Quanta Magazine’s mathematics coverage in 2023 included landmark results in Ramsey theory and a remarkably simple aperiodic tile capped a year of mathematical delight and discovery. Read about more math breakthroughs from this year at Quanta Magazine: https://www.quantamagazine.org/the-biggest-discoveries-in-math-in-2023-20231222/ 00:05 Ramsey Numbers One of the biggest mathematical discoveries of the past year was in graph theory where the proof of a new, tighter upper bound to Ramsey numbers. These numbers measure the size that graphs must reach before inevitably containing structures called cliques. The discovery, announced in March, was the first advance of its type since 1935. - Original story with links to research papers can be found here: https://www.quantamagazine.org/after-nearly-a-century-a-new-limit-for-patterns-in-graphs-20230502/ 06:21 Aperiodic Monotile The most attention-getting result of the year was the discovery of a new kind of tile that covers the plane but only in a pattern that never repeats. A two-tile combination that does this has been known since the 1970s, but the single tile, discovered by a hobbyist named David Smith and announced in March, has been a sensation. CORRECTION: In the video, the image presented as the 'turtle' tile is in fact a rotated 'spectre' tile. To see the correct version of the turtle tile, you can visit Dave Smith's webpage: https://hedraweb.wordpress.com/2023/03/23/its-a-shape-jim-but-not-as-we-know-it/ - Original story with links to research papers can be found here: https://www.quantamagazine.org/hobbyist-finds-maths-elusive-einstein-tile-20230404/ - Build your own aperiodic tiling patterns with Kaplan's online tool: https://cs.uwaterloo.ca/~csk/hat/h7h8.html 14:20 Three Arithmetic Progressions Two computer scientists, Zander Kelley and Raghu Meka, stunned mathematicians with news of an out-of-left-field breakthrough on an old combinatorics question: How many integers can you throw into a bucket while making sure that no three of them form an evenly spaced progression? Kelley and Meka smashed a long-standing upper bound on the number of integers smaller than some cap N that could be put in the bucket without creating such a pattern. - Original story with links to research papers can be found here: https://www.quantamagazine.org/surprise-computer-science-proof-stuns-mathematicians-20230321/ - VISIT our Website: https://www.quantamagazine.org/ - LIKE us on Facebook: https://www.facebook.com/QuantaNews - FOLLOW us Twitter: https://twitter.com/QuantaMagazine Quanta Magazine is an editorially independent publication supported by the Simons Foundation: https://www.simonsfoundation.org/