"Then when I reached college I realized that many people had thought about the problem during the 18th and 19th centuries and so I studied those methods"

In this quote, Andrew Wiles assesses an intellectual journey that started before his college years and matured as he pursued higher education. The core of the statement revolves around the realization of historic scholastic discourse and how it influenced his own intellectual pursuits. Wiles talks to a universal experience in learning: the recognition that our modern understanding is built on the foundations laid by thinkers of the past. When Wiles reached college, he found that lots of intellectuals before him, notably during the 18th and 19th centuries, had actually faced the very same problems that interested him. This historic continuum of thought prompted him to delve much deeper into these developed methods, recommending a modest recommendation of the depth and breadth of prior knowledge.

The reference of the 18th and 19th centuries is considerable. These centuries were durations of blossoming mathematical and scientific advancement, identified by the evolution of calculus, number theory, and other mathematical disciplines. The Enlightenment period, followed by the Industrial Revolution, promoted substantial developments in mathematical theories and applications. By studying the approaches of these ages, Wiles implicitly acknowledges the richness of development and the incremental nature of academic progress.

Moreover, Wiles' statement highlights the necessary scholastic practice of building upon prior work to advance understanding. By engaging with the ideas and services proposed by earlier scholars, Wiles was not simply replicating previous methods but was placing himself to refine, difficulty, and extend them. This process is at the heart of academic scholarship, where understanding the provenance of ideas is essential for development.

Wiles' quote encapsulates the transition from finding out as an isolated, possibly intuitive undertaking to a collective and historical one. It recommends that reaching a greater level of research study involves recognizing the lineage of intellectual pursuit and leveraging it to advance one's own understanding and add to the broader scholastic discussion. For Wiles, this journey culminated in his ultimate proof of Fermat's Last Theorem, a testimony to the power of building on the work of those who came before.