Category: International Maths Olympiad

What is the value of learning mathematics now that artificial intelligence (AI) can solve almost all the questions we throw at it? Will AI change the way we think of mathematics and the way we teach and learn it? Will learning mathematics even remain relevant in 10 years from now, in an age when AI will surely play a key role? These are all valid questions, regardless of whether one is a mathematician or an educator or not. Finding definite answers to such questions is a key challenge in times like these; governed by uncertainty, by the fact that many questions have no clear answers, and that most answers are questionable. It is challenging yet exciting at the same time though, just like mathematics! It is now that our human intelligence and character need to be fully activated to ensure we proceed confidently, and try to find answers that allow us to prosper as a civilisation. So, I cannot answer these big questions on behalf of everyone, but what I can and will do here is share my personal thoughts on mathematics in the age of AI, as a mathematician, an educator, and a human.

First, mathematics is here to stay, no matter how AI proliferates. Not necessarily as it is now, not necessarily as an independent subject, not necessarily in its current shape and form, but as something to be embraced and experienced, and as something to be learned as the Greek origins of the word imply. How will it be learned though? Not necessarily the same way as now, not necessarily in classrooms, not only through textbooks and assessments, and probably not just facilitated by a human. I am convinced that teaching and learning in general will change in theory and practice, sooner or later, as a result of AI and all the emerging technologies, all the new discoveries in various fields, and our own evolving understanding of the concepts of teaching and learning. A change in education models will surely accompany this, whether we are in favor of it or not. I am also certain that if we manage to perceive AI and technology as catalysts and not threats, and if we truly believe in our human intelligence and resilience and our ability to adapt while protecting our human characteristics, we can then conceive new resilient learning and education models, mostly human-led and AI- and technology-powered as a starting point, that take us to new levels of innovation, efficiency and progress.

Will mathematics remain relevant? Yes. Always. But again, what do we mean by mathematics and relevance here? Mathematics is not just a book or an assessment. It is more than a grade or a degree. Mathematics is relevant for how sublime it is, and we need to accentuate that. What do I mean by sublime? First, from a philosophical and aesthetic perspective, mathematics induces awe and exceeds the realm of senses; its infinite horizons and abstract beauty align with the scale and magnificence the word induces among philosophers, from Burke and the vastness beyond comprehension to Kant and triumph of reason. This somehow resonates with Kurt Gödel who said: “Either mathematics is too big for the human mind or the human mind is more than a machine.”1 For me personally, mathematics is SUBLIME in the way it embodies seven aspects: it is stimulating, ubiquitous, borderless, limitless, intriguing, monumental, and enduring. How, you ask?

Stimulating: Mathematics is not just memorising and applying formulas, sketching a graph, solving an equation, or finding the area of a 2D-shape, and we need to ensure it is not perceived as such. Nothing activates critical thinking, reasoning and problem-solving skills like mathematics. It pushes us to think about everything we deal with in real life from finances and measurements to more impalpable topics like the origin of the universe and the future of human intelligence, and even infinity and beyond. But not just that, mathematics teaches us to persevere while remaining patient, and to dream big while remaining humble. Maryam Mirzakhani was spot-on when she declared that “the beauty of mathematics only shows itself to more patient followers”.2 What is more humbling than the ‘simple’ prime numbers that still offer the most complex and challenging uncharted ramifications. Patience, and maybe AI, can help us explore these!

Ubiquitous: Mathematics is not just a ‘subject’ or a ‘course’ to be taught at school. While it has been tagged as such by many for a long time, for structural and practical reasons mainly, it might be time we rethink that. Purists may say that keeping it “independent” is an explicit acknowledgement of its importance, but is it? Maybe education systems should rethink how subjects are packaged and how content is delivered. Mathematics can (should?) be the element that beats the long-standing stagnation in the existing education models, which traditionally segregate subjects, with the help of new technologies, drawing upon how mathematics beats within so many other subjects that rely on mathematical concepts and reasoning to survive. Who said mathematics and computer science are totally independent, for example? Same for mathematics and physics or mathematics and medical sciences. Is teaching mathematics in context nowadays better or worse for learners? Joseph Fourier said: “Mathematics compares the most diverse phenomena and discovers the secret analogies that unite them”.3 What if mathematics gets taught, at least partially, in that way; following a unifying approach?

Borderless: Mathematics is not to be confined in curricula and textbooks; it is not to be framed as a collection of topics and domains or a list of theorems and formulas. It is and should be free to roam, as Georg Cantor wanted it to be when he said “the essence of mathematics lies precisely in its freedom”.4 One of the beautiful things about technology, and mainly AI, when used carefully, is that it allows us to break human-made borders between education resources and brings almost everything to our fingertips: we can now access real-time data related to a medical condition for use in a statistics course; we can create a mathematical model for climate change based on relevant and recent information; we can visualise and touch 3D graphs and interact with all sorts of holograms; we can juggle equations and play with charts in various ways; and much more. When all of this is available, why stick to the book and the blackboard? Technology allows us to amplify how free-spirited mathematics can and should be. After all, mathematics is not just something we learn: it is something we live, and that should be at the core of how mathematics is experienced.

Limitless: Mathematics is not a finite set of components. It never ceases to amaze us day after day, and this will be the case for an infinite amount of time! Speaking of infinity, who can think of different ‘sizes’ of infinity but a mathematician? That being said, new technologies should be seen and used as tools in support of this journey of ours to ensure more brains are triggered, more mysteries are unraveled, more conjectures are proven, and even new domains and fields are created and explored, just like with DeepMind. After all, keep in mind that there are still many unsolved problems in mathematics that require deep thinking and much perseverance, so why not let AI help us tackle these quests while we move on to think of new mounts to climb? Andrew Wiles once said: “The definition of a good mathematical problem is the mathematics it generates rather than the problem itself.”5 Mathematics builds on itself, and the more we discover the more there will be left to uncover.

Intriguing: Mathematics is not boring and should not be so. It never ceases to push intelligence, human or artificial, to the limit, as it tackles a combination of structured and irregular numbers and objects, as it deals with systematic and chaotic systems and models, and as it includes logical and counterintuitive theorems and results. How fascinating to study a Koch snowflake, with its infinite length enclosing a finite area? How captivating to learn about Gabriel’s horn, with its infinite surface area and finite volume? This is the never-ending generosity of mathematics, always breaking the norms of reason and common sense, while being the guardian of logic! Mathematics is that magical mixture of certainty and conjectures: a special key that opens the most basic locks and the most challenging ones at once; it helps you add two digits and has the power to reveal the mysteries of the universe. But while this is so, we should not forget that there is still a stigma associated with mathematics for many, from numeracy to advanced level topics, and the fact that it is not presented and delivered as fun, attractive, and useful for all, adds to this stigma. We need to keep that gripping aspect of mathematics alive and to eliminate the stigma, and technology can assist with that.

Monumental: Mathematics is not just a supporting actor in a play led by other ‘fields’. Mathematics always had a tremendous role to play in humanity’s flourishing, and this has been the case to a massive extent from the beginning of times. Imagine a world without ‘0’, without ‘pi’, without ‘x’, without ‘i’, without ‘e’! All tiny on paper but huge in impact on human civilisation, and not only theoretically or in closed labs. Mathematics, whether explicitly or implicitly, even makes our world more beautiful to look at and live in; imagine architecture without the golden ratio, or nature without fractals and the Fibonacci sequence. This impact of mathematics will be further amplified with AI and new technologies; new discoveries, new proofs, new unexplored areas. But maybe it is time we rebrand mathematics to highlight its role and impact even more? If you ask a student nowadays if they prefer taking a course titled “Linear Algebra and Statistics” or one titled “Machine Learning and AI”, I believe I know what most of them would choose (someone to do a survey?), because mathematics is not marketed as a key component to all the transformations we are now witnessing in technology, nor to so many discoveries. Maybe the status of mathematics and its stardom is not debatable among scholars, but that is not necessarily the case in society or among students; this should change.

Enduring: Mathematics is not confined in an era or a timeline. It keeps on giving and history provides numerous examples of this. Mathematics evolves and expands, but it never stops being vital. Mathematics is always there, with its facts guiding how everything works whether we feel it or not, whether we know they are facts or not. As Erwin Schrödinger eloquently put it: “A mathematical truth is timeless, it does not come into being when we discover it”.6 Mathematics has always been a companion and a guide to discoveries and progress; from Thales, Euclid, and Hypatia; to Al Khawarizmi, Al-Battani and Al-Kashi; to Euler, Gauss, and Germain; to Ramanujan, Turing, and Mandelbrot; the list is long. Mathematics will remain alive as long as humanity exists, and beyond. It will remain relevant as long as we have problems to solve, patterns and relationships to understand, and things to measure and compare. Mathematics will remain a core element of this universe as long as curiosity is burning.

So, with or without AI, or maybe because of it, it is time to highlight how SUBLIME mathematics is! What do you say?

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

*Credit for article given to Rachad Zaki*

Math teachers have to accommodate high school students’ different approaches to problem-solving. RJ Sangosti/MediaNews Group/The Denver Post via Getty Images

Among high school students and adults, girls and women are much more likely to use traditional, step-by-step algorithms to solve basic math problems – such as lining up numbers to add, starting with the ones place, and “carrying over” a number when needed. Boys and men are more likely to use alternative shortcuts, such as rounding both numbers, adding the rounded figures, and then adjusting to remove the rounding.

But those who use traditional methods on basic problems are less likely to solve more complex math problems correctly. These are the main findings of two studies our research team published in November 2025.

This new evidence may help explain an apparent contradiction in the existing research – girls do better at math in school, but boys do better on high-stakes math tests and are more likely to pursue math-intensive careers. Our research focuses not just on getting correct answers, but on the methods students use to arrive at them. We find that boys and girls approach math problems differently, in ways that persist into adulthood.

A possible paradox

In a 2016 study of U.S. elementary students, boys outnumbered girls 4 to 1 among the top 1% of scorers on a national math test. And over many decades, boys have been about twice as likely as girls to be among the top scorers on the SAT and AP math exams.

However, girls tend to be more diligent in elementary school and get better grades in math class throughout their schooling. And girls and boys across the grades tend to score similarly on state math tests, which tend to be more aligned with the school curriculum and have more familiar problems than the SAT or other national tests.

Beyond grades and test scores, the skills and confidence acquired in school carry far beyond, into the workforce. In lucrative STEM occupations, such as computer science and engineering, men outnumber women 3 to 1. Researchers have considered several explanations for this disparity, including differences in math confidence and occupational values, such as prioritizing helping others or making money. Our study suggests an additional factor to consider: gender differences in approaches to math problems.

When older adults think of math, they may recall memorizing times tables or doing the tedious, long-division algorithm. Memorization and rule-following can pay off on math tests focused on procedures taught in school. But rule-following has its limits and seems to provide more payoff among low-achieving than high-achieving students in classrooms.

More advanced math involves solving new, perplexing problems rather than following rules.

Math can be creative, not rote. AP Photo/Jacquelyn Martin

Differing strategies

In looking at earlier studies of young children, our research team was struck by findings that young boys use more inventive strategies on computation problems, whereas girls more often use standard algorithms or counting. We wondered whether these differences disappear after elementary school, or whether they persist and relate to gender disparities in more advanced math outcomes.

In an earlier study, we surveyed students from two high schools with different demographic characteristics to see whether they were what we called bold problem-solvers. We asked them to rate how much they agreed or disagreed with specific statements, such as “I like to think outside the box when I solve math problems.” Boys reported bolder problem-solving tendencies than girls did. Importantly, students who reported bolder problem-solving tendencies scored higher on a math problem-solving test we administered.

Our newer studies echo those earlier results but reveal more specifics about how boys and girls, and men and women, approach basic math problems.

Algorithms and teacher-pleasing

In the first study, we gave three questions to more than 200 high school students: “25 x 9 = ___,” “600 – 498 = ___,” and “19 + 47 + 31 = ___.” Each question could be solved with a traditional algorithm or with a mental shortcut, such as solving 25 x 9 by first multiplying 25 x 8 to get 200 and then adding the final 25 to get 225.

Regardless of their gender, students were equally likely to solve these basic computation items correctly. But there was a striking gender difference in how they arrived at that answer. Girls were almost three times as likely as boys – 52% versus 18% – to use a standard algorithm on all three items. Boys were far more likely than girls – 51% versus 15% – to never use an algorithm on the questions.

Girls were far more likely than boys to use an algorithm

When given three basic math problems, high school girls were three times more likely than boys to use a standard algorithm to solve all three. High school boys were nearly three times more likely than girls to use an alternative strategy for all three problems.

We suspected that girls’ tendency to use algorithms might stem from greater social pressure toward compliance, including complying with traditional teacher expectations.

So, we also asked all the students eight questions to probe how much they try to please their teachers. We also wanted to see whether algorithm use might relate to gender differences in more advanced problem-solving, so we gave students several complex math problems from national tests, including the SAT.

As we suspected, we found that girls were more likely to report a desire to please teachers, such as by completing work as directed. Those who said they did have that desire used the standard algorithm more often.

Also, the boys in our sample scored higher than the girls on the complex math problems. Importantly, even though students who used algorithms on the basic computation items were just as likely to compute these items correctly, algorithm users did worse on the more complex math problems.

Continuing into adulthood

In our second study, we gave 810 adults just one problem: “125 + 238 = ___.” We asked them to add mentally, which we expected would discourage them from using an algorithm. Again, there was no gender difference in answering correctly.

But 69% of women, compared to 46% of men, reported using the standard algorithm for their mental calculation, rather than using another strategy entirely.

We also gave the adults a more advanced problem-solving test, this time focused on probability-related reasoning, such as the chances that rolling a seven-sided die would result in an even number. Similar to our first study, women and those who used the standard algorithm on the computation problem performed worse on the reasoning test.

The importance of inventiveness

We identified some factors that may play a role in these gender differences, including spatial-thinking skills, which may help people develop alternate calculation approaches. Anxiety about taking tests and perfectionism, both more prevalent among women, may also be a factor.

We are also interested in the power of gender-specific social pressures on girls. National data has shown that young girls exhibit more studious behavior than do boys. And the high school girls we studied were more likely than boys to report they made a specific effort to meet teachers’ expectations.

More research definitely is needed to better understand this dynamic, but we hypothesize that the expectation some girls feel to be compliant and please others may drive teacher-pleasing tendencies that result in girls using algorithms more frequently than boys, who are more socialized to be risk-takers.

While compliant behavior and standard math methods often lead to correct answers and good grades in school, we believe schools should prepare all students – regardless of gender – for when they face unfamiliar problems that require inventive problem-solving skills, whether in daily life, on high-stakes tests or in math-intensive professions.

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

*Credit for article given to Sarah Lubienski, Colleen Ganley & Martha Makowski*

Ground Picture/Shutterstock

Mathematics at A-level is going from strength to strength. Maths is the most popular subject choice, and further maths, which is a separate A-level course, has seen the most growth in uptake. Despite this, concerns still remain about the mathematical skills of young people who do not choose to study maths after they are 16.

Students in England who have passed GCSE maths at grade four or above, but who are not taking A-level or AS-level maths, are eligible to take a core maths qualification.

Core maths was introduced in 2014-15 to attempt to remedy a lack in mathematics education after 16. But the number of entries remains well short of what they could be. Many students who would benefit from maths after 16 are not taking this subject.

A 2010 report from the Nuffield Foundation found students in the UK lag their peers in other countries in participation in mathematics after the age of 16. Further research from the Royal Society and higher education charity AdvanceHE showed that as a consequence, many were not well prepared for the demands of their university courses or careers. Survey data has also found that over half of UK adults’ maths skills are low.

Many courses at university include mathematical or quantitative elements, but do not require AS or A-level maths for entry. These include psychology, geography, business and management, sociology, health sciences, biology, education and IT. When many students have not studied mathematics since GCSE, this results in a lack of fluency and confidence in using and applying it.

Core maths consolidates and builds on students’ mathematical understanding. The focus is on using and applying mathematics to authentic problems drawn from study, work and life. This includes understanding and using graphs, statistics and tools such as spreadsheets, as well as understanding risk and probability.

Core maths includes topics such as probability. EF Stock/Shutterstock

Take-up remains low despite incentives – schools receive an additional £900 in funding for each student who studies core maths. In 2025, 15,327 students took core maths – a 20% increase on 12,810 entries in 2024, which is very encouraging. However, research from the Royal Society in 2022 found that fewer than 10% of the number of A-level students who were not taking A-level mathematics had taken core maths, which will not have changed significantly even with the current numbers.

Increasing enrolment

There remains strong commitment from the government for increasing participation in mathematics after 16 in England through core maths. Many schools and colleges have embraced the subject, and universities have expressed support too.

However, a real incentive for teenagers to study this subject would be if it was rewarded in entry to university. Universities can allow students entry to a course with lower A-level grade profiles than normally required if they also passed core maths, for instance. But the number of universities making this kind of offer is low.

Schools and colleges need stronger signals from universities to induce them to offer students the opportunity to study for a core maths qualification, and to encourage their students to do so. Shifting today’s landscape to one where the vast majority of learners aged 16 to 19 in England are studying some form of mathematics which is relevant to their current and future interests and needs will require reform.

The Royal Society’s 2024 report on mathematical and data education sets out several reforms necessary to develop the mass mathematical, quantitative and data skills needed for the careers of the future. These include compulsory maths and data education in some form until 18. Extending the take up of core maths would be an excellent way to begin achieving this.

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

*Credit for article given to Paul Glaister CBE*

Using the tools of computational complexity, researchers have discovered it is impossible to figure out whether certain Super Mario Bros levels can be beaten without playing them, even if you use the world’s most powerful supercomputer.

Figuring out whether certain levels in the Super Mario Bros series of video games can be completed before you play them is mathematically impossible, even if you had several years and the world’s most powerful supercomputer to hand, researchers have found.

“We don’t know how to prove that a game is fun, we don’t know what that means mathematically, but we can prove that it’s hard and that maybe gives some insight into why it’s fun,” says Erik Demaine at the Massachusetts Institute of Technology. “I like to think of hard as a proxy for fun.”

To prove this, Demaine and his colleagues use tools from the field of computational complexity – the study of how difficult and time-consuming various problems are to solve algorithmically. They have previously proven that figuring out whether it is possible to complete certain levels in Mario games is a task that belongs to a group of problems known as NP-hard, where the complexity grows exponentially. This category is extremely difficult to compute for all but the smallest problems.

Now, Demaine and his team have gone one step further by showing that, for certain levels in Super Mario games, answering this question is not only hard, but impossible. This is the case for several titles in the series, including New Super Mario Bros and Super Mario Maker. “You can’t get any harder than this,” he says. “Can you get to the finish? There is no algorithm that can answer that question in a finite amount of time.”

While it may seem counterintuitive, problems in this undecidable category, known as RE-complete, simply cannot be solved by a computer, no matter how powerful, no matter how long you let it work.

Demaine concedes that a small amount of trickery was needed to make Mario levels fit this category. Firstly, the research looks at custom-made levels that allowed the team to place hundreds or thousands of enemies on a single spot. To do this they had to remove the limits placed by the game publishers on the number of enemies that can be present in a level.

They were then able to use the placement of enemies within the level to create an abstract mathematical tool called a counter machine, essentially creating a functional computer within the game.

That trick allowed the team to invoke another conundrum known as the halting problem, which says that, in general, there is no way to determine if a given computer program will ever terminate, or simply run forever, other than running it and seeing what happens.

These layers of mathematical concepts finally allowed the team to prove that no analysis of the game level can say for sure whether or not it can ever be completed. “The idea is that you’ll be able to solve this Mario level only if this particular computation will terminate, and we know that there’s no way to determine that, and so there’s no way to determine whether you can solve the level,” says Demaine.

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

*Credit for article given to Matthew Sparkes*

Feedback plays a vital role in mathematics education, guiding students toward deeper understanding and fostering a supportive learning environment. This article delves into the importance of specific and actionable feedback in mathematics education and explores strategies for both giving and receiving feedback effectively.

Understanding Feedback:

In mathematics education, feedback transcends mere praise or criticism—it is a nuanced tool for academic growth. Effective feedback should be clear, and concise, and provide guidance for improvement. It should highlight students’ strengths, address any misunderstandings, and offer actionable steps for progress.

Key Components of Effective Feedback:

Specificity: Feedback should pinpoint areas for improvement and clarify the path to success. Students need to know precisely what they need to do to enhance their understanding.

Actionability: Feedback should be actionable, outlining steps for students to move forward. This empowers students to take ownership of their learning journey.

Importance of Feedback:

Feedback serves multiple critical purposes in mathematics education:

Promoting Learning: It catalyzes academic growth by guiding students towards deeper understanding and mastery.

Building Motivation: Constructive feedback inspires students to strive for excellence and fosters a growth mindset.

Fostering Relationships: Feedback provides an opportunity for educators to connect with students on a deeper level, building trust and rapport.

The Human Element: Empathy and Trust:

Effective feedback is rooted in empathy and trust. Creating a safe and supportive learning environment is essential for feedback to be received positively. Teachers should approach feedback with empathy, avoiding emotional reactions and prioritizing the emotional well-being of their students.

Integrating Feedback into Planning:

When planning lessons, educators should:

Set Clear Goals: Define learning objectives and success criteria to guide student progress.

Anticipate Misconceptions: Be prepared to address common misunderstandings and provide targeted support.

Establish Trust: Build a culture of trust and openness in the classroom to facilitate effective feedback exchanges.

Feedback Goes Both Ways:

Teachers should be open to receiving feedback from students. Seeking feedback encourages student engagement and provides valuable insights for improving teaching practices. Additionally, teachers can infer feedback by observing students’ understanding and addressing any gaps in comprehension proactively.

Conclusion:

Feedback is a cornerstone of effective mathematics education, fostering academic growth and cultivating a supportive learning environment. By prioritizing specificity, actionability, empathy, and trust, educators can create a feedback-rich classroom where every student has the opportunity to excel in mathematics.

Mathematics and engineering go hand in hand. Mathematics is an essential tool for engineers and plays a crucial role in helping students become better engineers. In this article, we will explore how math helps students become better engineers.

Understanding and Applying Principles:

Engineering is all about applying scientific principles to solve real-world problems. Mathematics is the language of science, and without it, engineers would not be able to understand the fundamental principles that govern the world around us. By studying math, students learn how to analyze and solve complex problems, which is a critical skill for any engineer. Moreover, math helps students understand the fundamental concepts of physics, which is essential to many engineering fields.

Analyzing and Solving Problems:

Engineers are problem solvers, and math is an essential tool for problem-solving. Math helps students develop critical thinking skills and teaches them how to analyze and solve problems systematically. Engineers use mathematical concepts to create models, analyze data, and make predictions. These models and predictions help engineers design and build products that meet specific needs and requirements. One standard approach to building your maths skills is by participating in Olympiads such as the International Maths Olympiad Challenge.

Design and Optimization:

Designing and optimizing systems is another essential part of engineering. Math plays a critical role in helping engineers design and optimize systems. Mathematical models help engineers simulate and optimize systems to ensure that they meet specific requirements. By understanding mathematical concepts like calculus, optimization, and linear algebra, students can learn how to design and optimize complex systems.

Communication:

Engineers must be able to communicate complex technical concepts to non-technical stakeholders. Math helps students develop this skill by teaching them how to use graphs, charts, and other visual aids to communicate complex data and concepts. By using math to present data and findings, engineers can help non-technical stakeholders understand the technical aspects of their work.

Mathematics is an essential tool for engineers. By studying math, students can develop critical thinking skills, learn how to solve complex problems, and design and optimize systems. Moreover, math helps students communicate complex technical concepts to non-technical stakeholders, an essential skill for any engineer. Therefore, it is important for engineering students to have a strong foundation in mathematics. By doing so, they can become better engineers and contribute to solving the world’s complex problems.

Mathematics is a significant aspect of developing technological advancements in children. Understanding the logic and concept of Math is important. And so is executing them in many useful areas. To participate and prepare for the International Maths Olympiads, it is essential to study mathematics comprehensively. Math preparation will help your child handle all academic career requirements.

The International Mathematical Challenge allows your child to upskill and understand the maths competition level that is taught in the classroom. For your child’s safe and robust future, as a parent, you must encourage them to participate in the International Maths Olympiad competition. Click here to register today.

Participating in international math Olympiads can benefit a child’s future. Some of the most important benefits of participating in math Olympiads include:

Improving Problem-Solving Skills: Math Olympiads involve solving complex and challenging math problems. This helps children develop critical thinking and problem-solving skills, which are important for success in many fields.

Enhancing Mathematical Knowledge: Participating in math Olympiads helps children learn new mathematical concepts and ideas and strengthens their existing knowledge.

Building Confidence: Solving challenging math problems can be difficult, but participating in math Olympiads helps children build confidence in their abilities to solve difficult problems.

Boosting Academic Performance: Participation in math Olympiads can improve academic performance in mathematics and other subjects.

Opportunities for Scholarships: High-performing students in math Olympiads may be eligible for scholarships and other academic opportunities.

Exposure to New Cultures: Math Olympiads are often international events, giving children the opportunity to meet and interact with students from different countries and cultures.

EndNote

Participating in math Olympiads can help children develop valuable skills and knowledge, build confidence, improve academic performance, and open up new opportunities for scholarships and international exposure.

Our laws of nature are written in the language of mathematics. But maths itself is only as dependable as the axioms it is built on, and we have to assume those axioms are true.

You might think that mathematics is the most trustworthy thing humans have ever come up with. It is the basis of scientific rigour and the bedrock of much of our other knowledge too. And you might be right. But be careful: maths isn’t all it seems. “The trustworthiness of mathematics is limited,” says Penelope Maddy, a philosopher of mathematics at the University of California, Irvine.

Maddy is no conspiracy theorist. All mathematicians know her statement to be true because their subject is built on “axioms” – and try as they might, they can never prove these axioms to be true.

An axiom is essentially an assumption based on observations of how things are. Scientists observe a phenomenon, formalise it and write down a law of nature. In a similar way, mathematicians use their observations to create an axiom. One example is the observation that there always seems to be a unique straight line that can be drawn between two points. Assume this to be universally true and you can build up the rules of Euclidean geometry. Another is that 1 + 2 is the same as 2 + 1, an assumption that allows us to do arithmetic. “The fact that maths is built on unprovable axioms is not that surprising,” says mathematician Vera Fischer at the University of Vienna in Austria.

These axioms might seem self-evident, but maths goes a lot further than arithmetic. Mathematicians aim to uncover things like the properties of numbers, the ways in which they are all related to one another and how they can be used to model the real world. These more complex tasks are still worked out through theorems and proofs built on axioms, but the relevant axioms might have to change. Lines between points have different properties on curved surfaces than flat ones, for example, which means the underlying axioms have to be different in different geometries. We always have to be careful that our axioms are reliable and reflect the world we are trying to model with our maths.

Set theory

The gold standard for mathematical reliability is set theory, which describes the properties of collections of things, including numbers themselves. Beginning in the early 1900s, mathematicians developed a set of underpinning axioms for set theory known as ZFC (for “Zermelo-Fraenkel”, from two of its initiators, Ernst Zermelo and Abraham Fraenkel, plus something called the “axiom of choice”).

ZFC is a powerful foundation. “If it could be guaranteed that ZFC is consistent, all uncertainty about mathematics could be dispelled,” says Maddy. But, brutally, that is impossible. “Alas, it soon became clear that the consistency of those axioms could be proved only by assuming even stronger axioms,” she says, “which obviously defeats the purpose.”

Maddy is untroubled by the limits: “Set theorists have been proving theorems from ZFC for 100 years with no hint of a contradiction.” It has been hugely productive, she says, allowing mathematicians to create no end of interesting results, and they have even been able to develop mathematically precise measures of just how much trust we can put in theories derived from ZFC.

In the end, then, mathematicians might be providing the bedrock on which much scientific knowledge is built, but they can’t offer cast-iron guarantees that it won’t ever shift or change. In general, they don’t worry about it: they shrug their shoulders and turn up to work like everybody else. “The aim of obtaining a perfect axiomatic system is exactly as feasible as the aim of obtaining a perfect understanding of our physical universe,” says Fischer.

At least mathematicians are fully aware of the futility of seeking perfection, thanks to the “incompleteness” theorems laid out by Kurt Gödel in the 1930s. These show that, in any domain of mathematics, a useful theory will generate statements about this domain that can’t be proved true or false. A limit to reliable knowledge is therefore inescapable. “This is a fact of life mathematicians have learned to live with,” says David Aspero at the University of East Anglia, UK.

All in all, maths is in pretty good shape despite this – and nobody is too bothered. “Go to any mathematics department and talk to anyone who’s not a logician, and they’ll say, ‘Oh, the axioms are just there’. That’s it. And that’s how it should be. It’s a very healthy approach,” says Fischer. In fact, the limits are in some ways what makes it fun, she says. “The possibility of development, of getting better, is exactly what makes mathematics an absolutely fascinating subject.”

HOW BIG IS INFINITY?

Infinity is infinitely big, right? Sadly, it isn’t that simple. We have long known that there are different sizes of infinity. In the 19th century, mathematician Georg Cantor showed that there are two types of infinity. The “natural numbers” (1, 2, 3 and so on forever) are a countable infinity. But between each natural number, there is a continuum of “real numbers” (such as 1.234567… with digits that go on forever). Real number infinities turn out not to be countable. And so, overall, Cantor concluded that there are two types of infinity, each of a different size.

In the everyday world, we never encounter anything infinite. We have to content ourselves with saying that the infinite “goes on forever” without truly grasping conceptually what that means. This matters, of course, because infinities crop up all the time in physics equations, most notably in those that describe the big bang and black holes. You might have expected mathematicians to have a better grasp of this concept, then – but it remains tricky.

This is especially true when you consider that Cantor suggested there might be another size of infinity nestled between the two he identified, an idea known as the continuum hypothesis. Traditionally, mathematicians thought that it would be impossible to decide whether this was true, but work on the foundations of mathematics has recently shown that there may be hope of finding out either way after all.

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

*Credit for article given to Michael Brooks*

Inspiring students to be exuberantly responsive is one of the most significant aspects of mathematics directions and a serious aspect of any curriculum. Successful teachers focus attentively on the less interested or weak students and the intelligent ones. Here are a few ways—based on intrinsic and extrinsic motivation—that can come into action to inspire primary and secondary school students in maths preparation.

Extrinsic and Intrinsic Motivation

Extrinsic motivation includes advantages that occur outside the student’s dominance. These may incorporate lucrative token rewards for top performance, escape “punishment” for accomplishing good, compliments for good work, and so on.

Although, many students show intrinsic motivation in their preference to understand a session or logic (task-related), to surpass others (ego-related), or to influence others. The ultimate aim gets to the barrier between intrinsic and extrinsic.

Strategies for Increasing Student Motivation in Math

Call attention to a gap in students’ skills: Disclosing to students a difference in their understanding abilities maximizes their desire to learn more. For example, you may present a few usual exercises or tasks that imply familiar circumstances, followed by exercises that include unfamiliar situations on the same maths topic. The more fiercely you find the gap in understanding, the more fruitful the motivation.

Display continuous achievement: Closely connected to the preceding technique is having students cherish a logical order of concepts. This varies from the earlier process in that it relies on students’ aspirations to increase, not complete, their knowledge skills. One instance of a sequential achievement method is how quadrilaterals differ from one to another from the point of view of
their properties.

Give a challenge: When students are challenged rationally, they respond with enthusiasm and attentiveness. Proper care must be taken in opting for the challenge for students like International Maths Olympiad Challenge offers maths test opportunities to students who want to prepare for the maths Olympiad from around the world. The maths challenge must lead into the curriculum and be within reach of the student’s abilities and grades.

Point out the usefulness of a topic: Introduce a practical implementation of genuine interest to the class at the start of a topic. For instance, in high school geometry, a student could be asked to find the diameter of a plate where all the relevant detail they have is a plate section smaller than a semicircle. The activity selected should be organized and easiest to motivate the students.

Use entertaining mathematics: Recreational motivation includes games, quizzes, contests, or puzzles. In addition to being chosen for their specific motivational advantage, these activities must be appropriate and uncomplicated. Effective implementation of this process will let students complete the recreation. Moreover, the fun and excitement that these recreational references create should be handled carefully.

Conclusion

Mathematics teachers must acknowledge the fundamental motives already exist in their learners or students who prepare hard to compete in International Maths Challenge. The teacher can then use these methods of motivation to increase engagement and improve the success rate of the teaching process. Utilizing student motivations and abilities can lead to the development of artificial mathematical problems and situations.

All kids are different and live with different skills and interests. Some kids are good at studies and some at sports, but no one can be good at everything. Many kids are good at mathematics, but many kids find maths a little confusing & challenging. There will be no other option for kids to skip this learning period; every kid has to learn all these subjects. Parents and teachers help their kids or students to learn these subjects with ease but there are a lot of ways by which students can easily enjoy these boring activities and enhance their learning skills.

Some of the ways to improve your child’s learning skills and abilities-

Visual Techniques

It’s a compelling technique to improve your kid’s learning skills. Generally, visual learners learn things by seeing what they are reading or writing. You should also provide your kid with all the tools and resources so they can learn hands-on. According to research, if kids have food like raisins or marshmallows on a daily basis, it can help them easily solve Maths Olympiad problems like addition or subtraction. This technique for addition or subtraction visually can upgrade your child’s understanding of maths skills and allow the child to become engaged in the process.

International Maths Olympiad Registration

Further, you can also register for the maths olympiad to enhance your child’s skills. These maths tests will help the child to build a positive perception regarding different subjects and enable them to think logically and achieve well in different phases of life.

Let them choose

One of the best ways for your kid to get engrossed in their studies is to let them choose their material and resources. They won’t even need to insist when they are already interested. It will be interesting for them, so they will pick up study material and read on their own. If you want your kid to solve IMO sample papers independently, you should first create interest. Allow them to pick books and find stories they can imagine.

Give them a reading book

All the kids need to know how to read, which is necessary for other learning activities. To improve a child’s performance, you should put a reading book in their room or motivate them to read books using the visualization technique. This will encourage them to read and solve IMO sample papers easily.

Create Environment

It’s essential to give them a clean and quiet environment to study so that they can give their complete focus without any distractions. Do they have proper space for books, computers, or laptops? Also, give them the required resources, like school supplies, folders, and International Maths Olympiad sample papers. So they don’t need to get up in the middle of their studies.

Allow them to ask for doubts

Your kid must feel free to ask you anything that they want. They should not hesitate to ask and provide them comfort so they can ask easily. Suppose they have any doubts in a lesson, you will be there and you should always be available for their help. This thing can also assist them to ask in their class without any hesitation.

Studying and preparing for the maths Olympiad will enhance students’ logical reasoning and thinking abilities and make them move toward strong career opportunities. If you are confused about participating in the International Maths Challenge, we are here to guide you at every step of your success. Click here to raise your query.