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#mathematics

27 posts23 participants7 posts today

"Mathematics is not arithmetic. Though mathematics may have arisen from the practices of counting and measuring it really deals with logical reasoning in which theorems [...] can be deduced from the starting assumptions. It is, perhaps, the purest and most rigorous of intellectual activities, and is often thought of as queen of the sciences." – Erik Christopher Zeeman (1925-2016)
#quote #mathematics #math #maths #reasoning

Continued thread

“…the AIs were never able to recognize when they had not solved the problem. In every case, rather than give up, they confidently output a proof that had a large gap or an outright error.”
—Ernest Davis & Gary Marcus, Reports of LLMs mastering math have been greatly exaggerated
#mathematics #llm #llms #ai

“The USA Math Olympiad is an extremely challenging math competition for the top US high school students… Hours after it was completed…a team of scientists gave the problems to some of the top large language models, whose mathematical and reasoning abilities have been loudly proclaimed… The results were dismal: None of the AIs scored higher than 5% overall”
—Ernest Davis & Gary Marcus, Reports of LLMs mastering math have been greatly exaggerated
garymarcus.substack.com/p/repo
#mathematics #llms #llm #ai

Marcus on AI · Reports of LLMs mastering math have been greatly exaggeratedBy Ernest Davis

These art pieces are generated starting with a rectangle of given proportions and iteratively generating two smaller rectangles from it, using a simple procedure (which could be easily done with ruler and compass).
Rectangles are coloured according to their proportion and orientation, each piece with a different palette . No randomness here (as usual). Generated using #Python .
#MathArt #Art #Mathematics

I have posted the 238th Carnival of Mathematics!

fractalkitty.com/238th-carniva

If I missed something please let me know.

There is an extremely slow bit of javascript for untouchable numbers that hopefully won't make the post untouchable.

Thank you @aperiodical for organizing this.

This month we have posts from @mjd Peter Cameron, @two_star, @j2kun, Brian Clegg, @fortnow @KarenCampe, Amédée d'Aboville, Ed Vogel, @standupmaths

There was also an amazing amount of math and art being shared on blueSky with @Ayliean 's math art March prompts

last night I went on a wiki walk starting with Donald Knuth's impressive body of work and the title of his novelette "Surreal Numbers" piqued my interest

this led me down a delightfully confusing but fascinating peek into the weird side of math ft. The Monster, Baby Monster, magic squares and phrases that cracked me up like "weakly inaccessible cardinal"

def gave me a new perspective on cardinality which I mostly deal with in the practical sense with system telemetry 😅

These two art pieces are based on the deformation of a hexagonal tiling into a topologically equivalent "tiling" composed of parts of concentric circles, all parts having the same area (third image). Selecting one hexagon as the center, we transform it into a circle of radius 1. Next concentric circle will hold the 6 adjacent tiles as sectors of rings. And so on, the circle of level n will have radius sqrt(1+3·n·(n+1)) (difference of radius when n tends to infinity approaches sqrt(3)). This map can be coloured with three colours, like the hexagonal tiling. For the artwork, suppose each sector of ring is in fact a sector of a circle hidden by inner pieces. Then choose a colour and delete all pieces not of this colour. Two distinct set of sectors can be produced, one choosing the central colour, one choosing another colour. Finally recolour the pieces according to its size.
#MathArt #Art #Mathematics #geometry #tiling

Continued thread

As I appear to be doing a Glasgow mini-thread, have I mentioned before how much I love the Mathematics and Statistics building at the University of Glasgow?

Because I love the Mathematics and Statistics building at the University of Glasgow.