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It is very common in Australian schools to “stream” students for subjects such as English, science and maths. This means students are grouped into different classes based on their previous academic attainment, or in some cases, just a perception of their level of ability.

Students can also be streamed as early as primary school. Yet there are no national or state policies on this. This means school principals are free to decide what will happen in their schools.

Why are students streamed in Australians schools? And is this a good idea? Our research on streaming maths classes shows we need to think much more carefully about this very common practice.

Why do schools stream?

At a maths teacher conference in Sydney in late 2023, WEdid a live survey about school approaches to streaming.

This survey was done via interactive software while WEwas giving a presentation. There were 338 responses from head teachers in maths in either high schools or schools that go all the way from Kindergarten to Year 12. Most of the teachers were from public schools.

In a sign of how widespread streaming is, 95% of head teachers said they streamed maths classes in their schools.

Respondents said one of the main reasons is to help high-achieving students and make sure they are appropriately challenged. As one teacher said:

[We stream] to push the better students forward.

But almost half the respondents said they believed all students were benefiting from this system.

We also heard how streaming is seen as a way to cope with the teacher shortage and specific lack of qualified maths teachers. These qualifications include skills in both maths and maths teaching. More than half (65%) of respondents said streaming can “aid differentiation [and] support targeted student learning interventions”. In other words, streaming is a way to cope with different levels of ability in the classrooms and make the job of teaching a class more straightforward. One respondent said:

[we stream because] it’s easier to differentiate with a class of students that have similar perceived ability.

Teachers said they streamed classes to push the best students ‘forward’.

The ‘glass ceiling effect’

But while many schools and teachers assume streaming is good for students, this is not what the research says.

Our 2020 study, on streaming was based on interviews with 85 students and 22 teachers from 11 government schools.

This found streaming creates a “glass ceiling effect” – in other words, students cannot progress out of the stream they are initially assigned to without significant remedial work to catch them up.

As one teacher told us, students in lower-ability classes were then placed at a “massive disadvantage”. This is because they can miss out on segments of the curriculum because the class may progress more slowly or is deliberately not taught certain sections deemed too complex.

Often students in our study were unaware of this missed content until Year 10 and thinking about their options for the final years of school and beyond. They may not be able to do higher-level maths in Year 11 and 12 because they are too far behind. As one teacher explained:

they didn’t have enough of that advanced background for them to be able to study it. It was too difficult for them to begin with.

This comes as fewer students are completing advanced (calculus-based) maths.

If students do not study senior maths, they do not have the background for studying for engineering and other STEM careers, which we know are in very high demand.

On top of this, students may also be stigmatised as “low ability” in maths. While classes are not labelled as such, students are well aware of who is in the top classes and who is not. This can have an impact on students’ confidence about maths.

What does other research say?

International research has also found streaming students is inequitable.

As a 2018 UK study showed, students from disadvantaged backgrounds are more likely to be put in lower streamed classes.

A 2009 review of research studies found that not streaming students was better for low-ability student achievement and had no effect on average and high-ability student achievement.

Streaming is also seen as a way to cope with teachers shortages, and teachers teaching out of their field of expertise.

What should we do instead?

Amid concerns about Australian students’ maths performance in national and international tests, schools need to stop assuming streaming is the best approach for students.

The research indicates it would be better if students were taught in mixed-ability classes – as long as teachers are supported and class sizes are small enough.

This means all students have the opportunity to be taught all of the curriculum, giving them the option of doing senior maths if they want to in Year 11 and Year 12.

It also means students are not stigmatised as “poor at maths” from a young age.

But to do so, teachers and schools must be given more teaching resources and support. And some of this support needs to begin in primary school, rather than waiting until high school to try and catch students up.

Students also need adequate career advice, so they are aware of how maths could help future careers and what they need to do to get there.

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

Credit of the article given to Karolina Grabowska/Pexels, CC BY

Here’s a game: Ask a friend to give you any number and you’ll return one that’s bigger. Just add “1” to whatever number they come up with and you’re sure to win.

The reason is that numbers go on forever. There is no highest number. But why? As a professor of mathematics, WEcan help you find an answer.

First, you need to understand what numbers are and where they come from. You learned about numbers because they enabled you to count. Early humans had similar needs – whether to count animals killed in a hunt or keep track of how many days had passed. That’s why they invented numbers.

But back then, numbers were quite limited and had a very simple form. Often, the “numbers” were just notches on a bone, going up to a couple hundred at most.

When numbers got bigger

As time went on, people’s needs grew. Herds of livestock had to be counted, goods and services traded, and measurements made for buildings and navigation. This led to the invention of larger numbers and better ways of representing them.

About 5,000 years ago, the Egyptians began using symbols for various numbers, with a final symbol for one million. Since they didn’t usually encounter bigger quantities, they also used this same final symbol to depict “many.”

The Greeks, starting with Pythagoras, were the first to study numbers for their own sake, rather than viewing them as just counting tools. As someone who’s written a book on the importance of numbers, WEcan’t emphasize enough how crucial this step was for humanity.

By 500 BCE, Pythagoras and his disciples had not only realized that the counting numbers – 1, 2, 3 and so on – were endless, but also that they could be used to explain cool stuff like the sounds made when you pluck a taut string.

Zero is a critical number

But there was a problem. Although the Greeks could mentally think of very large numbers, they had difficulty writing them down. This was because they did not know about the number 0.

Think of how important zero is in expressing big numbers. You can start with 1, then add more and more zeroes at the end to quickly get numbers like a million – 1,000,000, or 1 followed by six zeros – or a billion, with nine zeros, or a trillion, 12 zeros.

It was only around 1200 CE that zero, invented centuries earlier in India, came to Europe. This led to the way we write numbers today.

This brief history makes clear that numbers were developed over thousands of years. And though the Egyptians didn’t have much use for a million, we certainly do. Economists will tell you that government expenditures are commonly measured in millions of dollars.

Also, science has taken us to a point where we need even larger numbers. For instance, there are about 100 billion stars in our galaxy – or 100,000,000,000 – and the number of atoms in our universe may be as high as 1 followed by 82 zeros.

Don’t worry if you find it hard to picture such big numbers. It’s fine to just think of them as “many,” much like the Egyptians treated numbers over a million. These examples point to one reason why numbers must continue endlessly. If we had a maximum, some new use or discovery would surely make us exceed it.

Exceptions to the rule

But under certain circumstances, sometimes numbers do have a maximum because people design them that way for a practical purpose.

A good example is a clock – or clock arithmetic, where we use only the numbers 1 through 12. There is no 13 o’clock, because after 12 o’clock we just go back to 1 o’clock again. If you played the “bigger number” game with a friend in clock arithmetic, you’d lose if they chose the number 12.

Since numbers are a human invention, how do we construct them so they continue without end? Mathematicians started looking at this question starting in the early 1900s. What they came up with was based on two assumptions: that 0 is the starting number, and when you add 1 to any number you always get a new number.

These assumptions immediately give us the list of counting numbers: 0 + 1 = 1, 1 + 1 = 2, 2 + 1 = 3, and so on, a progression that continues without end.

You might wonder why these two rules are assumptions. The reason for the first one is that we don’t really know how to define the number 0. For example: Is “0” the same as “nothing,” and if so, what exactly is meant by “nothing”?

The second might seem even more strange. After all, we can easily show that adding 1 to 2 gives us the new number 3, just like adding 1 to 2002 gives us the new number 2003.

But notice that we’re saying this has to hold for any number. We can’t very well verify this for every single case, since there are going to be an endless number of cases. As humans who can perform only a limited number of steps, we have to be careful anytime we make claims about an endless process. And mathematicians, in particular, refuse to take anything for granted.

Here, then, is the answer to why numbers don’t end: It’s because of the way in which we define them.

Now, the negative numbers

How do the negative numbers -1, -2, -3 and more fit into all this? Historically, people were very suspicious about such numbers, since it’s hard to picture a “minus one” apple or orange. As late as 1796, math textbooks warned against using negatives.

The negatives were created to address a calculation issue. The positive numbers are fine when you’re adding them together. But when you get to subtraction, they can’t handle differences like 1 minus 2, or 2 minus 4. If you want to be able to subtract numbers at will, you need negative numbers too.

A simple way to create negatives is to imagine all the numbers – 0, 1, 2, 3 and the rest – drawn equally spaced on a straight line. Now imagine a mirror placed at 0. Then define -1 to be the reflection of +1 on the line, -2 to be the reflection of +2, and so on. You’ll end up with all the negative numbers this way.

As a bonus, you’ll also know that since there are just as many negatives as there are positives, the negative numbers must also go on without end!

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

Credit of the article given to The Conversation

Both arithmetic aficionados and the mathematically challenged will be equally captivated by new research that upends hundreds of years of popular belief about prime numbers.

Contrary to what just about every mathematician on Earth will tell you, prime numbers can be predicted, according to researchers at City University of Hong Kong (CityUHK) and North Carolina State University, U.S.

The research team comprises Han-Lin Li, Shu-Cherng Fang, and Way Kuo. Fang is the Walter Clark Chair Professor of Industrial and Systems Engineering at North Carolina State University. Kuo is a Senior Fellow at the Hong Kong Institute for Advanced Study, CityU.

This is a genuinely revolutionary development in prime number theory, says Way Kuo, who is working on the project alongside researchers from the U.S. The team leader is Han-Lin Li, a Visiting Professor in the Department of Computer Science at CityUHK.

We have known for millennia that an infinite number of prime numbers, i.e., 2, 3, 5, 7, 11, etc., can be divided by themselves and the number 1 only. But until now, we have not been able to predict where the next prime will pop up in a sequence of numbers. In fact, mathematicians have generally agreed that prime numbers are like weeds: they seem just to shoot out randomly.

“But our team has devised a way to predict accurately and swiftly when prime numbers will appear,” adds Kuo.

The technical aspects of the research are daunting for all but a handful of mathematicians worldwide. In a nutshell, the outcome of the team’s research is a handy periodic table of primes, or the PTP, pointing the locations of prime numbers. The research is available as a working paper in the SSRN Electronic Journal.

The PTP can be used to shed light on finding a future prime, factoring an integer, visualizing an integer and its factors, identifying locations of twin primes, predicting the total number of primes and twin primes or estimating the maximum prime gap within an interval, among others.

More to the point, the PTP has major applications today in areas such as cyber security. Primes are already a fundamental part of encryption and cryptography, so this breakthrough means data can be made much more secure if we can predict prime numbers, Kuo explains.

This advance in prime number research stemmed from working on systems reliability design and a color coding system that uses prime numbers to enable efficient encoding and more effective color compression. During their research, the team discovered that their calculations could be used to predict prime numbers.

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

Credit of the article given to Michael Gibb, City University of Hong Kong

Imagine if you enrolled your child in swimming lessons but instead of a qualified swimming instructor, they were taught freestyle technique by a soccer coach.

Something similar is happening in classrooms around Australia every day. As part of the ongoing teacher shortage, there are significant numbers of teachers teaching “out-of-field”. This means they are teaching subjects they are not qualified to teach.

One of the subjects where out-of-field teaching is particularly common is maths.

A 2021 report on Australia’s teaching workforce found that 40% of those teaching high school mathematics are out-of-field (English and science were 28% and 29%, respectively).

Another 2021 study of students in Year 8 found they were more likely to be taught by teachers who had specialist training in both maths and maths education if they went to a school in an affluent area rather than a disadvantaged one (54% compared with 31%).

Our new report looks at how we can fix this situation by training more existing teachers in maths education.

Why is this a problem?

Mathematics is one of the key parts of school education. But we are seeing worrying signs students are not receiving the maths education they need.

The 2021 study of Year 8 students showed those taught by teachers with a university degree majoring in maths had markedly higher results, compared with those taught by out-of-field teachers.

We also know maths skills are desperately needed in the broader workforce. The burgeoning worlds of big data and artificial intelligence rely on mathematical and statistical thinking, formulae and algorithms. Maths has also been identified as a national skill shortages priority area.

There are worrying signs students are not receiving the maths education they need. Aaron Lefler/ Unsplash, CC BY

What do we do about this?

There have been repeated efforts to address teacher shortages,including trying to retain existing mathematics teachers, having specialist teachers teaching across multiple schools and higher salaries. There is also a push to train more teachers from scratch, which of course will take many years to implement.

There is one strategy, however, that has not yet been given much attention by policy makers: upgrading current teachers’ maths and statistics knowledge and their skills in how to teach these subjects.

They already have training and expertise in how to teach and a commitment to the profession. Specific training in maths will mean they can move from being out-of-field to “in-field”.

How to give teachers this training

A new report commissioned by mathematics and statistics organisations in Australia (including the Australian Mathematical Sciences Institute) looks at what is currently available in Australia to train teachers in maths.

It identified 12 different courses to give existing teachers maths teaching skills. They varied in terms of location, duration (from six months to 18 months full-time) and aims.

For example, some were only targeted at teachers who want to teach maths in the junior and middle years of high school. Some taught university-level maths and others taught school-level maths. Some had government funding support; others could cost students more than A$37,000.

Overall, we found the current system is confusing for teachers to navigate. There are complex differences between states about what qualifies a teacher to be “in-field” for a subject area.

In the current incentive environment, we found these courses cater to a very small number of teachers. For example, in 2024 in New South Wales this year there are only about 50 government-sponsored places available.

This is not adequate. Pre-COVID, it was estimated we were losing more than 1,000 equivalent full-time maths teachers per year to attrition and retirement and new graduates were at best in the low hundreds.

But we don’t know exactly how many extra teachers need to be trained in maths. One of the key recommendations of the report is for accurate national data of every teacher’s content specialisations.

We need a national approach

The report also recommends a national strategy to train more existing teachers to be maths teachers. This would replace the current piecemeal approach.

It would involve a standard training regime across Australia with government and school-system incentives for people to take up extra training in maths.

There is international evidence to show a major upskilling program like this could work.

In Ireland, where the same problem was identified, the government funds a scheme run by a group of universities. Since 2012, teachers have been able to get a formal qualification (a professional diploma). Between 2009 and 2018 the percentage of out-of-field maths teaching in Ireland dropped from 48% to 25%.

To develop a similar scheme here in Australia, we would need coordination between federal and state governments and universities. Based on the Irish experience, it would also require several million dollars in funding.

But with students receiving crucial maths lessons every day by teachers who are not trained to teach maths, the need is urgent.

The report mentioned in this article was commissioned by the Australian Mathematical Sciences Institute, the Australian Mathematical Society, the Statistical Society of Australia, the Mathematics Education Research Group of Australasia and the Actuaries Institute.

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

Credit of the article given to Monstera Production/ Pexels , CC BY

This Easter season, as you tear open those chocolate eggs, have you ever wondered why they’re snugly wrapped in foil? Turns out the answer lies within the easter egg equation.

Mathematician Dr. Saul Schleimer, from the University of Warwick, sheds light on the delightful connection between Easter egg wrapping and mathematical curvature.

“When you wrap an egg with foil, there are always wrinkles in the foil. This doesn’t happen when you wrap a box. The reason is that foil has zero Gaussian curvature (a measure of flatness), while an egg has (variable) positive curvature. Perfect wrapping (without wrinkles) requires that the curvatures match,” explains Professor Schleimer.

So, unlike flat surfaces, eggs have variable positive curvature, making them challenging to wrap without creases or distortions. Foil, with its flat surface and zero Gaussian curvature, contrasts sharply with the egg’s curved shape.

Attempting to wrap an egg with paper, which also lacks the required curvature, would result in unsightly wrinkles and a less-than-ideal presentation. Therefore, by using tin foil, we can harmonize the egg’s curvature with the wrapping material, achieving a snug fit without compromising its shape, thus showcasing the delightful intersection of mathematics and Easter traditions.

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

Credit of the article given to University of Warwick

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

Chinese ice-ray lattice, or “binglie” as it is called in Chinese, is an intricate pattern that looks like cracked ice and is a common decorative element used in traditional Chinese window designs.

Originally inspired by fragmented patterns on ice or crackle-glazed ceramic surfaces, the design represents the melting of the ice and the beginning of a thriving spring.

When Dr. Iasef Md Rian, now an Associate Professor at Xi’an Jiaotong-Liverpool University’s Department of Architecture, arrived in China for the first time in 2019, he was immediately captivated by the latticed window designs in the classical gardens of Suzhou.

“Classical gardens in China strike me as very different from the Western ones, which are more symmetrical and organized,” he says. “Chinese gardens, however, have a more natural formation in their layout and design. The ice-ray window design is one of the manifestations.”

Having focused on fractal geometry in architectural design for many years, Dr. Rian felt an urge to explore the beauty in the patterns.

“My mind is always looking for this kind of inspiration source, so I was motivated right away to study the underlying geometric principles of the ice-ray patterns, he says.”

Revealing the underlying rule

Dr. Rian finds that the rule of creating ice-ray patterns is actually very simple.

He explains, “Take Type 1 as an example; a square is first divided into two quadrilaterals, and then each quadrilateral is further divided into two quadrilaterals. In each step, the proportions of the subdivided quadrilaterals are different, and this is how the random pattern is created using a simple rule.

“Through this configuration, Chinese craftsmen might have intended to increase its firmness so it can function as a window fence to provide protection. The random configuration of ice-ray lattices provides multi-angled connections, which transform the window into a collection of resultant forces and uniform stress distribution, in turn achieving a unique degree of stiffness.

“The microstructure of trabecular bone tissue in our own bodies serves as an excellent natural example of the potential of random lattices. It balances high stiffness, which contributes to strength, with a surprisingly lightweight structure.”

Dr. Rian recently published a paper in Frontiers of Architectural Research that explores the geometric qualities of ice-ray patterns and expands the possibilities of integrating random patterns into structural designs, especially the lattice shell design, which is often used in spherical domes and curved structures.

“In my research, I developed an algorithm to model the ice-ray patterns for lattice shell designs and assessed their feasibility and effectiveness compared to conventional gridshells. These gridshells, made from regular grids, contrast with continuous shells.

“While regular gridshells perform well under uniform loads, the ice-ray lattice offers strength under asymmetric loads. Some ice-ray patterns, resulting from optimization, surprisingly provide better strength than regular gridshells under self-weight. There is also an additional aesthetic advantage when applying the ice-ray pattern to a lattice shell design.

“I extend the application of this pattern to curved surfaces, which helps to unlock its potential in the geometric, structural, and constructional aspects of lattice shell design,” he says.

Dr. Rian has also integrated ice-ray patterns and complex geometries into his teaching. In 2022, he organized a workshop for students to design ice-ray lattice roofs.

He explains that learning the concept of fractal geometry can really push the students’ ideas toward a unique design.

“This is very different from what they’ve learned in high school. In learning to create this geometry system, they will also learn computational modeling and simulations. In the end, they’ll get comprehensive knowledge of advanced architectural and digital design,” he says.

Rediscovering traditional designs

To extend the research in this field, Dr. Rian is investigating the effectiveness of complex geometry in various aspects like micro-scale material design and structural design.

He says, “For instance, in facade design, we usually use conventional or parametric geometry to design regular shapes. However, the random shapes designed with complex geometry can offer a more natural impression and daylight penetration.”

He encourages design students and researchers to learn from the past.

“Any traditional design has a hidden rule in it. We can now use digital technologies and advanced tools to extend and expand the knowledge of traditional craftsmanship for contemporary design.

“There are many inspirations behind the traditional designs, and those principles can really inspire us designers to make innovative designs for the future,” he says.

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

Credit of the article given to Yi Qian, Xi’an jiaotong-Liverpool University

After losing an eye at the age of 5, the 2024 Abel prize winner Michel Talagrand found comfort in mathematics.

French mathematician Michel Talagrand has won the 2024 Abel prize for his work on probability theory and describing randomness. Shortly after he had heard the news, New Scientist spoke with Talagrand to learn more about his mathematical journey.

Alex Wilkins: What does it mean to win the Abel prize?

Michel Talagrand: I think everybody would agree that the Abel prize is really considered like the equivalent of the Nobel prize in mathematics. So it’s something for me totally unexpected, I never, ever dreamed I would receive this prize. And actually, it’s not such an easy thing to do, because there is this list of people who already received it. And on that list, they are true giants of mathematics. And it’s not such a comfortable feeling to sit with them, let me tell you, because it’s clear that their achievements are on an entirely other scale than I am.

What are your attributes as a mathematician?

I’m not able to learn mathematics easily. I have to work. It takes a very long time and I have a terrible memory. I forget things. So I try to work, despite handicaps, and the way I worked was trying to understand really well the simple things. Really, really well, in complete detail. And that turned out to be a successful approach.

Why does maths appeal to you?

Once you are in mathematics, and you start to understand how it works, it’s completely fascinating and it’s very attractive. There are all kinds of levels, you are an explorer. First, you have to understand what people before you did, and that’s pretty challenging, and then you are on your own to explore, and soon you love it. Of course, it is extremely frustrating at the same time. So you have to have the personality that you will accept to be frustrated.

But my solution is when I’m frustrated with something, I put it aside, when it’s obvious that I’m not going to make any more progress, I put it aside and do something else, and I come back to it at a later date, and I have used that strategy with great efficiency. And the reason why it succeeds is the function of the human brain, things mature when you don’t look at them. There are questions which I’ve literally worked on for a period of 30 years, you know, coming back to them. And actually at the end of the 30 years, I still made progress. That’s what is incredible.

How did you get your start?

Now, that’s a very personal story. First, it helps that my father was a maths teacher, and of course that helped. But really, the determining factor is I was unlucky to have been born with a deficiency in my retinas. And I lost my right eye when I was 5 years old. I had multiple retinal detachments when I was 15. I stayed in the hospital a long time, I missed school for six months. And that was extremely traumatic, I lived in constant terror that there will be a next retinal detachment.

To escape that, I started to study. And my father really immensely helped me, you know, when he knew how hard it was, and when I was in hospital, he came to see me every day and he started talking about some simple mathematics, just to keep my brain functioning. I started studying hard mathematics and physics to really, as I say, to fight the terror and, of course, when you start studying, then you become good at it and once you become good, it’s very appealing.

What is it like to be a professional mathematician?

Nobody tells me what I have to do and I’m completely free to use my time and do what I like. That fitted my personality well, of course, and it’s helped me to devote myself totally to my work.

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

*Credit for article given to Alex Wilkins*

Math enthusiasts around the world, from college kids to rocket scientists, celebrate Pi Day on Thursday, which is March 14 or 3/14—the first three digits of an infinite number with many practical uses.

Around the world many people will mark the day with a slice of pie—sweet, savory or even pizza.

Simply put, pi is a mathematical constant that expresses the ratio of a circle’s circumference to its diameter. It is part of many formulas used in physics, astronomy, engineering and other fields, dating back thousands of years to ancient Egypt, Babylon and China.

Pi Day itself dates to 1988, when physicist Larry Shaw began celebrations at the Exploratorium science museum in San Francisco. The holiday didn’t really gain national recognition though until two decades later. In 2009, Congress designated every March 14 to be the big day—to hopefully spur more interest in math and science. Fittingly enough, the day is also Albert Einstein’s birthday.

Here’s a little more about the holiday’s origin and how it’s celebrated today.

WHAT IS PI?

Pi can calculate the circumference of a circle by measuring the diameter—the distance straight across the circle’s middle—and multiplying that by the 3.14-plus number.

It is considered a constant number and it is also infinite, meaning it is mathematically irrational. Long before computers, historic scientists such as Isaac Newton spent many hours calculating decimal places by hand. Today, using sophisticated computers, researchers have come up with trillions of digits for pi, but there is no end.

WHY IS IT CALLED PI?

It wasn’t given its name until 1706, when Welsh mathematician William Jones began using the Greek symbol for the number.

Why that letter? It’s the first Greek letter in the words “periphery” and “perimeter,” and pi is the ratio of a circle’s periphery—or circumference—to its diameter.

WHAT ARE SOME PRACTICAL USES?

The number is key to accurately pointing an antenna toward a satellite. It helps figure out everything from the size of a massive cylinder needed in refinery equipment to the size of paper rolls used in printers.

Pi is also useful in determining the necessary scale of a tank that serves heating and air conditioning systems in buildings of various sizes.

NASA uses pi on a daily basis. It’s key to calculating orbits, the positions of planets and other celestial bodies, elements of rocket propulsion, spacecraft communication and even the correct deployment of parachutes when a vehicle splashes down on Earth or lands on Mars.

Using just nine digits of pi, scientists say it can calculate the Earth’s circumference so accurately it only errs by about a quarter of an inch (0.6 centimeters) for every 25,000 miles (about 40,000 kilometers).

IT’S NOT JUST MATH, THOUGH

Every year the San Francisco museum that coined the holiday organizes events, including a parade around a circular plaque, called the Pi Shrine, 3.14 times—and then, of course, festivities with lots of pie.

Around the country, many events now take place on college campuses. For example, Nova Southeastern University in Florida will hold a series of activities, including a game called “Mental Math Bingo” and event with free pizza (pies)—and for dessert, the requisite pie.

“Every year Pi Day provides us with a way to celebrate math, have some fun and recognize how important math is in all our lives,” said Jason Gershman, chair of NSU’s math department.

At Michele’s Pies in Norwalk, Connecticut, manager Stephen Jarrett said it’s one of their biggest days of the year.

“We have hundreds of pies going out for orders (Thursday) to companies, schools and just individuals,” Jarrett said in an interview. “Pi Day is such a fun, silly holiday because it’s a mathematical number that people love to turn into something fun and something delicious. So people celebrate Pi Day with sweet pies, savory pies, and it’s just an excuse for a little treat.”

NASA has its annual “Pi Day Challenge” online, offering people plenty of games and puzzles, some of them directly from the space agency’s own playbook such as calculating the orbit of an asteroid or the distance a moon rover would need to travel each day to survey a certain lunar area.

WHAT ABOUT EINSTEIN?

Possibly the world’s best-known scientist, Einstein was born on March 14, 1879, in Germany. The infinite number of pi was used in many of his breakthrough theories and now Pi Day gives the world another reason to celebrate his achievements.

In a bit of math symmetry, famed physicist Stephen Hawking died on March 14, 2018, at age 76. Still, pi is not a perfect number. He once had this to say,

“One of the basic rules of the universe is that nothing is perfect. Perfection simply doesn’t exist. Without imperfection, neither you nor I would exist.”

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Credit of the article given to Curt Anderson

Tiny particles like pollen grains move constantly, pushed and pulled by environmental forces. To study this motion, physicists use a “random walk” model—a system in which every step is determined by a random process. Random walks are useful for studying everything from tiny physics to diffusion to financial markets.

But what if the environment itself—and not just the walker—is random? “We can think of a town in which the elevation undulates in a random way, with the walker more likely to step downhill rather than uphill,” says physicist and SFI Professor Sidney Redner.

A fundamental question in this scenario, he says, is to determine the time for the system to move from one arbitrary point to another. This quantity is called the “first-passage time,” and researchers have solved it in one dimension, albeit using cumbersome calculations.

In a paper published in Physical Review E, Redner, together with SFI Program Postdoctoral Fellow James Holehouse, introduced a new way to efficiently determine all possible first-passage times and their probabilities. Their approach, which relies on heady math, captures the randomness of both the walker and the environment.

In the paper, they describe how to compute a “moment generating function”—a kind of mathematical machine for providing complete statistical information about the distribution of first-passage times.

Their approach could improve predictive analyses in a wide range of processes influenced by randomness, from changing biological populations to migration systems to the dynamics of financial instruments used to study markets. It builds on ideas that Redner first described in his 2001 book “A Guide to First Passage Processes” (and for which he’s preparing a second edition.)

Researchers typically approach first-passage problems using enormous simulations, which start with initial systems and run through time to predict the time to reach a certain state. “But simulations are a really poor way to study [these systems],” Holehouse says.

Redner adds, “If you simulate some of these systems, you’re guaranteed to get the wrong answer because you need to simulate so many instances of the system that to see the right answer would require a computation time that is beyond the age of the universe.”

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Credit of the article given to Santa Fe Institute