The combination of machine learning (ML) and neural networks (NN), specifically deep learning (DL), is making a big breakthrough to breast cancer studies. This scientometrics survey studies 200 highly cited publications to map the intellectual landscape and studies trends in this dynamic field. The survey discloses a dominant concentration on computer-aided diagnosis (CAD) systems using convolutional neural networks (CNNs) for the classification of breast cancer from different imaging modalities, including mammography, histopathology, ultrasound, and magnetic resonance imaging (MRI). Key survey directions identified include: (1) the development of comprehensive deep learning techniques for image-based detection and classification; (2) the application of transfer learning to resolve data scarcity; (3) the combination of multi-omics and clinical data for personalized prognosis and treatment prediction; and (4) the exploration of explainability and robustness in ML-driven clinical tools. This study synthesizes the methodological advancements, sheds light on the evolution from traditional machine learning to deep learning, and surveys the challenges associated with data heterogeneity, model interpretability, and clinical integration. By giving a structured overview of the seminal work and emerging paradigms, the study serves as a reference for graduate students and other interested parties to have a better understanding about the current state and future trajectories of AI in breast oncology.