Month: November 2022

Relating mathematics to questions that are relevant to many students can help address its image problem, argues Eugenia Cheng.

Mathematics has an image problem: far too many people are put off it and conclude that the subject just isn’t for them. There are many issues, including the curriculum, standardised tests and constraints placed on teachers. But one of the biggest problems is how maths is presented, as cold and dry.

Attempts at “real-life” applications are often detached from our daily lives, such as arithmetic problems involving a ludicrous number of watermelons or using a differential equation to calculate how long a hypothetical cup of coffee will take to cool.

I have a different approach, which is to relate abstract maths to questions of politics and social justice. I have taught fairly maths-phobic art students in this way for the past seven years and have seen their attitudes transformed. They now believe maths is relevant to them and can genuinely help them in their everyday lives.

At a basic level, maths is founded on logic, so when I am teaching the principles of logic, I use examples from current events rather than the old-fashioned, detached type of problem. Instead of studying the logic of a statement like “all dogs have four legs”, I might discuss the (also erroneous) statement “all immigrants are illegal”.

But I do this with specific mathematical structures, too. For example, I teach a type of structure called an ordered set, which is a set of objects subject to an order relation such as “is less than”. We then study functions that map members of one ordered set to members of another, and ask which functions are “order-preserving”. A typical example might be the function that takes an ordinary number and maps it to the number obtained from multiplying by 2. We would then say that if x < y then also 2x < 2y, so the function is order-preserving. By contrast the function that squares numbers isn’t order-preserving because, for example, -2 < -1, but (-2)² > (-1)². If we work through those squaring operations, we get 4 and 1.

However, rather than sticking to this type of dry mathematical example, I introduce ones about issues like privilege and wealth. If we think of one ordered set with people ordered by privilege, we can make a function to another set where the people are now ordered by wealth instead. What does it mean for that to be order-preserving, and do we expect it to be so? Which is to say, if someone is more privileged than someone else, are they automatically more wealthy? We can also ask about hours worked and income: if someone works more hours, do they necessarily earn more? The answer there is clearly no, but then we go on to discuss whether we think this function should be order-preserving or not, and why.

My approach is contentious because, traditionally, maths is supposed to be neutral and apolitical. I have been criticised by people who think my approach will be off-putting to those who don’t care about social justice; however, the dry approach is off-putting to those who do care about social justice. In fact, I believe that all academic disciplines should address our most important issues in whatever way they can. Abstract maths is about making rigorous logical arguments, which is relevant to everything. I don’t demand that students agree with me about politics, but I do ask that they construct rigorous arguments to back up their thoughts and develop the crucial ability to analyse the logic of people they disagree with.

Maths isn’t just about numbers and equations, it is about studying different logical systems in which different arguments are valid. We can apply it to balls rolling down different hills, but we can also apply it to pressing social issues. I think we should do both, for the sake of society and to be more inclusive towards different types of student in maths education.

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

*Credit for article given to Eugenia Cheng*

Mathematicians have grappled with a so-called “fixed point” theorem. An EPFL-based team has now found an elegant, one-page solution that opens up new perspectives in physics and economics

Take a map of the world. Now put it down on the ground in Central Park, against a rock on Mount Everest, or on your kitchen table; there will always be a point on the map that sits exactly on the actual physical place it represents. Obvious? Not for mathematicians. A more complex theorem, called a “fixed point theorem,” has eluded them since 1963. “Some ideas seem evident to the human mind, but in reality involve complicated concepts that are difficult to demonstrate mathematically,” says Nicolas Monod, head of EPFL’s Chair of Ergodic and Geometric Group Theory. It turns out that the answer was there all along, simple and elegant. To reach it, the team of mathematicians had take a different approach to the problem. Their discovery will impress their fellow mathematicians, of course; but on the longer term, it also will be of interest to physicists and economists.

Surprisingly, this theorem works for all kinds of maps, from a diagram of a metro route to a map of spaces used in quantum physics. But to prove it, a fixed point must be found for every possible case. Since the number of possible maps is infinite, the mathematicians were looking for a universal, purely mathematical method — one that would work in any situation.

The challenge for the mathematicians was to find that fixed point. It was a bit like designing a method that could pinpoint the center of gravity of any object, real or purely mathematical. It seemed like an impossible task for the specialists. “That’s why this approach hadn’t been more fully explored,” Monod explains. “It was in thinking about another space and exchanging our ideas that we realized that we actually could find that center of gravity.” It was possible to determine it in a parallel space. The center of gravity was definitely there … but outside the space you started from. It was a counterintuitive result, but one that allowed them to prove the theorem.

In 2008, a thirty-page article, full of technical jargon, almost arrived at a proof. Even Barry Edward Johnson, who formulated the theorem and worked hard to find a proof all the way up to his death in 2002, was ultimately unsuccessful. Today, the proof is only a few pages long. In addition to the indisputable intellectual satisfaction this elegant result represents, it also opens up long-term perspectives in other disciplines; theories in physics and economics, for example, both make use of the idea of fixed points.

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

Credit of the article given to Ecole Polytechnique Federale de Lausanne

Mathematics is an essential part of our daily lives, and it is crucial for children to develop strong math skills from a young age. Here are some reasons why math is important in kids’ daily lives:

Problem-solving skills: Mathematics teaches children how to solve problems, both in math-related situations and in real-life situations. The logical and analytical skills they develop through math help them find solutions to problems and make informed decisions.

Money management: Math skills are essential for managing finances. Children need to learn how to add, subtract, multiply, and divide money to manage their allowances and understand the value of different amounts.

Time management: Math skills also play a critical role in time management. Children need to be able to tell time, calculate elapsed time, and understand the concept of time zones to manage their schedules and keep appointments.

Measurements: Measurements are everywhere, from cooking to construction. Math skills are necessary for children to understand the different units of measurement and use them in everyday situations.

Technology: Math is essential for understanding and using technology. Programming, robotics, and computer science are all based on math concepts. Register for the International Maths Olympiad Challenge to improve your kid’s skill and thinking level.

Academic and career success: Strong math skills are essential for success in academic and career fields such as engineering, science, finance, and technology. Building a strong foundation in math from a young age can set children up for future success.

In summary, math is an essential subject that plays a crucial role in students’ academic and personal development. It helps students develop problem-solving and critical thinking skills, enhances their quantitative abilities, improves decision-making abilities, advances career opportunities, and improves overall academic performance.