Für Mathe ist man nie zu alt Beweis der Fermatschen Vermutung – Höhepunkt der Mathematik des 20. Jahrhunderts – Vortrag

Can the sum of two perfect squares be a perfect square itself? The answer is “Yes.” The simplest example is the perfect squares 32 and 42, whose sum is 52. Other examples include 52 and 122, whose sum is 132, as well as 332 and 562, whose sum is 652. Triples of natural numbers x, y, and z with the property x² + y² = z² are called Pythagorean triples. There are infinitely many of these, and as early as ancient times, a formula was known by which all Pythagorean triples can be calculated.
In the 17th century, Pierre de Fermat (1607–1665) generalized the question: Can the sum of two third powers of natural numbers be a third power, the sum of two fourth powers of natural numbers be a fourth power, and, in general, the sum of two nth powers of natural numbers be an nth power? Fermat conjectured that this is never the case for n greater than two. Formally, this means: The equation
x^n + y^n = z^n
has no solution for positive integers x, y, z, and n if n is greater than two.
It was not until 1994 that Fermat’s Conjecture was proven by the British mathematician Andrew Wiles, after more than 350 years of leading mathematicians attempting to do so in vain. The proof is considered the crowning achievement of 20th-century mathematics.

Mathematician Dr. Michael Laska explains the basic ideas behind the proof in a way that is accessible to laypeople.