Maya glyph names maths powerhouse

A mathematical formula inscribed on a wall at the Maya site of Xultun in Guatemala has revealed the name of an important Maya mathematician-astronomer. Sak Tahn Waax, or ‘White-Chested Fox’, was a scholar comparable with mathematical giants of the past, researchers suggest. The calculations inscribed in this set of hieroglyphs expresses the relationships between several calendar systems in a playful manner that hasn’t been seen before in Mayan texts, says archaeologist and study co-author Heather Hurst. “I think it was a mathematical flex,” she says.

A Powerful New ‘QR Code’ Untangles Math’s Knottiest Knots

Mathematicians have long tried to untangle exactly what makes a knot a knot. There are several ways to define a knot’s characteristics, referred to as ‘invariants’, but “most invariants are either very strong but impossible to compute, or easy to compute but very weak,” says mathematician Daniel Tubbenhauer. Now researchers Dror Bar-Natan and Roland van der Veen have proposed what they dub “a fast, strong, topologically meaningful, and fun knot invariant” — or Θ for short — that can describe even very complex knots as a rather lovely 2-dimensional pattern.

Flowers hint at maths before numerals

Pottery made by people of the Halafian culture, who inhabited northern Mesopotamia between around 6200 and 5500 BC, is painted with flowers that have 4, 8, 16 or 32 petals, and some show arrangements of 64 flowers. These patterns show a clear understanding of symmetry and spatial division long before written numbers came into use around 3400 BC, argue scientists in a new study. The skill might have helped the Halafian people with tasks such as sharing harvests or dividing communal fields, the authors say.

First Shape Found That Can’t Pass Through Itself

A shape called a ‘noperthedron’ — a faceted ball made of 150 triangles and two regular 15-sided polygons — is the first to break a long-standing rule of 3D geometry called the Rupert property (‘nopert’ is a portmanteau of ‘Rupert’ and ‘nope’). In short, there’s no way a noperthedron can pass through a straight hole in an identical shape.

The breakthrough proof bringing mathematics closer to a grand unified theory

The Langlands programme is a group of interconnected conjectures that is often hailed as the grand unified theory of mathematics — but it remains largely unproven. Last year, researchers unveiled a proof of a key piece — the geometric Langlands conjecture — and that accomplishment is now forging bridges between different mathematical lands.

Mathematicians Find Proof to 122-Year-Old Triangle-to-Square Puzzle

A long-standing shape mystery has finally been solved.

Mathematicians discover new class of shape seen throughout nature

Mathematicians have described a new class of shape — soft cells. These shapes have corners that are deformed into thin points with internal angles of zero, which let them tessellate on a 2D plane with no gaps. Soft cells are common in nature, from the inside of onions to mollusc shells, but this new work is the first time they’ve been formally described.

Mathematicians Reinvent the Wheel in Higher Dimensions to Solve Decades-Old Geometry Problem

Mathematicians have created a new family of shapes, similar to a multidimensional guitar pick, that roll like a wheel in higher dimensions. Wheels and spheres roll smoothly without wobbling because they are objects with constant width. In two and three dimensions, mathematicians have previously created smaller rolling objects called Reuleaux triangles and Meissner bodies — both similar in shape to guitar picks — that have constant width but less volume than wheels and spheres. Now a concise three-page proof offers a solution for higher dimensions.

Decimal point is older than thought

The decimal point was invented by Italian merchant and astronomer Giovanni Bianchini some 150 years before what was considered to be its first appearance. Bianchini’s training in economics might have given him a perspective different to that of his astronomer peers — who would have exclusively been using the sexagesimal (base 60) system — and his approach was perhaps too revolutionary to catch on until much later.

Mathematicians Identify the Best Versions of Iconic Shapes

In mathematics, an ‘optimal shape’ is the most extreme version of a simple shape, whether it’s a Möbius strip, a twisted paper cylinder or a trefoil knot. Topology devotees have identified a handful of such shapes in recent years. Each new discovery is about minimising the amount of paper or string used to make the shape.

Mathematicians finally solve Feynman’s “reverse sprinkler” problem

In normal operation, an S-shaped lawn sprinkler rotates because of the ‘jets’ of water shooting from its nozzles. But if the sprinkler is underwater and sucking in water, which way does it spin? The riddle of ‘Feynman’s sprinkler’ was popularized by physicist Richard Feynman. “The answer is perfectly clear at first sight,” he wrote in his memoir Surely You’re Joking, Mr. Feynman. “The trouble was, some guy would think it was perfectly clear one way, and another guy would think it was perfectly clear the other way.”

The complexities of flow and turbulence mean that past experiments have given inconclusive or contradictory results (or, in Feynman’s case, broken glass and a thorough soaking). Now, researchers have carefully designed a sprinkler to remove confounding effects and found that the underwater sprinkler rotates in the opposite direction to the normal one, but unsteadily, and about 50 times slower. Detailed observations backed up by mathematical modelling suggest that a weak jet effect inside the device dominates the sprinkler’s motion.

DeepMind AI outdoes human mathematicians on unsolved problem

An artificial intelligence (AI) system, called FunSearch, has improved on mathematicians’ previous solutions to problems inspired by the card game Set. Until now, researchers have used AI to solve mathematics problems with known solutions. This time, FunSearch went further than what had already been solved by humans in combinatorics, a field of mathematics that studies how to count the possible arrangements of sets containing finitely many objects.

This infinite tiling pattern could end a 60-year mathematical quest

After 60 years of searching, mathematicians might have finally found a true single aperiodic tile — a shape that can cover an infinite plane and never make a repeating pattern. In March, a team of hobbyist and professional mathematicians found a shape that, together with its mirror image, could be used to build infinite aperiodic tilings. The same team has now modified the shape so it doesn’t need its mirror image to create the never-repeating pattern.

Mathematicians have finally discovered an elusive ‘einstein’ tile

Researchers have discovered the first example of a single shape that can cover a surface with an infinite pattern that never repeats. The shape is surprisingly simple: a 13-sided polykite that the team has dubbed ‘the hat’. The hat’s sides can vary in length without it losing the ability to create ‘aperiodic tiling’. Previous examples of aperiodic tilings, such as Penrose tiles, required two or more shapes.

Extreme numbers get new names

By the 2030s, the world will generate around a yottabyte of data per year — that’s 10²⁴ bytes, or the amount that would fit on DVDs stacked all the way to Mars. The data boom has prompted the governors of the metric system to agree on new prefixes to describe the outrageously big and small. The prefixes ronna and quetta represent 10²⁷ and 10³⁰, and ronto and quecto signify 10⁻²⁷ and 10⁻³⁰. Earth weighs around one ronnagram, and an electron’s mass is about one quectogram. Ronna and quetta might sound strange now, but so did giga and tera once, says metrologist Olivier Pellegrino. This is the first update to the prefix system since 1991, when zetta (10²¹), zepto (10⁻²¹), yotta (10²⁴) and yocto (10⁻²⁴) were added.

Mathematician who solved prime-number riddle claims new breakthrough

Number theorist Yitang Zhang, who went from obscurity to luminary status in 2013 for cracking a century-old question about prime numbers, now claims to have solved another. The problem is similar to — but distinct from — the Riemann hypothesis, which is considered one of the most important problems in mathematics. Zhang posted his proposed solution — a 111-page preprint — on arXiv, and it has not yet been validated by his peers. If it checks out, it will help to tame the randomness of prime numbers, but Zhang and other scientists have previously proposed solutions to this problem that turned out to be faulty. It will take a while for researchers to comb through Zhang’s argument to see whether it is correct.

DeepMind’s AI helps untangle the mathematics of knots

Artificial-intelligence (AI) powerhouse DeepMind has teamed up with mathematicians to spot previously unseen patterns and seek new discoveries. Researchers trained a machine-learning algorithm on vast amounts of data about knots and revealed a formula linking two properties of knots — which the mathematicians then proved rigorously. In a separate test, the team found a potential pattern related to symmetries, which had been sought for decades.

Pi calculated to the 62.8 trillionth digit

Researchers have broken a world record by calculating the mathematical constant pi to 62.8 trillion digits, beating the previous record of 50 trillion digits. The calculation took a supercomputer 108 days to complete. Researchers say the effort was an important benchmarking exercise for computational hardware and software.

A universal law of turbulence

Mathematicians have uncovered a simple universal law to describe the type of turbulence you see when mixing paint or stirring milk into coffee. Researchers harnessed the handy statistical characteristics of randomness to show that these systems, although chaotic, mix with a predictable structure.

Fragile topology

The mathematics hidden in materials keeps getting more exotic. Topological states of matter — which derive exotic properties from their electrons’ ‘knotty’ quantum states — have shot from rare curiosity to one of the hottest fields in physics. Now, theorists are finding that topology is ubiquitous, and recognising it as one of the most significant ways in which solid matter can behave.