A Glowing Geometric Proof that Root-2 is Irrational

It was a great shock to the Pythagoreans to discover that the diagonal of a unit square could not be expressed as a ratio of whole numbers. This discovery represented a fundamental fracture between the mathematical domains of Arithmetic and Geometry: since the Greeks recognized only whole numbers and ratios of whole numbers, the result … Continue reading A Glowing Geometric Proof that Root-2 is Irrational →

Mathematics at the Science Museum

The new Winton Gallery at London's Science Museum in South Kensington holds a permanent display on the history of mathematics over the past 400 years. The exhibition shows how mathematics has underpinned astronomy, navigation and surveying in the past, and how it continues to pervade the modern world [see TM139, or search for “thatsmaths” at … Continue reading Mathematics at the Science Museum →

Marden’s Marvel

Although polynomial equations have been studied for centuries, even millennia, surprising new results continue to emerge. Marden's Theorem, published in 1945, is one such -- delightful -- result. For centuries, mathematicians have struggled to find roots of polynomials like p(x) ≡ xn + an-1 xn-1 + an-2 xn-2 + an-3 xn-3 + … a1 x … Continue reading Marden’s Marvel →

Stan Ulam, a mathematician who figured how to initiate fusion

Stanislaw Ulam, born in Poland in 1909, was a key member of the remarkable Lvov School of Mathematics, which flourished in that city between the two world wars. Ulam studied mathematics at the Lvov Polytechnic Institute, getting his PhD in 1933. His original research was in abstract mathematics, but he later became interested in a … Continue reading Stan Ulam, a mathematician who figured how to initiate fusion →