Explore the fascinating world of "Poly Number theory" in this 29-minute video lecture on Chebyshev and Spread Polynumbers. Discover why this field offers a compelling alternative to classical number theory for amateur mathematicians seeking accessible areas of investigation. Learn about the rich algebra of polynomials, focusing on Chebyshev polynomials and their modern variants, the spread polynomials. Examine the remarkable Goh factorization of spread polynumbers, which sets them apart from Chebyshev polynomials and suggests their fundamental nature. Gain insights into the number theory emerging from this factorization, originally discovered by Shuxiang Goh. Challenge your understanding of the "Fundamental Theorem of Algebra" and explore a more concrete approach to trigonometric identities using power series. This lecture, part of a series on advice for prospective research mathematicians, offers valuable perspectives on foundational issues in mathematics and their connections to modern computation. Read more