain tough topics without alienating student averse to STEM – science, technology, engineering and math. Even for students who already like math and physics, graphic novels provide a way to dive into topics beyond what is possible in a time-constrained class. In our book “Using Graphic Novels in the STEM Classroom,” we discuss the many reasons why graphic novels have a unique place in math and physics education. Here are three of those reasons:

Explaining complex concepts with rigor and fun

Increasingly, schools are moving away from textbooks, even though studies show that students learn better using print rather than digital formats. Graphic novels offer the best of both worlds: a hybrid between modern and traditional media.

This integration of text with images and diagrams is especially useful in STEM disciplines that require quantitative reading and data analysis skills, like math and physics.

For example, our collaborator Jason Ho, an assistant professor at Dordt University, uses “Max the Demon Vs Entropy of Doom” to teach his physics students about entropy. This topic can be particularly difficult for students because it’s one of the first times when they can’t physically touch something in physics. Instead, students have to rely on math and diagrams to fill in their knowledge.

 

Rather than stressing over equations, Ho’s students focus on understanding the subject more conceptually. This approach helps build their intuition before diving into the algebra. They get a feeling for the fundamentals before they have to worry about equations.

After having taken Ho’s class, more than 85% of his students agreed that they would recommend using graphic novels in STEM classes, and 90% found this particular use of “Max the Demon” helpful for their learning. When strategically used, graphic novels can create a dynamic, engaging teaching environment even with nuanced, quantitative topics.

 

Combating quantitative anxiety

Students learning math and physics today are surrounded by math anxiety and trauma, which often lead to their own negative associations with math. A student’s perception of math can be influenced by the attitudes of the role models around them – whether it’s a parent who is “not a math person” or a teacher with a high level of math anxiety.

Graphic novels can help make math more accessible not only for students themselves, but also for parents or students learning to be teachers.

In a geometry course one of us (Sarah) teaches, secondary education students don’t memorize formulas and fill out problem sheets. Instead, students read “Who Killed Professor X?”, a murder mystery in which all of the suspects are famous mathematicians. The suspects’ alibis are justified through problems from geometry, algebra and pre-calculus.

While trying to understand the hidden geometry of suspect relationships, students often forget that they are doing math – focusing instead on poring over secret hints and notes needed to solve the mystery.

Although this is just one experience for these students, it can help change the narrative for students experiencing mathematical anxiety. It boosts their confidence and shows them how math can be fun – a lesson they can then impart to the next generation of students.

 

Helping students learn and readers dream big

In addition to being viewed favourably by students, graphic novels can enhance student learning by improving written communication skills, reading comprehension and critical literacy skills. And even outside the classroom, graphic novels support long-term memory for those who have diagnoses like dyslexia.

Pause and think about your own experience – how do you learn about something new in science?

If you’re handed a textbook, it’s extremely unlikely that you’d read it cover to cover. And although the internet offers an enormous amount of math and physics content, it can be overwhelming to sift through hours and hours of videos to find the perfect one to get the “aha!” moment in learning.

Graphic novels provide a starting point for such a broad range of niche topics that it’s impossible for anyone to be experts in them all. Want to learn about programming? Try the “Secret Coders” series. Want to understand more about quantum physics? Dive into “Suspended in Language: Niels Bohr’s life, discoveries, and the century he shaped.” Searching for more female role models in science? “Astronauts: Women on the Final Frontier” could be just what you’re looking for.

With all that they offer, graphic novels provide a compelling list of topics and narratives that can capture the attention of students today. We believe that the right set of graphic novels can inspire the next generation of scientists as much as any single individual can.

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

Artificial intelligence firm DeepMind has tackled games like Go and Starcraft, but now it is turning its attention to more sober affairs: how to solve school-level maths problems.

Researchers at the company tasked an AI with teaching itself to solve arithmetic, algebra and probability problems, among others. It didn’t do a very good job: when the neural network was tested on a maths exam taken by 16-year-olds in the UK, it got just 14 out of 40 questions correct, or the equivalent of an E grade.

There were also strange quirks in the AI’s ability. For example, it could successfully add up 1+1+1+1+1+1 to make 6, but failed when an extra 1 was added. On the other hand, it gave the correct answer for longer sequences and much bigger numbers.

Other oddities included the ability to correctly answer 68 to the question “calculate 17×4.”, but when the full stop was removed, the answer came out at 69.

Puzzling behaviour

The DeepMind researchers concede they don’t have a good explanation for this behaviour. “At the moment, learning systems like neural networks are quite bad at doing ‘algebraic reasoning’,” says David Saxton, one of the team behind the work.

Despite this, it is still worth trying to teach a machine to solve maths problems, says Marcus du Sautoy, a mathematician at the University of Oxford.

“There are already algorithms out there to do these problems much faster, much better than machine-learning algorithms, but that’s not the point,” says du Sautoy. “They are setting themselves a different target – we want to start from nothing, by being told whether you got that one wrong, that one right, whether it can build up how to do this itself. Which is fascinating.”

An AI capable of solving advanced mathematics problems could put him out of a job, says du Sautoy. “That’s my fear. It may not take too much for an AI to get maturity in this world, whereas a maturity in the musical or visual or language world might be much harder for it. So I do think my subject is vulnerable.”

However, he takes some comfort that machine learning’s general weakness in remaining coherent over a long form – such as a novel, rather than a poem – will keep mathematicians safe for now. Creating mathematical proofs, rather than solving maths problems for 16-year-olds, will be difficult for machines, he says.

Noel Sharkey at the University of Sheffield, UK, says the research is more about finding the limits of machine-learning techniques, rather than promoting advancements in mathematics.

The interesting thing, he says, will be to see how the neural networks can adapt to challenges outside of those they were trained on. “The big question is to ask how well they can generalise to novel examples that were not in the training set. This has the potential to demonstrate formal limits to what this type of learning is capable of.”

Saxton says training a neural network on maths problems could help provide AI with reasoning skills for other applications.

“Humans are good at maths, but they are using general reasoning skills that current artificial learning systems don’t possess,” he says. “If we can develop models that are good at solving these problems, then these models would likely be using general skills that would be good at solving other hard problems in AI as well.”

He hopes the work could make a small contribution towards more general mathematical AIs that could tackle things such as proving theorems.

The DeepMind team has published its data set of maths questions, and encouraged people to train their own AI.

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

*Credit for article given to Adam Vaughan*

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.

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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.”

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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.

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Credit of the article given to Manil Suri, The Conversation