Cheapest AI Cost to Score 25% on FrontierMath Tiers 1-3 (Epoch AI)

## What this measures

The cheapest way, in US dollars per task (one question), to get an AI model to score at least 25% on FrontierMath Tiers 1-3, using any model released up to that day. Scores are counted from guessing to perfect: 0% is what guessing gets, 100% is every answer right. One reading per day. The value steps down each time a newly released model sets a new low.

FrontierMath is Epoch AI's own set of unpublished, research-level math problems written by mathematicians; tiers 1-3 are its three easier difficulty tiers (tier 4 is the hardest). The private problem set is used, so models cannot have seen the answers. Answers are exact values, so guessing scores 0.

## Why it matters

This is the price of a fixed level of machine intelligence, the thing "AI is getting cheaper" refers to. List price per token misleads here: reasoning models spend many more tokens per answer, so a cheaper token can mean a dearer answer. Cost per task counts the tokens a model actually spends. It is an input to the Palanor AI Inference Cost Index.

## How to read it

Lower is cheaper. Read the slope on a log scale: a fall from one dollar to ten cents is the same tenfold drop as ten cents to one cent. Compare the 25% level with the other levels on the same benchmark: the cost of a level usually falls fastest soon after models first reach it. Each point records which model and reasoning setting holds the record.

## What it does not say

It covers only the models and settings Epoch has tested, and Epoch tests mostly models that look near the cost or capability frontier, so an untested cheaper model would not show. Costs are estimated: Epoch runs each model once at a generous token budget, then works out the score it would have got under tighter budgets from the transcript (the method of the U.S. Center for AI Standards and Innovation). Prices are the providers' list prices when the run was made (mostly from OpenRouter, via the Internet Archive), or rented-GPU cost for open-weights models with no API, so they leave out discounts, batch pricing and caching. A benchmark score is not workplace performance. Epoch revises runs and prices, and the whole history is rebuilt on each sync.

## Source

Epoch AI, "The plunging price of thought" (Luke Emberson and David Roodman, 2026), epoch.ai/publications/the-plunging-price-of-thought. Data: github.com/droodman/inference-cost (data/cost_truncated_curves.csv and Epoch's model registry), linked from the report as its data. Licence: "Epoch AI’s work is free to use, distribute, and reproduce provided the source and authors are credited under the Creative Commons Attribution license." Palanor computes the daily cost frontier with Epoch's own method, which reproduces the report's Figure 2. Refreshed weekly by Palanor's epoch-sync job.