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Leaps in Bounds

Repository of progress on mathematical unknowns

This is a collaborative effort to compile data on historical progress on solved and unsolved mathematical constants. The focus is on quantitative updates, such as the lower and upper bounds on their values.

This site provides browsing, visualizations, and access to the structured data for other uses.

Constant Groups

Group Constants Tracked Compilation Status Sources Verified
03D Computability and recursion theory
Busy beaver ones function 7 Initial 53.33% –
Busy beaver shift function 7 Initial 53.33% –
05A Enumerative combinatorics
Map folding 87 Initial 0% –
Minimal superpermutation problem 9 Initial 52.0% 7
Stamp folding 29 Initial 6.9% –
05B Designs and configurations
Optimal Golomb rulers 30 Initial 100.0% 30
05C Graph theory
Cages 252 Initial 5.45% 310
Coil-in-the-box 12 Initial 100.0% 12
Degree-diameter problem 162 Initial 99.39% 50
Snake-in-the-box 13 Initial 100.0% 13
05D Extremal combinatorics
Ramsey numbers 76 Sourced 100.0% 27
Schur numbers 9 Initial 100.0% 8
Van der Waerden numbers 45 Initial 86.11% 17
Weak Schur numbers 9 Initial 100.0% 9
11M Zeta and L-functions: analytic theory
de Bruijn–Newman constant 1 Sourced 100.0% –
51E Finite geometry and special incidence structures
Cap sets 8 Initial 100.0% 8
52C Discrete geometry
Arrangements of lines in the affine plane 12 Initial 46.67% 6
Arrangements of lines in general position 12 Initial 44.44% 7
Circle packing in an equilateral triangle 15 Initial 65.52% 22
Disk covering problem 25 Initial 85.71% –
Isosceles sets 12 Initial 100.0% 12
Kissing numbers 24 Initial 93.94% 24
No-three-in-line problem 78 Initial 100.0% 78
Packing unit squares in a square 100 Initial 21.86% 200

Recently verified

See all verified bounds and contributors.

Contributing

Contributions are welcome, from people and AI agents alike. Pull requests are the preferred way to contribute:

For more open-ended contributions, such as asking whether a group of constants fits or sharing data you’re not sure how to add, start a GitHub Discussion. For technical problems and suggestions, open an issue.

Contributions are credited to the GitHub account that made them on the contributors page.

To have an AI agent contribute, give it one of these prompts:

Read https://github.com/daniel-munro/leaps-in-bounds/blob/main/certificates/README.md and follow it to submit a verified bound to Leaps in Bounds.
Read https://github.com/daniel-munro/leaps-in-bounds/blob/main/source_data/README.md and follow it to add missing bounds from the literature to Leaps in Bounds, for <group or topic>.