Frontiers

Quantities mathematicians have pushed for decades, drawn as the staircase they are: every step is a paper, and the coloured steps at the end are the ones a model took. A frontier appears here only once an entry in the catalog sits on it. Historical steps are cited one by one and are context, not claims of this site.

Frontiers tracked: 19; each with at least one AI step
Steps by AI: 16; rows that moved a frontier when they landed
Moved in the last 30 days: 0; frontiers with a new best
Historical rows cited: 86; the human staircase, one source each

All frontiers

Lower bounds for the Shannon capacity of C₁₁
6 steps · 2 by AI · last moved 9 Sept 2026 · Combinatorics
$5.295526013632343$
current best · higher is better
Lower bounds for the union-closed sets constant
4 steps · 0 by AI · last moved 15 Jun 2023 · Combinatorics
$0.382709$
current best · higher is better
Lower bounds for the complex Grothendieck constant
2 steps · 0 by AI · last moved 1984 · Analysis
$1.338$
current best · higher is better
Long gaps between primes
5 steps · 2 by AI · last moved 3 Sept 2026 · Number theory
$\gg \log X (\log_2 X)^2 \log_4 X / (\log_3 X)^2$
current best · higher is better
Bounded gaps between primes
6 steps · 2 by AI · last moved 3 Sept 2026 · Number theory
$212$
current best · lower is better
Randomized metric distortion
2 steps · 1 by AI · last moved Aug 2026 · Theoretical computer science
$2.3282$
current best · lower is better
Systole growth in every large genus
3 steps · 1 by AI · last moved 27 Aug 2026 · Geometry & topology
$1$
current best · higher is better
Largest known rank of an elliptic curve over Q
14 steps · 2 by AI · last moved 23 Aug 2026 · Number theory
$\ge 31$
current best · higher is better
Upper bounds for the de Bruijn-Newman constant
3 steps · 0 by AI · last moved May 2020 · Number theory
$0.2$
current best · lower is better
Exponent of matrix multiplication
16 steps · 1 by AI · last moved 17 Aug 2026 · Theoretical computer science
$2.371177$
current best · lower is better
How large must a counterexample to Seymour's second-neighborhood conjecture be?
2 steps · 1 by AI · last moved 12 Aug 2026 · Combinatorics
$17$
current best · higher is better
Proportion of zeta zeros on the critical line
6 steps · 1 by AI · last moved 10 Aug 2026 · Number theory
$> 67.25\%$
current best · higher is better
The approximation constant for Boolean Max-k-CSP
2 steps · 0 by AI · last moved 2012 · Algorithms & optimization
$0.626612$
current best · higher is better
Upper bounds on sphere-packing density in high dimension
4 steps · 1 by AI · last moved 1 Aug 2026 · Geometry & topology
$0.6044$
current best · higher is better
Upper bounds on the dimer constant of the cubic lattice
2 steps · 0 by AI · last moved 2001 · Combinatorics
$0.457547$
current best · lower is better
Smallest dimension where Borsuk's conjecture fails
10 steps · 1 by AI · last moved 26 May 2026 · Geometry & topology
$63$
current best · lower is better
Runners for which the lonely runner conjecture is proved
7 steps · 0 by AI · last moved 26 Apr 2026 · Number theory
$13$
current best · higher is better
Approximation ratio for Multiway Cut
5 steps · 0 by AI · last moved 2014 · Theoretical computer science
$1.2965$
current best · lower is better
Kissing number in dimension 19
2 steps · 1 by AI · last moved 11 Mar 2026 · Geometry & topology
$11{,}948$
current best · higher is better

Latest movement

9 Sept 2026Shannon capacity of C₁₁→ $5.295526013632343$ by Astra 6 Pro; Codex GPT-6 Astra Extra-High · entrycurrent best
8 Sept 2026Union-closed constant→ $0.38284$ by Fable 5.1 · entrycandidate
7 Sept 2026Complex Grothendieck constant→ $1.35584631827168$ by Odin Automatic AI Research Agent · entrycandidate
3 Sept 2026Long prime gaps→ $\gg \log X (\log_2 X)^2 \log_4 X / (\log_3 X)^2$ by GPT 6 Astra · entrycurrent best
3 Sept 2026Bounded prime gaps→ $212$ by AxiomProver · entrycurrent best
1 Sept 2026Bounded prime gaps→ $236$ by unspecified AI agents · entry
30 Aug 2026Bounded prime gaps→ $186$ by GPT 6 Astra · entrycandidate
29 Aug 2026Metric distortion→ $2.3282$ by GPT-5.6 Sol; Claude Opus 5.0 · entrycurrent best