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Mathematics for Humanity – Math Making the World a Better Place


Minhyong Kim rejects being called an optimist, but he sounds an awful lot like one. “If we take reality exactly as it is, I don’t think we have any real grounds for pessimism,” he said in a recent conversation.

That outlook is behind Mathematics for Humanity, a program Kim recently started that aims to apply mathematics to perhaps the most ambitious possible challenge: making the world a better place.

For Kim, 59, it’s the next turn in a career that has always maintained an outward gaze. As a mathematician, he’s worked at the highly abstract intersection of number theory and geometry. Yet he’s often looked outside the field for inspiration. In particular, he has embraced physical intuition, attempting to draw a precise analogy between millennia-old mathematical problems and ideas from modern physics, as Quanta reported in 2017.

At the same time, Kim has published nine books about mathematics for the general public in his native South Korea. Many hit the bestseller list, including his 2018 title The Moment You Need Mathematics. “The motivation there primarily, it was just fun. I just enjoyed doing it,” Kim said.

With Mathematics for Humanity, Kim’s intent is more serious. He’s leading the program as the recently appointed director of the International Center for Mathematical Sciences in Edinburgh, and he’s organized it to encompass several interrelated goals. First, he wants to give grants to mathematicians and scientists who want to apply math to pressing social challenges. Applicants include researchers at the Institute for Mathematics and Democracy in Boston, which seeks to shape public policy through mathematical thinking, and the Vietnam Institute for Advanced Study in Mathematics, which is developing mathematical tools to address climate change.

A second goal is educational. He wants to broaden the history of the field to more accurately reflect the uncertain origins of many foundational ideas. For example, the core of the mathematical canon is popularly assumed to originate in the teachings of white men in ancient Greece. But in fact, much of that knowledge emerged in the vastness of the ancient Greek empire, which included the modern-day Middle East and North Africa. For Kim, this whitewashing pushes away young people who might contribute to mathematics but don’t see it as belonging to them.

Kim’s perspective, broadly, is that more people in math, and more math in the world, can only be a good thing.

A Stable Solar System? Not According to Latest Math


In 2009, a pair of astronomers at the Paris Observatory announced a startling discovery. After building a detailed computational model of our solar system, they ran thousands of numerical simulations, projecting the motions of the planets billions of years into the future. In most of those simulations — which varied Mercury’s starting point over a range of just under 1 meter — everything proceeded as expected. The planets continued to revolve around the sun, tracing out ellipse-shaped orbits that looked more or less the way they have throughout human history.

But around 1% of the time, things went sideways — quite literally. Perhaps the solar system was not as stable as people once thought. But, “You want to understand what mathematical mechanisms drive instabilities, and to prove that they actually exist,” said Marcel Guàrdia, a mathematician at the University of Barcelona (on the left in this picture).

Now, in three papers that together exceed 150 pages, Guàrdia and two collaborators have proved for the first time that instability inevitably arises in a model of planets orbiting a sun.

“The result is really very spectacular,” said Gabriella Pinzari, a mathematical physicist at the University of Padua in Italy. “The authors proved a theorem that is one of the most beautiful theorems that one could prove.” It could also help explain why our solar system looks the way it does. Together with Jacques Fejoz (on right in this pic) of the University of Paris Dauphine, Guàrdia first attempted to prove instability in the three-body problem (one sun, two planets) in 2016. Though they were able to show that chaotic dynamics arose in the flavor of Poincaré, they couldn’t prove that this chaotic behavior corresponded to large and long-term changes. Andrew Clarke, a postdoc studying under Guàrdia, joined them in September 2020, and they decided to give the problem another go, this time adding an extra planet to the mix. In their model, three planets revolve around a sun at increasingly large distances from each other. Clarke, Fejoz and Guàrdia proved that the orbits can grow arbitrarily large. “They finally get the size of the orbit to increase, as opposed to just the shape or something like that,” Moeckel said. “That’s the ultimate instability.”

The ultimate goal would be to prove instability in our own solar system. “I wake up in the middle of the night thinking about it,” Clarke said. “I would say that would be the real dream, but it would be a nightmare, wouldn’t it? Because we’d be screwed.” [read full article here]

We’ll Soon be on the Moon


Nasa’s first uncrewed Artemis mission returned to Earth in December 2022 after almost four weeks in space. Travelling far beyond the Moon, it proved the capabilities of the Orion capsule, its European Space Agency (Esa) Service Moduleand the giant SLS rocket that blasted it on its way. Artemis II is due to carry the first astronauts to lunar orbit in 2024 and, sometime in the middle of the decade during Artemis III, two astronauts will land near the lunar south pole. At least one of them will be a woman. Read more from the BBC article here. Factoid: The Moon makes Earth a more liveable planet by moderating our home planet’s wobble on its axis, leading to a relatively stable climate. It also causes tides, creating a rhythm that has guided humans for thousands of years. Without the moon, live here would be impossible.

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There’s a Winnie the Pooh song about counting. “Counting, counting, numbers are for counting…” the wise Owl sung to little Roo who was trying to help Pooh to count his honey pots for the party. Counting is an integral part of our lives today. We count our income and our expenses, we count calories and the likes and comments we get on social media, we count down to the next vacation or special event that we will be having, we count the number of years since our birth, though most of us would prefer that number to be a bit smaller!

There is a countdown to midnight for the New Year and a countdown for a space launch; and we countdown to a big event, such as the royal coronation of King Charles III and Camilla in the UK. Counting is integral to Time and both are different sides of the same coin. We can’t count without time and time requires a counting. Yes, you can count on it when it comes to counting in Mathematics! Oh, and did you count the cost of the coronation? About $US125m and counting.

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Paper airplane designed by engineers breaks world distance record


(just in from cnn): The world record for the farthest flight by paper airplane has been broken by three aerospace engineers with a paper aircraft that flew a grand total of 289 feet, 9 inches (88 meters), nearly the length of an American football field. The feat required months of effort, as the team put in nearly 500 hours of studying origami and aerodynamics to create and test multiple prototypes. The engineers put their final design to the test on December 2, 2022, in Crown Point, Indiana, where the record was achieved on their third throw.

The team had decided their best chance at beating the world record would be with an airplane design that focused on speed and minimized drag, so that the plane could fly a far distance in a short amount of time.

To find the best technique when it came to throwing the paper airplane, the team ran various simulations and analyzed slow-motion videos of their previous throws.

“We found the optimal angle is about 40 degrees off the ground. Once you’re aiming that high, you throw as hard as possible. That gives us our best distance. It took simulations to figure that out. I didn’t think we could get useful data from a simulation on a paper airplane. Turns out, we could.”

Even down to the paper, which the team had decided that A4 (slightly longer than typical letter sized paper) was the best for manipulating and folding into the winning airplane. With these meticulously thought-out design choices, and careful attention to the numerous rules and guidelines set forth by the Guinness World Record Team, the three were set to break a record.

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The Shape of Things to Come


A geometry problem that has been puzzling scientists for 60 years has likely just been solved by an amateur mathematician with a newly discovered 13-sided shape.

Called “The hat” because it vaguely resembles a fedora, the elusive shape is an “einstein” (from the German “ein stein,” or “one stone”). That means it can completely cover a surface without ever creating a repeated pattern — something that had not yet been achieved with a single tile. “I’m not really into math, to be honest — I did it at school, but I didn’t excel in it,” Smith said. That’s why I got these other guys involved, because there’s no way I could have done this without them. I discovered the shape, which was a bit of luck, but it was also me being persistent.”

Most wallpapers or tiles in the real world are periodic, meaning you can identify a small cluster that’s just constantly repeated to cover the whole surface. “The hat,” however, is an aperiodic tile, meaning it can still completely cover a surface without any gaps, but you can never identify any cluster that periodically repeats itself to do so.

Fascinated by the idea that such aperiodic sets of shapes could exist, mathematicians first mulled the problem in the early 1960s, but they initially believed the shapes were impossible. That turned out to be wrong, because within years a set of 20,426 tiles that — when used together — could do the job was created. That number was soon reduced to just over 100, and then down to six.

In the 1970s, the work of British physicist and Nobel Prize winner Roger Penrose further reduced the number of shapes from six down to two in a system that has since been known as Penrose tiling. And that’s where things were stuck for decades.

There’s nothing inherently magical about “The hat,” according to Kaplan.

“It’s really a very simple polygon to describe. It doesn’t have weird, irrational angles, it’s basically just something you get by cutting up hexagons.” For that reason, he adds, it might have been “discovered” in the past by other mathematicians creating similar shapes, but they just did not think about checking its tiling properties.

The finding has created quite a stir since its release in late March. As Kaplan points out, it has inspired artistic renditions, knitted quilts, cookie cutters, TikTok explainers and even a joke in one of Jimmy Kimmel’s opening monologues.

“I think it might open a few doors,” Smith said, “I’ve got a feeling we’ll have a different way of looking at how to find these sorts of anomalies, if you like.”

Far from being content with having rewritten math history, Smith has already discovered a “sequel” to “The hat.” Called “The turtle,” the new shape is also an einstein, but it’s made of 10 kites, or sections, rather than eight, and therefore bigger than “The hat.”

“It’s a bit of an addiction,” Smith confessed about his constant quest for new shapes.

“Tilings have many applications in physics, chemistry and beyond, for example in the study of crystals,” he said in an email. “The discovery of aperiodic tilings, now many years ago, created a stir, since their existence was so unexpected.

“This new discovery is a strikingly simple example. There are no standard techniques known for finding new aperiodic tiles, so this involved a really new idea. That is always exciting,” he added.

Mazzeo said it’s also nice to hear of a mathematical discovery that is so easy to visualize and explain: “This illustrates that mathematics is still a growing subject, with many problems that have not yet been solved.” [source: from cnn]

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Blame the Parents!


Eddie Woo says it only takes nine words from a parent to make a student struggle with numbers for the rest of their 13 years of schooling: “Don’t worry, I was never any good at maths.”

Often used to console a child struggling with the subject, Woo said it usually makes a student feel worse about their inability to solve maths problems – and has a long-lasting effect on their numeracy skills.

“It is a well-meaning statement, but it has disastrous effects,” he said.

“It is meant to reassure a kid and say don’t stress; the irony is, it has the opposite effect … it reinforces mathematics anxiety.”

Mathematics anxiety is the name given to the feeling of being overwhelmed and confused when faced with a mathematical problem.

Researchers in 1972 defined it as the feeling of tension and anxiety that interferes with the solving of mathematical problems in both ordinary life and academic situations.

Unlike generalised anxiety, it is not an official psychiatric disorder, but academics have been studying it in some form for more than 60 years.

It affects girls more than boys. Studies estimate between six and 17% of the population are afflicted by it. Researchers who scanned the brains of children who suffer from it found high levels of activity in the parts of the brain which process negative emotions – and less in regions associated with mathematical problem-solving.

Woo – who teaches at Cherrybrook High and last week took up a new job at the University of Sydney’s school of education – said while parents might sow the seeds of maths anxiety, teachers asking questions of pupils in front of the whole class could unintentionally worsen it.

“If the student doesn’t get the right answer, there is a fairly immediate psychological effect on someone when you say they’re wrong,” he said.

University of Sydney mathematics education lecturer Dr Ben Zunica said the phenomenon of maths anxiety did not occur in other subjects like reading and writing because answers to basic maths sums were either right or wrong.

“The teacher will say, ‘sorry, that’s not the right answer’,” he said.

“In English you don’t have such a black and white answer; with maths you do, especially with younger kids.”

Compounding the problem was that maths tests had become high-stakes due to the emphasis in recent years on STEM (science, technology, engineering, maths) subjects when it comes to leaving school and getting a job.

“The kids these days have been told, if they’re going to make something of themselves, maths is something they have to be really good at,” he said.

“I have seen students finish a test, been emotionally upset and in tears and this is another way maths anxiety manifests itself; they know what to do – but when they’re asked to do it, they can’t recall the information.”

Mathematics teacher Dr Karen McDaid said the problem was made worse because it is socially acceptable to develop a negative mindset toward maths compared to other subjects – meaning children were more likely to mirror their parents’ mindset when it came to maths. [read the full article here]

Editor’s Note: After more than 45 years teaching, I have reached the conclusion that a child’s upbringing (i.e. the parents) are largely to blame for their math anxiety, which can be a real fear of the subject. However, a great teacher will ease any child into a love for Mathematics in all its beautiful forms.

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Changing the Subject


Up for free use is the following powerpoint, designed for middle grade Mathematicians, called “Changing the Subject” (Algebra basics). Download, enjoy and share.

Changing the subject

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Numbers are Fun


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Master Painters leave Mathematical Clues

In a letter to his wife in March 1901, pioneering French painter Claude Monet lamented the bad weather that prevented him from working, as well as another conspicuous impediment to his creativity. “Everything is as good as dead, no train, no smoke, no boat, nothing to excite the inspiration a little,” he wrote.
Monet, now celebrated as a founder of Impressionism, was in London during one of three trips he took to the city between 1899 and 1901, which yielded over 100 paintings. His reference to smoke — which would have come abundantly from the steam engines of boats and trains — as a potential creative spark seems to support a theory long held by some art historians about what was behind the distinctive dreamy haze in Monet’s work. Now a recent study by climate scientistshas found new evidence to confirm it.
“I work on air pollution and while seeing Turner, Whistler and Monet paintings at Tate in London and Musée d’Orsay in Paris, I noticed stylistic transformations in their works,” said Anna Lea Albright, a postdoctoral researcher for Le Laboratoire de Météorologie Dynamique at Sorbonne University in Paris, in a phone interview. Albright coauthored the study with Peter Huybers, a professor of Earth and planetary sciences at Harvard University. “The contours of their paintings became hazier, the palette appeared whiter and the style changed from more figurative to more impressionistic: Those changes accord with physical expectations of how air pollution influences light,” she added.
The team looked at over 100 paintings by Monet and British painter Joseph Mallord William Turner, who was active before Monet, with the goal of finding an empirical basis to the hypothesis that the paintings capture increasingly polluted skies during the Industrial Revolution.
The focus was on these two artists because they prolifically painted landscapes and cityscapes, often with repeated motifs, according to the study authors.

A visual chronicle of atmospheric change

In the period covered by the paintings, 1796 to 1901, a huge amount of coal was mined to support industrial manufacturing and steam engines. Britain alone went from producing 2.9 million tons of coal per year in 1700 to 275 million tons by 1900, leading to visible air pollution that caused widespread health problems. The soot from the coal created a thick, dark fog, and the number of foggy days in London rose threefold between 1850 and 1890, from 25 to 75 per year, according to the National Bureau of Economic Research.
“In general, air pollution makes objects appear hazier, makes it harder to identify their edges, and gives the scene a whiter tint, because pollution reflects visible light of all wavelengths,” Albright said.
The team looked for these two metrics, edge strength and whiteness, in the paintings — by converting them into mathematical representations based on brightness — and then compared the results with independent estimates of historical air pollution.
Jonathan Ribner, a professor of European art at Boston University, was among the first art historians to suggest a connection between the two artists’ work and pollution, in a 2004 essay written for “Turner Whistler Monet,” an exhibition of 100 Impressionist paintings that toured Toronto, Paris and London. “Turner and Monet are both artists who had to go to places to see certain conditions,” he added. “There was this phenomenon of fog tourism, where French visitors like Monet went to London deliberately to see the fog, because they loved the atmospheric effects. He didn’t like it when the fog was so thick that he just couldn’t see anything, but he hated it when there was no fog and it was blue skies, because it didn’t look like London. Apparently he destroyed some of those canvases with a clear sky.” [Read more here]
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Post Support

Hidden Rabbit? Clue: check the trees

How long for the stadium to fill? 45 minutes.

Where are you? the North Pole

Prize Object Puzzle: If Sue does not know where the prize is in the first question, it can’t be under the square. She must have been told it is under another shape. Apply this same logic to Colin. It is then obvious that the prize cannot be under a yellow object. That helps Sue eliminate her yellow shapes. Got the idea?

Algebra Puzzle: Answer = 1

Popular Math Problems Answers: 1, 1

Number of tabs? According to Lifehacker, the ideal number of tabs you should have open is nine. Yes, a single digit. To some, this is like playing a piano and only using a fraction of the notes!

Worst Graph? Where to start. What a visual mess and even some of the lines merge and are impossible to follow. A graph is a visual display of data, with the goal to identify trends or patterns. This is a spider’s web of information which fails to show a clear pattern at all. Solution? Well, different colors would help, or why not group in two or three graphs where trends are similar?

Number of different nets to make a cube is eleven – see this link

Homework Puzzle; The total value of the counters is 486, so halve this to get 243. Now, arrange the counters to equal this amount twice.

The graph on the left (Coronavirus) is for a time period of 30 days, while the one on the right (SARS) is for 8 months! Very poor graphical comparison and hardly relevant, unless it is attempting to downplay the seriousness of the coronavirus?

10 x 9 x 8 + (7 + 6) x 5 x 4 x (3 + 2) x 1 = 2020

NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]


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