CTK Insights

Archive for October, 2012

24 Oct

Highway Musings

On long drives I made it a habit to talk math, so I prepared a few problems to discuss from the night before. But this time I had to rack my brain all by myself, if only to fight away drowsiness. The warm-up problem was simple: The product of 22 integers is equal to 1. Show that their sum cannot be zero. I would modify it in several ways

23 Oct

The Best Writing on Mathematics

If we learn to say things simply and build up slowly from the concrete to the abstract, we may be able to build many bridges among our various specialties. For me, this style will always be The Best Writing on Mathematics, and this book is full of excellent examples of it.

22 Oct

A Property of the Power of 5

My late father was an inveterate human calculator. During the 1930s at the height of the New Economic Policy (NEP) that allowed a degree of post-revolution entrepreneurship in the Soviet Union, he made a living by giving on-stage mental math performances. He became an electrical engineer when the NEP was curtailed.

Browsing through his notes I have recently come across an observation concerning the fifth powers of integers and its relevance to the absence of integer solutions of x^5 + y^5 = z^5 - Fermat's equation for n=5.

15 Oct

The Half-Life of Facts and Phase Transitions

Our knowledge is also subject to state transitions. Two 1995 papers by Andrew Wiles and Richard Taylor marked the end of a 300 years long search for a proof of Fermat's Last Theorem. Interestingly and surprisingly, there are other laws - expressed pretty much mathematically - that govern the rate with which knowledge accrues and spreads, and how long it remains current. The latter is reflected in the title of the book.

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