# Test-Time Compute Scaling Mathematics: Snell 2024 Paper — The New Science of Spending Compute on 'Thinking'

> Source: https://sukruyusufkaya.com/en/learn/llm-muhendisligi/test-time-compute-scaling-snell-2024-matematik
> Updated: 2026-05-13T13:00:30.723Z
> Category: LLM Mühendisliği
> Module: Module 17: Reasoning Models — Test-Time Compute Revolution
**TLDR:** Mathematics of new scaling dimension: Snell et al. 2024 'Scaling LLM Test-Time Compute Optimally' paper. Multi-sample (best-of-N, self-consistency) vs deep thinking (long reasoning chain) trade-offs. Optimal compute allocation: how to best distribute same budget? Paradox with pre-training compute: %20 less pre-training + %50 more test-time = same quality. Planning 'thinking budget' for Turkish.