Featuring the roots of various polynomials whose coefficients are the binary digits of numbers like π. Complex roots cluster around the circle, and the few real ones are on the horizontal X-axis (positive on the right, negative on the left). Download the free paper to see how to interpret the colors and get the code and full explanations, with state-of-the-art material on the topic.
This research is part of a project at BondingAI to build an AI agent specializing in scientific and high-performance computing, as well as AI–generated art. Also, one of the goals is to share beautiful mathematical results with the public at large, thanks to the video and the connection to polynomial roots. The latter is familiar to most high school students, but the classroom material is usually dry and lacks exciting experiments. I hope that my contribution fills this gap and will boost the interest in mathematics, probability, and engineering, as these fields are typically considered as unwelcoming by many.
Finally, my work raises an interesting question: when you automatically generate thousands of examples (video frames here,) can AI select which ones are the most beautiful and enriching, to include them in the final video? The answer is yes if you train AI, but can it do it well with little training and detect on its own a set of diversified images that are universally considered spectacular or enlightening by everyone? Finally, if you are interested in adding an AI-generated mathematical soundtrack (music) to my video, matching the frames, please contact me at vincent@bondingAI.io.
Get your copy of the free book and the new article
This new article — the technical paper — has been added to the book. It comes with detailed technical explanations and more results, along with references, illustrations and Python code. The links in the PDF are clickable only in the full (free) book.
- Read and download the full technical paper, here.
- Get your free copy of the new updated book, here.
- See long review of my book, here.
- The Python code to produce video is also on GitHub, here.
- Watch video on YouTube, here.
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About the Author
Vincent Granville is a pioneering GenAI scientist, co-founder at BondingAI.io, the LLM 2.0 platform for hallucination-free, secure, in-house, lightning-fast Enterprise AI at scale with zero weight and no GPU. He is also author (Elsevier, Wiley), publisher, and successful entrepreneur with multi-million-dollar exit. Vincent’s past corporate experience includes Visa, Wells Fargo, eBay, NBC, Microsoft, and CNET. He completed a post-doc in computational statistics at University of Cambridge.