Learning calculus at school, we soon find out that while differentiation is relatively easy, at least for simple functions, integration is hard. So hard indeed that, in many cases, it is impossible to find a nice function that is the integral (or anti-derivative) of a given one. Thus, given we can usually find , whereas we may not be able to find .

## Archive for May, 2020

### The Monte-Carlo Method

Published May 28, 2020 Occasional ClosedTags: Algorithms, Numerical Analysis

Albrecht Dürer was born in Nuremberg in 1471, third of a family of eighteen children. Were he still living, he would be celebrating his 549th birthday today. Dürer’s artistic genius was clear from an early age, as evidenced by a self-portrait he painted when just thirteen [TM187; or search for “thatsmaths” at irishtimes.com ].

In 1494, Dürer visited Italy, where he travelled for a year. A novel connection between art and mathematics was emerging around that time. By using rules of perspective, artists could represent objects in three-dimensional space on a plane canvas with striking realism. Dürer was convinced that “the new art must be based upon science; in particular, upon mathematics, as the most exact, logical, and graphically constructive of the sciences”*.*

Continue reading ‘Changing the way that we look at the world’

The development of perspective in the early Italian Renaissance opened the doors of perception just a little wider. Perspective techniques enabled artists to create strikingly realistic images. Among the most notable were Piero della Francesca and Leon Battista Alberti, who invented the method of perspective drawing.

### John Casey: a Founder of Modern Geometry

Published May 7, 2020 Irish Times ClosedTags: Geometry, Ireland

Next Tuesday – 12th May – is the 200^{th} anniversary of the birth of John Casey, a notable Irish geometer. Casey was born in 1820 in Kilbeheny, Co Limerick. He was educated in nearby Mitchelstown, where he showed great aptitude for mathematics and also had a gift for languages. He became a mathematics teacher, first in Tipperary Town and later in Kilkenny [TM186; or search for “thatsmaths” at irishtimes.com ].