Mathematics has been described by Carl Friedrich Gauss (acknowledged as one of the greatest mathematicians of the 19th Century), as the “Queen of the Sciences”. More recently, in the early 20th Century, Bertrand Russell defined Mathematics as “the subject in which we never know what we are talking about, nor whether what we are saying is true”. (Which might ring a bell with those struggling to get to grips with their own mathematics courses!) Mathematical reasoning is based on the construction of a hierarchical system of proofs using a system of deductive logic. In this sense it is a ruthlessly rigorous discipline. However, of particular relevance to learners of mathematics, profound and beautiful mathematical insights can nevertheless be revealed by an enquiring mind with the aid of a few basic principles, use of visual representations and recognizing patterns. The Europe Tutorial Academy currently offers pre-university courses in Mathematics for A-level, International Baccalaureate Diploma, French Baccalauréat, and American Advanced Placement students, as well as a selection of Enrichment Workshops on specific topics in Mathematics. Also, refer to the Articles Page on this website, for our current ETA academic papers on Physics and related Mathematical articles on Mechanics and Astronomy.