2023's Biggest Breakthroughs in Math
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Published 2023-12-22
Read about more math breakthroughs from this year at Quanta Magazine: www.quantamagazine.org/the-biggest-discoveries-in-…
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: www.quantamagazine.org/after-nearly-a-century-a-ne…
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: hedraweb.wordpress.com/2023/03/23/its-a-shape-jim-…
- Original story with links to research papers can be found here: www.quantamagazine.org/hobbyist-finds-maths-elusiv…
- Build your own aperiodic tiling patterns with Kaplan's online tool: 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: www.quantamagazine.org/surprise-computer-science-p…
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All Comments (21)
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Crazy that a tiling enthusiast just found the right Einstein tiles.
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Smith’s story is an inspiration to all of us math hobbyists outside of a formal academic environment!
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The second tile that I found (10-kite) was correctly named the turtle but was shown in the video as the spectre (at least one other person noticed this). Really, just thrilled the story got covered, thank you all.
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Smith is a god damn beast putting out aperiodic monotiles one after another.
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Smith did not have luck. That is genius. He did it three times.
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It is incredible that Paul Erdos had a hand in all these initial discoveries. What an incredible Mathematician and human.
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"Tiling enthusiast". I absolutely love that description.
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Love the story of Dave smith. He’s three totally independent and super fast reacted discoveries are definitely NOT good luck, but a really deep insight about symmetry and patterns, which is built throughout his life being a puzzle enthusiast. Professional mathematicians may have good skills proving and generalizing stuff, but he deserved a recognition of creative originality. That tells us that mathematics can be down in not only one way.
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I love how the huge improvement in the Ramsey bound is from 4 to 3.997. I know this is huge, but I still had to laugh when reading it.
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Dave is literally a genius in his own geeky passion for tiles and that’s amazing ❤
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Love these reviews. I genuinely get more excited about Quanta's annual reviews than I ever was for the Nobel. Fantastic to see the bleeding edge of humanity's advancements.
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Props to David Smith for making several discoveries . I can only imagine the thousands of hours he put into his tile hobby, and how he found something a mathematician , or a computer scientist couldn’t find . Genius !
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The tile section was absolutely nuts lol
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Props to David Smith. This shows how members of the public, even those who don't have professional scientific training, can still contribute to knowledge if they have the will. We can all learn something from him about where to focus our attentions in life, towards things that move us forwards as a species, even a little bit, and away from the vapid materialism that we're told will fully satisfy us.
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I like that there are so many computer scientists involved in these math breakthroughs :D
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Thanks for highlighting the contributions of an amateur mathematician. There are many and they can have important ideas too. Researching something outside the regular systems doesn't make you a crank.
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Smith is such an inspiration. It's incredible that in a world with over 8 billion people and advanced technology, there is still room for passionate amateurs to make their mark on the academic world.
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8:36 Knowledge. Fame. Scientific papers. The man who had studied everything in this world... Sir Roger Penrose. The words he said at his death spurred many to do research. Roger Penrose: The one aperiodic tile? It exists! Go out there and find it! Words he spoke drove countless men out to the field. And so men set sights on the Einstein Tile, in pursuit of their dreams of an aperiodic plane. The world has truly entered a Great Math Era!
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I heard about the Einstein tile discovery a while back and thought "wow what a lucky guy". Now I understand it's not luck, he understands it in some way clearly to have done it three times.
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I was just thinking: I’d rarely see programes like this in the old days of tv only. It’s such a gift to be able to watch this!
