NeuroMath: Bridging EEG Dynamics and Explainable AI through Polynomial and Fourier Modeling.

Despite extensive research using EEG and machine‑learning models for ADHD diagnosis—achieving up to 96.7% accuracy, 95.1% sensitivity and 98.3% specificity with Wavelet‑Attention deep models and even 99.8% accuracy with explainable ML frameworks validated on clinical data—conventional AI approaches remain opaque and lack reproducibility in real‑world settings, limiting clinical trust and objective interpretation. In this work, we present NeuroMath, a mathematically interpretable EEG analysis framework that segments real‑time signals and models them with polynomial, sinusoidal, and Fourier representations to derive explicit coefficient‑based features that quantitatively distinguish healthy individuals from those with ADHD, capturing clinically relevant slow‑frequency abnormalities often observed in theta/beta ratios. Evaluations on benchmark EEG datasets demonstrate that these mathematically derived coefficients not only separate ADHD and control patterns robustly, but also offer transparent, real‑time, hardware‑agnostic analysis, reducing dependence on expensive equipment and black‑box models, and thus advancing towards accessible, interpretable, and clinically meaningful neurodiagnostics.