Hypatia contributed to the study of philosophy primarily through her role as a teacher at Alexandria and her deep engagement with mathematics and science. While it is true that she was educated in both science and mathematics, her most significant contributions were her teachings and her promotion of Neoplatonism, a philosophy rooted in the works of Plato.
She did not improve upon the works of Plato in a way that is commonly noted, nor is there evidence that she studied Euclid's theories and proved them incorrect. Instead, she is known for her commentaries on existing works and her contributions to the intellectual culture of her time. Her influence helped to preserve and promote philosophical thought during a period of significant turmoil.
In summary, her primary contributions to philosophy were through her teaching and engagement with both philosophy and mathematics at the School of Alexandria.
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