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 a model demonstrating the consistency of hyperbolic geometry emerged.
Archive for May, 2013
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. The greatest English mathematician prior to Newton was John Wallis.
Continue reading ‘The Sholders of Giants’
Tags: Applied Maths, History, Wave Motion
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 logic in the twentieth century” through his work on model theory.
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.