All posts tagged: maths

Maths teacher targets don’t add up when demand is growing

Maths teacher targets don’t add up when demand is growing

Published by skeptic

The goal for new teachers appears to have been shifted to ensure the ball hit the net, but you can’t fool a mathematician with statistics, says Bobby Seagull  Next month, the government will unveil its latest teacher recruitment targets. Last year they trumpeted progress in filling vacancies and achieving their goals. In my subject, maths, they overshot their own target of 2,300 new teachers by over 10 per cent. I want more specialist maths teachers and those with a passion for the subject in classrooms, passing on wonder and energy for a topic too often wrongly characterised as dull and dusty. When my class is fully immersed in a rich mathematical problem, such as how everything on our phones – the apps, the pics, their friends’ contact details – are all stored as binary numbers, you can see the moment it clicks. Maths isn’t just all around us, it’s the foundation of our technological future.  Maths is the fuel on which AI runs. It’s the key to mobile phone technology, driverless cars and contactless payments. …

The secret to guessing more accurately with maths

The secret to guessing more accurately with maths

Published by skeptic

What’s in the box? Professor25/Getty Images Suppose I showed you a box and asked you to guess what is inside, without providing any more details. You might think this is completely impossible, but the nature of the container provides some information – the contents must be smaller than the box, for example, while a solid metal box can hold liquids and withstand temperatures that a cardboard box would struggle with. Is there a way to describe this process of guessing with limited information in a mathematically sensible way? Clearly, there are some things that cannot be reliably guessed – the flip of a coin, the roll of dice – and we call these random. But for everything else, a few handy tools can make you a lot better at constraining your guesses, rather than picking an answer out from the ether. A constrained guess is really an estimate, and these have a long history. Perhaps the most impressive early example is that of the ancient Greek philosopher Eratosthenes, who lived in Alexandria, Egypt, in the …

The maths quirk that can cheer you up if you’re feeling unpopular

The maths quirk that can cheer you up if you’re feeling unpopular

Published by skeptic

Orlando Gili/Millenium Images Your friends are likely to have more friends than you do. Don’t worry, it’s nothing personal. It’s just about how networks organise. We can represent a friendship group as a network. Draw a node (dot) for each person and a line between two nodes if those two people are friends. By doing this for a group of people who interact in person or online, we can build a representation of friendship connections. This network allows us to explore questions such as the number of degrees of separation. If someone is a friend of your friend, they are connected to you at degree 2. Their friends are at degree 3, and so on. How many links must we follow to get from one person to another? Connections tend to cluster together. Think of a group of friends – people you live near, some of your work colleagues or people who attend your astrophotography club. It’s likely that a lot of these people are friends with each other, so many of your “friends of …

Bored of snakes and ladders? Some maths can help bring back the fun

Bored of snakes and ladders? Some maths can help bring back the fun

Published by skeptic

Does skill have any influence on the outcome when playing Snakes and Ladders? Sipa US/Alamy Have you ever played snakes and ladders (also known as Chutes and Ladders)? Are you sure? This game has its origins in ancient Indian games in which players roll dice to progress across a board of squares, such as Pachisi. While Pachisi mixes luck and skill, early forms of snakes and ladders used pure chance to teach players a spiritual lesson about accepting their fate. Players climbed the board, liberating the soul from earthly desires to reach the goal of spiritual enlightenment, with versions associated with Hindu, Jain and Sufi philosophies. On the way, they might exhibit virtues, shown as ladders lifting them to a higher position, but must avoid vices, represented by snakes. The game travelled with families returning from the British Raj to the UK. From 1892, UK versions appeared with more simplistic morals and lacking the spiritual journey. Over time, the moral lessons vanished and just the snakes and ladders remained. I would define playing a game …

Amateur mathematicians solve long-standing maths problems with AI

Amateur mathematicians solve long-standing maths problems with AI

Published by skeptic

AI tools are helping to decipher long-standing maths problems andresr/Getty Images Amateur mathematicians are using artificial intelligence chatbots to solve long-standing problems, in a move that has taken professionals by surprise. While the problems in question aren’t the most advanced in the mathematical canon, the success of AI models in tackling them shows that their mathematical performance has passed a significant threshold, say researchers, and could fundamentally change the way we do mathematics. The questions being solved by AI originate from Hungarian mathematician Paul Erdős, who was famous for his ability to pose useful but difficult questions during a career that spanned over six decades. “The questions tended to be very simple, but very hard,” says Thomas Bloom at the University of Manchester, UK. By his death in 1996, there were more than 1000 of these unsolved Erdős problems, spanning a wide range of mathematical disciplines, from combinatorics (the study of combinations) to number theory. Today, they are seen as signposts for progress in these fields, says Bloom, who runs a website that catalogues the …

Why it’s easy to be misunderstood when talking about probability

Why it’s easy to be misunderstood when talking about probability

Published by skeptic

The words we have for probability make it hard to say what we mean Makhbubakhon Ismatova/Getty Images If someone told you that they were “probably” going to have pasta for dinner, but you later found out that they ate pizza, would you feel surprised – or even lied to? More seriously, what does it mean to be told that it is “very likely” that Earth will exceed 1.5°C of warming within the next decade, as the United Nations reported last year? Translating between the vagaries of language and the specifics of mathematical probability can be tricky, but it turns out it can be more scientific than you might think – even if it took us quite a long time to arrive at a translation. There are two words that most of us can agree on when it comes to probability. If something is “impossible”, its chance of occurring is 0 per cent, while a “certain” event has a 100 per cent chance of coming to pass. In between, it gets murky. Ancient Greeks like Aristotle …

These images explore a ‘utopic’ village built for teaching maths

These images explore a ‘utopic’ village built for teaching maths

Published by skeptic

In a sunlit amphitheatre, a student writes on a blackboard Piero Castellano In 2007, Ali Nesin set out to solve a mathematics problem by building a village. Nesin, a Turkish mathematician, had noticed that even students who came to his Istanbul Bilgi University classroom from Turkey’s most elite schools were struggling with maths. Instead of thinking critically, they were memorising formulas and approaching their education with a troubling passivity, Nesin concluded. He decided to do something about it, eventually getting a literal village – the Nesin Mathematics Village, in western Turkey – off the ground. Ali Nesin teaching in his Maths Village Piero Castellano Photographer Piero Castellano recently captured Nesin teaching there. In the above photograph, Nesin’s eyes are fixed on a blackboard set against a tree, some leafy vines, a stone floor and a stone wall. Castellano says that the tree, the vines and the stones are crucial to Nesin’s vision. He wanted the village to be in a secluded location, where students could immerse themselves in maths and communal living and learn better …

Festive maths puzzles – answers and explanations

Festive maths puzzles – answers and explanations

Published by skeptic

Here are the answers to the festive maths quiz I set on December 23. I hope you enjoyed it. Read more: The magic of maths: festive puzzles to give your brain and imagination a workout nestdesigns/Shutterstock Puzzle 1: You are given nine gold coins that look identical. You are told that one of them is fake, and that this coin weighs less than the real ones. Using a set of old-fashioned balance scales, what is the smallest number of weighings you need to determine which is the fake coin? Solution: You can do this in just two weighings: (1) Divide the nine coins into three sets of three, and choose two of these sets to weigh against one another. If one set is lighter than the other, then the fake is one of these three coins. If the two sets weigh the same, then the fake is in the three unweighed coins. (2) Now take the set with the fake coin, and weigh two of its coins against each other. If one is lighter, that is …