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: 8; each with at least one AI step
Steps by AI: 11; rows that moved a frontier when they landed
Moved in the last 30 days: 7; frontiers with a new best
Historical rows cited: 45; the human staircase, one source each

All frontiers

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
Exponent of matrix multiplication
16 steps · 1 by AI · last moved 17 Aug 2026 · Theoretical computer science
$2.371177$
current best · lower 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
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

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
27 Aug 2026Systoles→ $1$ by GPT-5.6 Sol · entrycurrent best
25 Aug 2026Long prime gaps→ $\gg \log X \log_2 X / \log_4 X$ by GPT 5.6 Sol · entry
23 Aug 2026Elliptic curve rank→ $\ge 31$ by Claude · entrycurrent best