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% | 308 |
| Coil-in-the-box | 12 | Initial | 100.0% | 12 |
| Degree-diameter problem | 162 | Initial | 98.74% | 50 |
| Snake-in-the-box | 13 | Initial | 100.0% | 13 |
| 05D Extremal combinatorics | ||||
| Ramsey numbers | 76 | Sourced | 100.0% | 26 |
| Schur numbers | 9 | Initial | 100.0% | 8 |
| Van der Waerden numbers | 45 | Initial | 86.11% | 17 |
| Weak Schur numbers | 9 | Initial | 100.0% | 6 |
| 11M Zeta and L-functions: analytic theory | ||||
| de Bruijn–Newman constant | 1 | Sourced | 100.0% | – |
| 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% | – |
| Kissing numbers | 24 | Initial | 93.94% | 24 |
| Packing unit squares in a square | 100 | Initial | 21.86% | 200 |
Contributing
Contributions are welcome, from people and AI agents alike. Pull requests are the preferred way to contribute:
- Bounds from the literature: add updates and their sources in
source_data/(see Data Organization), and run the build script to check them. - Verified bounds: submit a certificate, either a construction checked by a program or a proof in Lean. See how to submit one, and the unverified bounds for bounds from the literature that don’t have one yet.
For more open-ended contributions, such as suggesting a new group of constants or sharing data you’re not sure how to add, start a GitHub Discussion. For technical problems and suggestions, open an issue.
To have an AI agent contribute a verified bound, give it this prompt:
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.Related Projects
- Big O Speedrun - Leaderboards of recent progress on bounds for algorithm running times and other constants, with Lean-verified submissions.
- Optimization Constants in Mathematics - A curated collection of optimization constants in mathematics, often arising from solving a variational problem, or finding the best constant in a functional inequality.