More than two thirds of the zeros of the Riemann zeta function lie on the critical line https://lobste.rs/s/8sojbt #math
https://www.anthropic.com/research/riemann-zeta
math
Hilariously Fast Volume Computation with the Divergence Theorem (2018) https://lobste.rs/s/dbavwl #graphics #math
https://alyssarosenzweig.ca/blog/hilariously-fast-volume-computation-with-the-divergence-theorem.html
Curvature Beziers via @fanf https://lobste.rs/s/r7kppl #graphics #math
https://acko.net/blog/curvature-beziers/
Making [etched] holograms with a pen plotter https://lobste.rs/s/9iliea #show #art #graphics #math
https://blog.jordan.matelsky.com/Penplotter-holography/
A noob learns FFT via @abnv https://lobste.rs/s/aeur9s #math #visualization
https://entropicthoughts.com/fft
Systems and Delays (2026) https://lobste.rs/s/yia0pc #math
https://martin.janiczek.cz/2026/07/24/systems-and-delays.html
N-body gravity simulation in O(N) https://lobste.rs/s/v1ejq9 #video #math #performance #programming #science
https://www.youtube.com/watch?v=FhMftauQZqU
Towards a Theory of Bugs: The Ruliology of the Unexpected via @ahelwer https://lobste.rs/s/e0nmps #math
https://writings.stephenwolfram.com/2026/07/towards-a-theory-of-bugs-the-ruliology-of-the-unexpected/
Additional Publications (2005) via @fanf https://lobste.rs/s/phafdg #math #satire
https://jeremymartinmath.github.io/morepubs.html
Regarding the LB, https://fedi.kbg.sh/users/kevin/statuses/117085582358711627
There's an interesting thing about strongly typed programming languages, especially dependently typed ones (1), wherein if you know the type signature of a function there is sometimes only one implementation of it, and that implementation will have lots of nice properties (e.g. Philip Wadler's Theorems for free! paper, also Jose Oliveira's work, and the followups to these). It's a fascinating set of results that holds out the possibility of at least some amount of automatic programming that has desirable, provable properties concerning correctness, resource use, security, and so on.
However, that "some amount" is very important to remember. I'd argue that no matter how far such work is pushed, there will always be an infinite space of things one might wish to express in software that cannot be automatically programmed in that way. That's the Therac-25 space the LB evokes. We all know this intuitively, I think, yet in the various mystifications thrown up about computers and software and now LLMs it can be hard to remember.
For example, I'd say so-called "side effects" or just "effects" are still a large blind spot of these methods. Without effects functional programming does little more than heat up a CPU (but the heat is an effect oops), so if we're being snarky we might say functional programming without effects isn't programming at all. But in spite of the gazillion attempts to do so, you really cannot faithfully capture all side effects of interest in a type system, for the simple reason that the real world is open-ended.(2) There's a funny contradiction that functional programming languages could not exist were it not for irreducibly effectful computational architectures to exist on. Asking the CPU to execute an instruction, and all the statefulness this necessarily involves, is a "side effect" in this view of computation, which is absurd.
For these reasons I've found it fruitful to conceive of functional programming as an intricate bureaucracy sitting between the programmer and the real world.(3) Set up enough bureaucracy and you can comfortably pretend most of the real world isn't there most of the time. Some people do this for so long that they begin to think the bureaucracy is the real world (4); or they try to warp the real world till it becomes more and more like the bureaucracy.(5) But the real world is oozy and eventually squishes around all attempts to constrain it in this way. Neglecting this is how people end up being harmed by digital technology.
#AI #GenAI #GenerativeAI #LLMs #Lean #math #ComputerScience #theory #FunctionalProgramming #philosophy
(1) "leanslop" in the linked post refers to Lean, a dependently typed functional programming language that's being used to formalize mathematical ideas. We should always remember that Lean originated from Microsoft Research
(2) There's a long history of philosophical arguments hiding behind that assertion but there's no space to get into that here. A less contentious way to put it would be that the claim that all side effects worth caring about can be captured in a type system is a philosophical commitment, not a fact about the world, and therefore it's possible it cannot be done
(3) We use terms like runtimes, preludes, standard libraries, or APIs/ABIs (among others) for this bureaucracy
(4) "Touch grass"
(5) Financialization and neoliberalism, e.g.
There's an interesting thing about strongly typed programming languages, especially dependently typed ones (1), wherein if you know the type signature of a function there is sometimes only one implementation of it, and that implementation will have lots of nice properties (e.g. Philip Wadler's Theorems for free! paper, also Jose Oliveira's work, and the followups to these). It's a fascinating set of results that holds out the possibility of at least some amount of automatic programming that has desirable, provable properties concerning correctness, resource use, security, and so on.
However, that "some amount" is very important to remember. I'd argue that no matter how far such work is pushed, there will always be an infinite space of things one might wish to express in software that cannot be automatically programmed in that way. That's the Therac-25 space the LB evokes. We all know this intuitively, I think, yet in the various mystifications thrown up about computers and software and now LLMs it can be hard to remember.
For example, I'd say so-called "side effects" or just "effects" are still a large blind spot of these methods. Without effects functional programming does little more than heat up a CPU (but the heat is an effect oops), so if we're being snarky we might say functional programming without effects isn't programming at all. But in spite of the gazillion attempts to do so, you really cannot faithfully capture all side effects of interest in a type system, for the simple reason that the real world is open-ended.(2) There's a funny contradiction that functional programming languages could not exist were it not for irreducibly effectful computational architectures to exist on. Asking the CPU to execute an instruction, and all the statefulness this necessarily involves, is a "side effect" in this view of computation, which is absurd.
For these reasons I've found it fruitful to conceive of functional programming as an intricate bureaucracy sitting between the programmer and the real world.(3) Set up enough bureaucracy and you can comfortably pretend most of the real world isn't there most of the time. Some people do this for so long that they begin to think the bureaucracy is the real world (4); or they try to warp the real world till it becomes more and more like the bureaucracy.(5) But the real world is oozy and eventually squishes around all attempts to constrain it in this way. Neglecting this is how people end up being harmed by digital technology.
#AI #GenAI #GenerativeAI #LLMs #Lean #math #ComputerScience #theory #FunctionalProgramming #philosophy
(1) "leanslop" in the linked post refers to Lean, a dependently typed functional programming language that's being used to formalize mathematical ideas. We should always remember that Lean originated from Microsoft Research
(2) There's a long history of philosophical arguments hiding behind that assertion but there's no space to get into that here. A less contentious way to put it would be that the claim that all side effects worth caring about can be captured in a type system is a philosophical commitment, not a fact about the world, and therefore it's possible it cannot be done
(3) We use terms like runtimes, preludes, standard libraries, or APIs/ABIs (among others) for this bureaucracy
(4) "Touch grass"
(5) Financialization and neoliberalism, e.g.
Edited 28d ago
The Dark Night of Mathematics https://lobste.rs/s/hrhb42 #math #philosophy
https://kirwinhampshire.substack.com/p/the-dark-night-of-mathematics
A long division story https://lobste.rs/s/d857ms #compsci #math
https://kolja.rs/algorithm-d
I'm a combo of Neutral Good, Chaotic Neutral, and Lawful Evil, a little bit of everything 🤔 Nerds are gonna nerd I guess 😂
@reading @bookstodon @books @fantasy
@humor @humor@lemmy.world @aiop
#GeekMemes #Geek #Meme
#Science #Books #Theatre #Math #History #Gaming #Computer #Sport #Anime #Humor #Humour #Funny
#Alignment #Chart
Logic for Programmers https://lobste.rs/s/l03yv1 #math #programming
https://logicforprogrammers.com/
A SAT Attack on Tarski's High School Algebra Problem via @fanf https://lobste.rs/s/syxqrd #math
https://arxiv.org/abs/2608.08421
A faster way to calculate the day-of-the-week https://lobste.rs/s/ln3dao #assembly #c++ #math #performance
https://www.benjoffe.com/fast-day-of-week
Methinks it is a weasel https://lobste.rs/s/8tnxna #math #philosophy
https://diatone.net/methinks
did you know that Fibonacci numbers (where each number is the sum of the previous two) can convert miles to kilometres?
1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...
pick any number in the sequence as your miles, and the next number in the sequence approximates the number of kilometres
this works because the ratio of consecutive Fibonacci numbers converges to 1.6180334 (the golden ratio φ), while the number of kilometres in a mile is 1.609344
to see how close this is, consider the approximation compared to the actual kilometres
miles km actual km
1 2 1.61
2 3 3.22
3 5 4.83
5 8 8.05
8 13 12.87
13 21 20.92
21 34 33.79
34 55 54.71
55 89 88.50
89 144 143.20
#math
How Is Compression Prediction? https://lobste.rs/s/hxur8w #math
https://lukefleed.xyz/posts/compression/
Special Relativity Boot Camp https://lobste.rs/s/uo3yff #math #science
https://www.acsu.buffalo.edu/~whkinney/SpecialRelativityBootCamp/
Ten advances in mathematics and theoretical computer science https://lobste.rs/s/n6rg1c #math #vibecoding
https://openai.com/index/ten-advances-in-mathematics/
Mathematics Without Mathematicians https://lobste.rs/s/foagiq #math #vibecoding
https://borretti.me/article/mathematics-without-mathematicians
Programming Pearl: Sampling Unique (x, y) Pairs via @abnv https://lobste.rs/s/kely6n #math #programming
https://pagedout.institute/webview.php?issue=9&page=50&article=Programming+Pearl%3A+Sampling+Unique+%28x%2Cy%29+Pairs
Accurate color conversions (2023) https://lobste.rs/s/zyuk9c #graphics #math
http://lomont.org/posts/2023/accuratecolorconversions/