Definition of the Reasoning Model
Reasoning models are specialized Large Language Models (LLMs) that solve complex problems through logical reasoning, chain of thought, and internal reflection. Unlike “standard AIs,” reasoning models think before they output an answer, making them particularly strong in mathematics, programming, and logic tasks. Well-known examples include OpenAI’s o1/o3 series and DeepSeek R1.
It may feel that way to you , and some may wish it were real , but it is not.
Mathematical methods demystified
When you enter text, the Reasoning model processes it purely mathematically in three successive steps (simplified).
Step 
Tokenization & Embeddings
Your text is broken down into fragments (tokens). These tokens are placed in a mathematical dimensional space as vectors (sequences of numbers). The LLM learns that concepts and entities that are often related are located close to each other in this space.
- IBM – What is tokenization?
- IBM – What is Embedding?
Step 
Self-Attention Mechanism
The transformer architecture uses matrix multiplication to calculate the strength of the relationship between each token in your text. This mathematically resolves grammatical and logical relationships.
- IBM – What is Self-Attention?
Step 
Next-Token Prediction
The mathematical process of an LLM culminates in a probability distribution. The reasoning model calculates: Do the previous calculations indicate which token is statistically most likely to follow the next token?
However, the models “ know ” the syntax and relations with almost perfect precision : the exact geometric distances of the token “apple” to the tokens “red”, “sweet”, “eat” and “tree”.
Chain of Thought & Reinforcement Learning
These two technical terms are the magic potion of modern reasoning models compared to their predecessors, a “standard AI”, which always generated the calculated and predicted next word in a single pass .
Reasoning models simulate slow, analytical thinking. However, they do not achieve sudden consciousness; instead, they utilize new technical principles.
Hidden thought processes
Instead of providing an immediate answer, reasoning models often internally generate “chains of thought” thousands of tokens long. The model algorithmically breaks down a problem into sub-steps. This is called a chain of thought.
Practice, learning, reward, memorization
Through so-called reinforcement learning , reasoning models were extensively trained not only to predict text but also to evaluate solution paths . While the model is thinking , it internally searches probability trees.It generates a hypothesis, recognizes through learned patterns that this path leads to a mathematical or logical contradiction,discards the path and seeks a new one, which promises a higher reward.
Conclusion of understanding
Do reasoning models possess an intrinsic ( human ) understanding? Absolutely not.
Do reasoning models possess a functional ( machine ) understanding? YesThey have perfectly mapped the logic, grammar, and structure of human knowledge as a mathematical topography.
