December 12, 2024
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The 7 Coolest Mathematical Discoveries of 2024
Unsolvable problems, multi-dimensional wheels and new prime numbers are among the new mathematical discoveries this year.
The search for an Einstein tile, a form never seen before in mathematics.
Mathematicians have been very busy this year: they found it the highest number one yeta new pi formulamysterious patterns Music by Johann Sebastian Bach and also a whole new type of shape. Some of these discoveries are practical: the shapes found, for example, appear in nature and have been used for creative architectural designs. Others, such as the 41-million-digit prime number, are less useful, but all are fascinating. Here are some of the most exciting mathematical discoveries we’ve written about this year.
New shape drops
A mathematician asked how few corners a shape could have and still completely cover a surface with no gaps between them. This doubt led him and his colleagues discover hitherto mathematically undescribed forms, called soft cells. Although new to mathematicians, soft cells are found in nautilus shells, red blood cells, and other elements in nature.
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Superlong Prime
Prime numbers—numbers divisible by 1 and only themselves—have long fascinated mathematicians. This year a researcher found it the largest known prime numberwith 41,024,320 digits. It’s been six years since the last new prime number was discovered, and the search is getting harder and harder as prime numbers spread further apart as they grow.
Pi’s new recipe
The concept of pi (π), the ratio of the circumference of a circle to its diameter, has been known for 4,000 years, since ancient Babylon. But calculating the exact figures of this irrational number has always been a challenge. Physicists recently used string theory to create one entirely A new method for calculating pi.
A wheel of multiple dimensions
For 40 years, mathematicians have pondered a question: How can we find shapes of constant width with minimal volume in any dimension? Researchers recently he envisioned a new type of wheel with many dimensions to answer this question. New wheels can be built to any size at a fraction of the size of more common shapes, such as circles or spheres.
Calculating the incalculable
This breakthrough has to do with a fundamental truth of mathematics: not everything can be calculated, no matter how hard you try (or how busy the beaver is). A certain non-evaluated statement is called the busy beaver function. Its values, BB(n), will never be known for all quantities in but recently an international collaborative project called the Busy Beaver Challenge succeeded in determining the fifth value of the function—the amazing mathematicians who thought it would be impossible.
Prelude to Bach’s clavier score.
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JS Bach’s Hidden Messages
The scientists turned the scores written by the Baroque composer Johann Sebastian Bach into mathematical networks and analyzed how his different styles varied. They he used information theory to find patterns in his music They help explain how Bach conveyed messages—including musical, mathematical, and emotional information—through his works.
Missing tab
Mathematicians have long wondered whether a single shape could tile a surface—that is, completely cover a plane—without creating a repeating pattern. Many doubted that such a shape, dubbed an einstein slab, could exist, but researchers finally found one. Although the sheet was announced in 2023, it was given to us by one of the mathematicians involved in the background of his story this year
