How do OpenAI's o1 and o3 models 'think' before answering?

The answer

OpenAI released o1 in September 2024 and o3 in December 2024, introducing a new paradigm called 'reasoning models.' Unlike standard LLMs that generate responses token by token, o1 and o3 produce an internal chain-of-thought before answering, spending extra compute to reason through problems step by step. The results are dramatic: o1 scored 83% on the 2024 AIME math competition with consensus sampling, while o3 achieved 91.6% - compared to GPT-4o's roughly 13%. OpenAI skipped the name 'o2' to avoid trademark conflict with the European telecom brand O2. These models represent a fundamental shift from simply scaling training data to scaling inference-time reasoning.