Dr. Oksana Shatalov (Instructional Professor at Texas A&M)

For over a thousand years, ancient Greek mathematicians used only a straightedge and compass to create astonishing geometric constructions. They could bisect angles, double squares, and construct regular polygons with 3, 4, 5, 6, 8, and 10 sides. But despite their genius, they hit an unbreakable wall when attempting certain challenges—trisecting an arbitrary angle, doubling a cube, squaring a circle, and constructing regular 7- and 9-sided polygons. These puzzles became legendary, known as the Three Great Problems of Antiquity.

Why did the greatest mathematical minds of the time fail? Was it simply a lack of ingenuity, or was something deeper at play? The shocking truth, revealed only in the 19th century, was that these problems weren’t just difficult—they were impossible to solve using only a straightedge and compass, the tools central to Greek geometric construction. But why did it take 2,000 years to prove this? What changed in mathematics that finally unlocked the answers?

Join us as we unravel one of the most fascinating sagas in mathematical history—a tale of brilliant discoveries, frustrating dead ends, and the ultimate realization that even in mathematics, some problems have no solution.