Machine learning (ML) has transformed neuroscience research by providing powerful tools to analyze neural data, uncover brain connectivity, and guide therapeutic interventions. This paper presents core mathematical frameworks in ML that address critical challenges in neuroscience. We introduce state-space models for closed-loop neurostimulation and discrete representation learning methods that improve the interpretability of time-series analysis by extracting meaningful patterns from complex neural recordings. We also describe approaches for revealing inter-regional brain connectivity through high-dimensional time series analysis using Gaussian processes. In the context of multi-subject neuroimaging, we explore independent vector analysis to identify shared patterns that preserve individual differences. Finally, we examine distributed beamforming techniques to localize seizure sources from EEG data, an essential component of surgical planning for epilepsy treatment. These methodological innovations illustrate the growing role of ML in neuroscience via interpretable, adaptive, and personalized tools that analyze brain activity and support data-driven interventions.