Formalization of X Created 2025-11-30 Updated 2026-02-08
This section is about formalization efforts of specific fields of mathematics.
Project Euler problem 971 Created 2025-11-23 Updated 2026-02-08
Project Euler problem 970 Created 2025-11-19 Updated 2026-02-08
ORCA Benchmark Created 2025-11-19 Updated 2025-11-30
This one doesn't seem to exciting to be honest, but it might be useful. Sample question:and it expects the correct answer down to the cents:It should be noted that Project Euler has such "precision matters" problems.
53892.27
Closed AI math benchmark Created 2025-11-19 Updated 2025-12-13
Even more than in other areas of benchmarking, in maths where you only have a right or wrong answer, and it is costly to come up with good sample problems, some benchmarks have adopted private test data sets.
The situation is kind of sad, in that ideally we should have open data sets and only test them on models that were trained on data exclusively published before the problem publish date.
However this is not practical for the following reasons:
List of math AI benchmarks Created 2025-11-19 Updated 2025-12-13
3D-printed firearm 2025-11-18
Here's an execution for 2, 3. When Furthermore, note that if therefore we can always make
a != 1 we use a as the extra numbers instead of b: 1 | 2 2(1) ...
2 | 2 2(0) 2(1) ...
3 | 3 2(1) 2(0) 2(1) ...
4 | 3 2(0) 2(0) 2(1) ...
5 | 2 3(2) 2(1) 2(0) 2(0) ...
6 | 2 3(1) 2(1) 2(0) 2(1) ...
7 | 2 3(0) 2(1) 2(0) 2(1) ...
8 | 3 3(2) 2(0) 2(0) 2(1) ...
9 | 3 3(1) 2(0) 2(0) 2(1) ...
10 | 3 3(0) 2(0) 2(0) 2(1) ...
11 | 2 2(1) 3(2) 2(1) 2(0) 2(1) ...
12 | 2 2(0) 3(2) 2(1) 2(0) 2(1) ...
13 | 3 2(1) 3(1) 2(1) 2(0) 2(1) ...
14 | 3 2(0) 3(1) 2(1) 2(0) 2(1) ...
15 | 2 2(1) 3(0) 2(1) 2(0) 2(1) ...
16 | 2 2(0) 3(0) 2(1) 2(0) 2(1) ...
17 | 3 3(2) 3(2) 2(0) 2(0) 2(1) ...a = 1, then the a, b sequence is a subset of the b, a sequence e.g.:1, 2 = [1, 2, 2, 1, 1, 2, 1, ...]
2, 1 = [ 2, 2, 1, 1, 2, 1, ...]a not be 1 by switching the pair and then using the generalized algorithm with a != 1. Nilsson algorithm for the Kolakoski sequence 2025-11-18
This algorithm is more efficient in space, using only , as it recursively compresses the state required to keep track of what to do next.
Time is still .
The table at maths-people.anu.edu.au/~brent/pd/Kolakoski-UNSW.pdf page 20 has a summary image, but it is hard to understand.
1 2(0) 1(1)The starting state is:which means that it implicitly contains infinitely many The actual algorithm will of course omit as many trailing
2 | 2 2(1) 2(1) 2(1) 2(1) ...2(1) at the end which we abbreviate just as:2 | 2 2(1) ...2(1) as it can.The update rules are:Note that both rules don't overlap so that each update is always determined by only one of them at a time.
- go left to right:
- flip:continue going left to right.
x(0) y(0) !x((!x)-1) unchanged - repeat:and then stop further updates.
x(0) y(n > 0) x(x-1) y(n - 1)
- flip:
Also the first column is always implicitly
(0).2 | 2 2(1) ...
3 | 2 2(0) 2(1) ...Here we:
2 | 2 2(1) ...
3 | 2 2(0) 2(1) ...
4 | 1 2(1) 2(0) 2(1) ...2 | 2 2(1) ...
3 | 2 2(0) 2(1) ...
4 | 1 2(1) 2(0) 2(1) ...
5 | 1 2(0) 2(1) 2(0) 2(1) ... 2 | 2 2(1) ...
3 | 2 2(0) 2(1) ...
4 | 1 2(1) 2(0) 2(1) ...
5 | 1 2(0) 2(0) 2(1) ...
6 | 2 1(0) 2(1) 2(0) 2(1) ...
7 | 1 1(0) 2(0) 2(0) 2(1) ...
8 | 2 2(1) 1(0) 2(1) 2(0) 2(1) ...
9 | 2 2(0) 1(0) 2(1) 2(0) 2(1) ...
10 | 1 1(0) 1(0) 2(0) 2(0) 2(1) ...
11 | 2 2(1) 2(1) 1(0) 2(1) 2(0) 2(1) ...
12 | 2 2(0) 2(1) 1(0) 2(1) 2(0) 2(1) ...
13 | 1 2(1) 2(0) 1(0) 2(1) 2(0) 2(1) ...
14 | 1 2(0) 2(0) 1(0) 2(1) 2(0) 2(1) ...
15 | 2 1(0) 1(0) 1(0) 2(0) 2(0) 2(1) ...
16 | 1 2(1) 2(1) 2(1) 1(0) 2(1) 2(0) 2(1) ... Generalized Kolakoski sequence 2025-11-18
The generalized Kolakoski sequence is the generalization of the Kolakoski sequence where you don't need to restrict yourself to 1,2 but can instead use any a,b pair.
MP4 2025-11-18
Video container format 2025-11-18
Project Euler problem 967 Created 2025-11-05 Updated 2026-02-08
Project Euler problem 966 Created 2025-11-05 Updated 2026-02-08
Box and arrow diagram in Inkscape 2025-11-05
Nerd 2025-11-05
Inkscape constraints 2025-11-05
What would be really amazing is if they had constraints like proper CAD software, it would make it possible to not have to redo entire diagrams when you want to change a small part of them.
Bibliography:
- gitlab.com/inkscape/inbox/-/issues/1465 Feature Request: Geometric Construction Tool (Constraints and constraint solver) for CAD, CAM etc.
- www.reddit.com/r/Inkscape/comments/1fvhil4/constraints_or_parameters/
It should be noted however that path effects can accomplish some of it.
Personality trait 2025-11-05
Monero Chan 2025-11-05
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