A curated collection of optimization constants
- Here is an initial blog post introducing the project: A crowdsourced repository for optimization constants?, 22 Terence Tao, January 2026.
We are arbitrarily numbering the constants as
| Number | Description | Best lower bound | Best upper bound |
|---|---|---|---|
| 1a | Sidon set autocorrelation constant | 1.2802 | 1.5029 |
| 1b | Erdős minimum overlap constant | 0.379005 | 0.380876 |
| 2 | Crouzeix constant | 2 | |
| 3a | Gyamarti-Hennecart-Ruzsa sum-difference constant | 1.173077 | 1.33333 |
| 3b | Kakeya sums-differences constant | >1.77898 | 1.83333 |
| 4 | Cap set constant | 0.724851 | 0.782597 |
| 5 | Sidon set size constant | 0 | 0.97633 |
| 6 | Union-closed sets conjecture constant | 0.38271 | 0.5 |
| 7 | Irrationality measure of |
2 | 7.103205334137 |
| 8 | Classical zero-free region constant | 0.755106 | 5.558691 |
| 9 | Shannon capacity of the 7-cycle | 3.2578 | 3.3177 |
| 10 | Real Grothendieck constant | 1.67696 | 1.782214 |
| 11a |
|
||
| 11b | Critical exponent for isoperimetric inequality on the Hamming cube | 0.5 | 0.50057 |
| 12 | The Beardwood–Halton–Hammersley constant | 0.6277 | 0.90304 |
| 13a | Moser's convex worm cover constant | 0.232239 | 0.2617993878 |
| 13b | Lebesgue's convex universal cover constant | 0.832 | 0.8440935944 |
| 14 | Smallest |
6 | 432 |
| 15 | Matrix multiplication exponent | 2 | < 2.3728596 |
| 16 | Brezis–Gallouet–Wainger remainder constant on the 2D torus | ||
| 17 | Exponential growth constant of diagonal Ramsey numbers | 3.7992027396 | |
| 18 | Marton's conjecture constant (PFR) | 1 | 9 |
| 19 | Berry–Esseen constant | 0.4097321837 | 0.4690 |
| 20 | Thin shell conjecture constant | 2 | |
| 21 | Isotropic constant of a log-concave probability measure | ||
| 22 | de Bruijn–Newman constant | 0 | 0.2 |
This site is maintained by Damek Davis, Paata Ivanisvili and Terence Tao.
Use this BibTeX entry:
@misc{optimization-constants-repo,
title = {Optimization Constants in Mathematics},
author = {Davis, Damek and Ivanisvili, Paata and Tao, Terence and contributors},
year = {2026},
howpublished = {GitHub repository},
url = {https://github.com/teorth/optimizationproblems}
}
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