Estimating π with “fake circles” using Python. This short shows how to simulate the geometry, calculate the approximation step by step, and see how accuracy improves as the model gets refined. #Python ...

Math teacher Emma Chiappetta uses a three-round exercise to help students not only recognize their errors, but also generate ...

GPT-5.2 Pro delivers a Lean-verified proof of Erdős Problem 397, marking a shift from pattern-matching AI to autonomous ...

Learn how gradient descent really works by building it step by step in Python. No libraries, no shortcuts—just pure math and code made simple.

Pupil dilation provides a physiological readout of information gain during the brain's internal process of belief updating in the context of associative learning.