☕ October Math & AI News
How AI Is Becoming Everyone’s Personal Math Assistant
Scroll down to get the solution to last week’s puzzles.
Welcome back to the Math Café, where math meets its modern counterpart, AI.
This week, we explore how reasoning models are evolving from brilliant students into dependable tutors and assistants, as well as what that means for learning, research, and everyday curiosity… and most of all for you!
🎓 From “Gifted Student” to Reliable Personal Tutor
🧭 The last few weeks of 2025 marked a decisive moment in AI’s evolution.
Systems that once dazzled researchers with clever problem-solving are now maturing into disciplined, ready-to-use assistants.
At the University of Maine’s Responsible AI in K–12 Mathematics summit, educators are testing adaptive tutoring platforms like ALEKS for Calculus, which deliver personalized, context-aware learning.
🤖 AI can now serve as your own study companion — one that adapts to your level and goals.
Here’s one way to start your own “personal tutor” session:
💬 Prompt example
“You are a domain expert in [field]. I already know [related topics you’ve studied]. I want to [your goal]. Walk me through how to study efficiently.”
🧠 Reasoning Models Enter the Research Labs
AI is no longer just answering questions — it’s beginning to discover truths. 🌟
Recent scientific breakthroughs show what reasoning-capable systems can achieve:
🥇 Harmonic Team’s Aristotle combines informal reasoning with formal verification in Lean, achieving gold-medal-level performance on Olympiad math problems — and checking its own proofs.
🔢 O-Forge integrates large language models with computer algebra systems to to solve complex inequalities.
🇫🇷 Telecom SudParis and École Polytechnique researchers used GPT-5 to solve five of six IMO problems and even prove new theorems, producing Lean-verifiable proofs, this with minimal human intervention.
🌌 Oxford researchers, in collaboration with Gemini, classified stellar events — asteroid collisions, supernovae, and black hole disruptions — with 96.7% success explaining their reasoning along the way.
⚛️ At Los Alamos, the THOR system combines tensor networks with AI to solve solve PDEs in materials science.
Together, these developments mark a shift:
from using AI to assist thinking to building systems that can think alongside us. 🧩
⚙️ The Hardware Race Behind the Reasoning Revolution
💾 None of this would be possible without a tectonic shift in computing infrastructure.
AMD and OpenAI have launched a a multi-year, multi-billion-dollar chip partnership.
And Broadcom joined in, designing custom accelerators expected to exceed 10 GW of compute.
Together, they’re fueling an AI supercycle that’s driving semiconductor innovation, and making reasoning-capable AI models more accessible than ever. 🚀
🔧 Your Turn: How You Can Experiment Today
You don’t need a lab to explore reasoning AI; just curiosity and a few smart prompts. 💡
💭 To check a solution’s reliability
“You are an expert in [field]. Review the solution rigorously and point out any flaws.”
🎯 To learn a new skill
“You are a mentor guiding a new [role]. Teach me [task/workflow] step by step, flagging risks.”
Try these prompts, adapt them to your needs, and see how AI performs as a collaborator, not just a calculator. 🧮
So, what do you think?
Are you already working closely with AI, or just starting to explore it?
💬 Share your thoughts in the comments: I’d love to hear how you use (or challenge!) these tools.
🗓️ Next Week’s Teaser
Next Tuesday, the Café will dive deeper into one of the puzzles — with a twist you might not expect. 🕵️♀️
Until then, have a wonderful week.
With love and curiosity,
Sybille ☕
🧮 Detailed Solutions to Last Week’s Puzzles
Puzzle 1
❗ There is a division by zero!
Puzzle 2
📐 Bhāskara’s diagram offers a geometric proof of the Pythagorean Theorem.
Pick a right triangle, with hypothenuse of length c, and whose other sides are of length a (for the smallest one) and b (for the remaining one). Note that each triangle has area ab/2. Arrange four copies of this triangle in a square as shown in the initial diagram:
Note that the blue space in the middle of the figure is a square of area (b-a)². The four triangles and the blue square have total area equal to 2ab+(b-a)², which according to the diagram is the same as the area of the square of side c, i.e. is equal to c².
We obtain: 2ab+(b-a)²=c², which after simplification yields c²= a² + b², which is indeed the Pythagorean Theorem.📐
