https://aphinum.com/tags/number-theory/ Recent content in Number Theory on Philosophy Structured Notes Hugo en-US Sat, 03 Jan 2026 22:51:43 +0000 https://aphinum.com/posts/the-geometrical-theory-of-proportion-a-new-foundation-for-mathematics/ Fri, 02 Jan 2026 19:42:28 +0000 https://aphinum.com/posts/the-geometrical-theory-of-proportion-a-new-foundation-for-mathematics/ <p><strong>The Geometrical Theory of Proportion: A New Foundation for Mathematics</strong></p> <p><strong>Overview</strong> The discovery of irrationals by ancient Greek mathematicians led to significant advancements in mathematical thought, particularly in the development of a geometrical theory of proportion. This new approach, attributed to Eudoxus (ca. 408 - ca. 355 B.C.), revolutionized the field by introducing a more comprehensive and versatile framework for understanding ratios and proportions. The geometrical theory of proportion, as described in Euclid&rsquo;s works, has had a lasting impact on mathematics, laying the groundwork for later developments in calculus and analysis.</p> https://aphinum.com/posts/the-development-of-irrational-numbers-a-philosophical-exploration/ Fri, 02 Jan 2026 19:37:03 +0000 https://aphinum.com/posts/the-development-of-irrational-numbers-a-philosophical-exploration/ <p><strong>The Development of Irrational Numbers: A Philosophical Exploration</strong></p> <h2 id="overview">Overview</h2> <p>Irrational numbers have been a subject of interest for philosophers and mathematicians throughout history, particularly in ancient Greece. <strong>Irrationals</strong>, by definition, are real numbers that cannot be expressed as the ratio of two integers. This concept has far-reaching implications for mathematics, philosophy, and our understanding of reality. In this study, we will examine the development of irrational numbers, from their initial discovery to their incorporation into philosophical debates.</p>