How Do AI Models Paint and Write? The Secrets of Generative AI Unlocked by Mathematics

Imagine this: you ask the Generative AI you use every day to “summarize tomorrow’s meeting notes,” and it organizes the key points in an instant. We marvel at how magically smart the AI is and enjoy the results, but it is not easy to understand ‘how’ the AI perceives data and ‘why’ it produces such text. It is similar to being a skilled driver without having a specific understanding of how a car engine actually works.

Recently, there has been welcome news for those curious about the inner workings of AI. In 2026, ‘The Little Book of Generative AI Foundations: An Intuitive Mathematical Primer,’ written by Tianhua Chen, was released as an open-access preprint [Source 4, Source 9].

Why is this book important?

Until now, most users have simply consumed results through convenient interfaces known as APIs (Application Programming Interfaces, the connectors that facilitate communication between applications). However, as AI technology advances rapidly, fundamental questions are growing among researchers and students: “What mathematical calculations are actually happening inside AI?”

This book is not a technical manual on ‘how to use AI.’ Its goal is to transparently reveal the mathematical foundations of how AI perceives and represents the world [Source 1, Source 10]. For those with a mathematical curiosity who want to understand the core principles rather than just the surface of the technology, this book will be an invaluable guide [Source 2].

Simply put: An engine named mathematics

Let’s compare Generative AI to a massive ‘photo filter.’ Just as applying a ‘black and white’ filter in a photo app changes the colors, AI passes our input questions and data through mathematical ‘filters.’ These filters are intricately interconnected. The process by which AI writes text and draws pictures can be described as refining data through tens of thousands of mathematical filters.

This book breaks down the foundations of how those mathematical filters learn data and the principles by which they create new data, one step at a time [Source 10]. It is a work that stands out for its effort to explain intuitively how generative models actually represent and understand data, without getting bogged down in theory alone [Source 8].

Current landscape: Steps toward transparent AI

As of 2026, while generative AI models have achieved remarkable progress, their internal workings are still sometimes considered a ‘black box’ (a system whose internal structure is difficult to know). The newly released primer by Tianhua Chen is filled with the author’s strong commitment to reducing this complexity and making mathematical foundations more transparent and accessible to the public [Source 1]. The data science community has already evaluated the book’s mathematical approach as being highly helpful for understanding the essence of generative AI [Source 7, Source 8].

What happens next?

AI technology is now moving beyond the era of ‘what can it build’ into an era of defining ‘by what principles does it work.’ As more primers like this become available, the general public will be able to more actively understand and utilize the tool called artificial intelligence. It appears that the attempt to understand the mathematical basis of generative AI will become an essential skill for everyone who coexists with AI, not just for researchers.

MindTickleBytes AI Reporter’s Perspective

We live in an age of incredibly convenient AI. However, if we know ‘why’ the answers provided by AI are derived, we can grow beyond mere users into subjects who control and advance the technology. Mathematics may feel difficult, but it is the most certain key to grasping the essence of AI.

References

1. The Little Book of Generative AI Foundations: An Intuitive Mathematical Primer, https://arxiv.org/html/2605.29713
2. The Little Book of Generative AI Foundations: An Intuitive Mathematical Primer, https://www.alphaxiv.org/abs/2605.29713
3. Generative AI Foundations: An Intuitive Primer, https://www.emergentmind.com/papers/2605.29713
4. Computer Languages (clcoding): Generative AI, https://www.clcoding.com/search/label/Generative+AI
5. Data Science – Telegram, https://t.me/datascienceiot/3717
6. 195 pages of mathematics to understand how Generative AI is built…, https://vk.ru/wall-138477641_72760

7. Foundations of Large Language Models

   alphaXiv, https://www.alphaxiv.org/abs/2501.09223

8. The Little Book of GenAI Foundations: A Math Primer, https://www.linkedin.com/posts/michael-erlihson-phd-8208616_the-little-book-of-genai-foundations-a-math-activity-7469282109233463297-qMFH