Erdős Problem Forecast
Dated forecast from Questboy23/ai-math-forecast, scored by Brier score on 2027-01-22, 2027-04-22, 2027-10-22.
1. Backtest
4458 problem-origin rows, 152 events, 7 monthly origins from 2026-01 to 2026-07, 68 problems, 3-month windows.
| Model | AUC | 95% CI | Brier | Base rate |
|---|---|---|---|---|
random | 0.424 | [0.376, 0.471] | 0.3367 | 0.0341 |
lr_obs | 0.571 | [0.511, 0.632] | 0.0385 | 0.0341 |
lr_obs_bridge | 0.567 | [0.507, 0.629] | 0.0386 | 0.0341 |
hgb_all | 0.490 | [0.417, 0.558] | 0.0340 | 0.0341 |
Source. forecaster/out/backtest_results.json
Hypothesis 1.
Obscurity and attention features give with 95% CI . The bar was . H1 is not supported.
Hypothesis 2.
Adding bridge distance changes AUC from 0.571 to 0.567, , DeLong , permutation . H2 is not supported, so the forecast ranking has no demonstrated skill (low confidence).
2. Robustness: dropping one feature
Baseline logistic AUC with bridge features is 0.567.
| Feature dropped | AUC without | Change in AUC |
|---|---|---|
prize | 0.5591 | -0.0081 |
source age | 0.5666 | -0.0007 |
formalization | 0.5789 | +0.0117 |
statement len | 0.5745 | +0.0072 |
status edits | 0.5238 | -0.0435 |
oeis | 0.5632 | -0.0040 |
tags | 0.5773 | +0.0100 |
prior ai attempts | 0.5232 | -0.0441 |
bridge d near | 0.5681 | +0.0009 |
bridge d mass | 0.5692 | +0.0019 |
bridge d 2hop | 0.5678 | +0.0005 |
bridge concept cost | 0.5658 | -0.0015 |
hub | 0.5686 | +0.0014 |
3. Forecast of 593 open Erdős problems
Expected AI resolutions in 3 months: (model hgb_all, forecast date 2026-10-22). SHA-256 of forecast.csv: 2c9a9d86ec22b205717723ce04ad9d8d6e013372f0f79b897e6813b3f1245981.
| Rank | Problem | Statement | P (3 mo) | P (12 mo) |
|---|---|---|---|---|
| 1 | 11 | Is every large odd integer $n$ the sum of a squarefree number and a power of 2? | 0.083 | 0.293 |
| 2 | 873 | Let $A=\{a_1<a_2<\cdots\}\subseteq \mathbb{N}$ and let $F(A,X,k)$ count the number of $i$ such that\[[a_i,a_{i | 0.081 | 0.286 |
| 3 | 1183 | Let $f(n)$ be maximal such that in any $2$-colouring of the subsets of $\{1,\ldots,n\}$ there is always a mono | 0.079 | 0.280 |
| 4 | 75 | Is there a graph of chromatic number $\aleph_1$ with $\aleph_1$ vertices such that for all $\epsilon>0$ if $n$ | 0.077 | 0.274 |
| 5 | 408 | Let $\phi(n)$ be the Euler totient function and $\phi_k(n)$ be the iterated $\phi$ function, so that $\phi_1(n | 0.073 | 0.261 |
| 6 | 1194 | Let $A\subset\mathbb{N}$ be such that every integer $n\geq 1$ can be written uniquely as $a_n-b_n$ for some $a | 0.073 | 0.261 |
| 7 | 749 | Let $\epsilon>0$. Does there exist $A\subseteq \mathbb{N}$ such that the lower density of $A+A$ is at least $1 | 0.070 | 0.251 |
| 8 | 52 | Let $A$ be a finite set of integers. Is it true that for every $\epsilon>0$\[\max( \lvert A+A\rvert,\lvert AA\ | 0.065 | 0.236 |
| 9 | 595 | Is there an infinite graph $G$ which contains no $K_4$ and is not the union of countably many triangle-free gr | 0.064 | 0.231 |
| 10 | 1188 | Call a set of distinct integers $1<n_1<\cdots<n_k$ with associated congruence classes $a_i\pmod{n_i}$ a distin | 0.060 | 0.219 |
| 11 | 1143 | Let $p_1<\cdots<p_u$ be primes and let $k\geq 1$. Let $F_k(p_1,\ldots,p_u)$ be such that every interval of $k$ | 0.058 | 0.213 |
| 12 | 12 | Let $A$ be an infinite set such that there are no distinct $a,b,c\in A$ such that $a\mid (b+c)$ and $b,c>a$. I | 0.057 | 0.210 |
| 13 | 1201 | Is it true that for every $\epsilon,\eta>0$ there exists a $k$ such that the density of $n$ for which\[P(n(n+1 | 0.056 | 0.207 |
| 14 | 396 | Is it true that for every $k$ there exists $n$ such that\[\prod_{0\leq i\leq k}(n-i) \mid \binom{2n}{n}?\] | 0.056 | 0.207 |
| 15 | 1209 | Let $A=\{a_1<a_2<\cdots\}$ be a sequence of integers which tends to infinity sufficiently fast. If there is an | 0.054 | 0.200 |
| 16 | 1151 | Given $a_1,\ldots,a_n\in [-1,1]$ let\[\mathcal{L}^nf(x) = \sum_{1\leq i\leq n}f(a_i)\ell_i(x)\]be the unique p | 0.052 | 0.193 |
| 17 | 550 | Let $m_1\leq\cdots\leq m_k$ and $n$ be sufficiently large. If $T$ is a tree on $n$ vertices and $G$ is the com | 0.046 | 0.172 |
| 18 | 1218 | Assume the Generalised Continuum Hypothesis and let $\beta=\omega_{\omega+1}$. Is it true that\[\aleph_{\beta+ | 0.046 | 0.171 |
| 19 | 1207 | Let $P_d(n)$ be such that in any set of $n$ points in $\mathbb{R}^d$ there exist at least $P_d(n)$ many points | 0.046 | 0.170 |
| 20 | 1206 | Does $\{1,2^3,\ldots,N^3\}$ contain a Sidon set of size $\gg N$? Is there an infinite set $A\subset \mathbb{N} | 0.045 | 0.169 |
4. Summary for Epoch AI
EPOCH_SUMMARY.pdf, one page.