Carl Friedrich Gauss is generally regarded as the greatest mathematician of all time. The profundity and scope of his work is remarkable. So, it is amazing that, while he studied non-Euclidian geometry and defined the curvature of surfaces in space, he overlooked a key connection between curvature and geometry. As a consequence, decades passed before … Continue reading Gauss Misses a Trick
Month: May 2013
The Sholders of Giants
Isaac Newton gave credit to his predecessors for his phenomenal vision and insight with the phrase that he was “standing on the shoulders of giants”. But just who were those giants? Foremost amongst them must have been Galileo, who formulated some fundamental mechanical principles that underlie Newton's work in dynamics. But there were many others. … Continue reading The Sholders of Giants
Ducks & Drakes & Kelvin Wakes
The theme of this week’s That’s Maths column in the Irish Times ( TM021 ) is Kelvin Wakes, the beautiful wave patterns generated as a duck or swan swims through calm, deep water or in the wake of a ship or boat. Group Velocity A stone dropped in a pond generates waves in a beautiful changing … Continue reading Ducks & Drakes & Kelvin Wakes
The Loaves and the Fishes
One of the most amazing and counter-intuitive results in mathematics was proved in 1924 by two Polish mathematicians, Stefan Banach and Alfred Tarski. Banach was a mathematical prodigy, and was the founder of modern functional analysis. Tarski was a logician, educated at the University of Warsaw who, according to his biographer, “changed the face of … Continue reading The Loaves and the Fishes
Monster Symmetry
The That's Maths column in the Irish Times this week is about symmetry and group theory, and the possible link, through string theory, with the fundamental structure of the universe ( TM020 ). In the arts, symmetry is intimately associated with aesthetic appeal. In science, it provides insight into the properties of physical systems. In … Continue reading Monster Symmetry
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