"There are proofs that date back to the Greeks that are still valid today"

In the quote "There are proofs that go back to the Greeks that are still valid today", Andrew Wiles highlights the enduring legacy and foundational impact of ancient Greek mathematics on modern-day mathematical idea and practice. This declaration highlights numerous essential ideas about the nature of mathematical fact, the historical advancement of mathematics, and the enduring influence of Greek mathematicians.

To start with, the quote emphasizes the timelessness of mathematical evidence. Unlike scientific theories, which can be customized or discarded with brand-new empirical proof or insights, a mathematical evidence, when developed, remains real indefinitely, as long as the facilities and rational thinking are sound. This impressive attribute of mathematics is exhibited by the works of ancient Greek mathematicians such as Euclid, Pythagoras, and Archimedes. Their contributions, including Euclid's "Elements", which methodically put together the understanding of geometry, continue to form the bedrock of mathematical education and understanding.

Secondly, the declaration acknowledges the Greeks' essential role in laying the foundation for the methodical and sensible technique that characterizes modern mathematics. Greek mathematicians presented extensive methods of evidence and reduction that have actually shaped mathematical questions ever since. Their dedication to abstract thinking and the pursuit of fact through reasoning led the way for future advancements, making it possible for subsequent generations to build upon their work.

Moreover, the quote also subtly mentions the interconnectedness of mathematical history. The continuity from ancient Greek mathematics to modern mathematics is a testimony to the cumulative nature of the discipline. Discoveries and theories construct on one another, showing a discussion across centuries that boosts our understanding of mathematical principles.

In essence, Wiles' observation speaks with the extensive and long lasting influence of Greek mathematical achievements. It serves as a suggestion of the withstanding beauty and coherence of mathematics, a discipline that goes beyond temporal and cultural boundaries, continually notifying and motivating present and future generations of mathematicians.