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Traditionally, deep learning methods for breast cancer classification perform a single-view analysis. However, radiologists simultaneously analyze all four views that compose a mammography exam, owing to the correlations contained in mammography views, which present crucial information for identifying tumors. In light of this, some studies have started to propose multi-view methods. Nevertheless, in such existing architectures, mammogram views are processed as independent images by separate convolutional branches, thus losing correlations among them. To overcome such limitations, in this paper, we propose a methodological approach for multi-view breast cancer classification based on parameterized hypercomplex neural networks. Thanks to hypercomplex algebra properties, our networks are able to model, and thus leverage, existing correlations between the different views that comprise a mammogram, thus mimicking the reading process performed by clinicians. This happens because hypercomplex networks capture both global properties, as standard neural models, as well as local relations, i.e., inter-view correlations, which real-valued networks fail at modeling. We define architectures designed to process two-view exams, namely PHResNets, and four-view exams, i.e., PHYSEnet and PHYBOnet. Through an extensive experimental evaluation conducted with publicly available datasets, we demonstrate that our proposed models clearly outperform real-valued counterparts and state-of-the-art methods, proving that breast cancer classification benefits from the proposed multi-view architectures. We also assess the method generalizability beyond mammogram analysis by considering different benchmarks, as well as a finer-scaled task such as segmentation. Full code and pretrained models for complete reproducibility of our experiments are freely available at https://github.com/ispamm/PHBreast.