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The core teachings of Pythagorean philosophy, particularly its mathematical aspects, have had a profound and lasting impact on modern mathematics and science. This literature review explores the influence of Pythagorean philosophy, focusing on its mathematical contributions and their significance in contemporary fields.

Pythagorean philosophy, as discussed by Horky, emphasizes the importance of mathematical Pythagoreanism, which introduced innovative approaches to science by reconciling empirical knowledge with abstract mathematical theories 1. This mathematical orientation provided a foundation for fundamental philosophical questions that Plato and subsequent philosophers grappled with, influencing the development of philosophical and scientific methods.

The revival of Pythagoreanism in the Neoplatonic school, as detailed by Iamblichus, further illustrates the enduring influence of Pythagorean mathematical concepts on later philosophical thought 2. This revival underscores the adaptability and relevance of Pythagorean teachings in evolving philosophical contexts.

Moreover, the essay by Sayre presents an inductive argument that reinforces the Pythagorean underpinnings of Plato's philosophy, particularly through stichometric analyses of the dialogues, which reveal a structural reflection of Pythagorean metaphysics 3. This connection between the structure of philosophical texts and Pythagorean principles highlights the deep integration of Pythagoreanism into the fabric of philosophical inquiry.

The exploration of the philosophy of mathematics, as discussed in the context of Pythagoras and Plato, sheds light on the enduring question of mathematical existence and the nature of mathematical objects 4. This philosophical inquiry into mathematics reveals the profound impact of Pythagorean thought on our understanding of abstract mathematical concepts and their relation to the physical and ideal realms.

Furthermore, the application of Pythagorean principles in modern cryptography demonstrates the practical implications of Pythagorean mathematics in contemporary science and technology 6. This direct application of Pythagorean circles in cryptography exemplifies the ongoing relevance of Pythagorean mathematical concepts in solving modern problems.

In summary, the core teachings of Pythagorean philosophy, particularly its emphasis on mathematical principles, have significantly influenced the development of modern mathematics and science. From the foundational philosophical inquiries of Plato to the practical applications in cryptography and beyond, the mathematical legacy of Pythagoreanism continues to permeate various scientific disciplines, demonstrating its enduring relevance and impact.

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