The Basel problem was solved by Leonhard Euler in 1734 [see previous post]. His line of reasoning was ingenious, with some daring leaps of logic. The Basel series is a particular case of the much more general zeta function, which is at the core of the Riemann hypothesis, the most important unsolved problem in mathematics. … Continue reading Euler’s Product: the Golden Key
Month: January 2021
Euler: a mathematician without equal and an overall nice guy
Mathematicians are an odd bunch. Isaac Newton was decidedly unpleasant, secretive and resentful while Carl Friedrich Gauss, according to several biographies, was cold and austere, more likely to criticize than to praise. It is frequently claimed that a disproportionate number of mathematicians exhibit signs of autism and have significant difficulties with social interaction and everyday … Continue reading Euler: a mathematician without equal and an overall nice guy
The Basel Problem: Euler’s Bravura Performance
The Basel problem was first posed by Pietro Mengoli, a mathematics professor at the University of Bologna, in 1650, the same year in which he showed that the alternating harmonic series sums to $latex {\ln 2}&fg=000000$. The Basel problem asks for the sum of the reciprocals of the squares of the natural numbers, $latex \displaystyle … Continue reading The Basel Problem: Euler’s Bravura Performance
We are living at the bottom of an ocean
Anyone who lives by the sea is familiar with the regular ebb and flow of the tides. But we all live at the bottom of an ocean of air. The atmosphere, like the ocean, is a fluid envelop surrounding the Earth, and is subject to the influence of the Sun and Moon. While sea tides … Continue reading We are living at the bottom of an ocean
ThatsMaths 