Maths and philosophy
Links between mathematics and philosophical thought, epistemological questions
The pitfalls of rates
Our thinking seems naturally additive. If we add 10% and then another 10%, we expect the total to be 20%. Yet that is wrong! Rates are not added; they are multiplied. How can we avoid the pitfalls of percentages? How can we work out the cost of a loan?
The foundations of differential calculus: the 1700 quarrel | Tangente
A famous scientific quarrel over infinitesimals pitted Rolle against Varignon.
The Liouville Journal: a key mathematics publication | Tangente
In 1832, the Annales de mathématiques pures et appliquées, better known as the Annales de Gergonne, ceased publication after twenty-two years.
John von Neumann: means and excess
The Banach–Tarski paradox claims that, in theory, the pieces of a single loaf can be turned into two loaves. It fell to the protean genius John von Neumann to explain the underlying reason for this mathematical miracle. The notion of amenability that he introduced then spread widely.