Abstract: Science discovery empowered by artificial intelligence (AI) demonstrates remarkable potential in reshaping the paradigm of modern scientific research. Deeply integrating AI tools into physics teaching is of great significance for cultivating innovative research capabilities. Taking the discovery process of the Balmer formula for the hydrogen atom as a teaching case, this paper employs symbolic regression technology to re-explore physical laws in the era of intelligence. By constructing the original experimental dataset of the Balmer series and combining it with the Feyn symbolic regression tool, the entire process of reconstructing the characteristic formula from limited spectral data is systematically demonstrated. The research highlights the principle of “dual-driven by the quantity and quality of data” and reveals the complementary relationship between “mathematical discovery” and “physical interpretation” under the human-machine collaboration model. While AI can accelerate the induction of mathematical laws, the physical interpretation behind formulas still relies on the wisdom of scientists. This case empirically reveals the effectiveness of AI tools in accelerating the induction of mathematical laws. At the same time, it more prominently demonstrates the key supporting role of physical thinking in guiding the iteration of the model, providing a useful idea for the innovation of physics education empowered by intelligent technology.

Key words:  artificial intelligence, Balmer formula, symbolic regression