Introduction to Bayesian Scientific Computing

The book of nature, according to Galilei, is written in the language of mat- matics. The nature of mathematics is being exact, and its exactness is und- lined by the formalism used by mathematicians to write it. This formalism, characterized by theorems and proofs, and syncopated with occasional l- mas, remarks and corollaries, is so deeply ingrained that mathematicians feel uncomfortable when the pattern is broken, to the point of giving the - pression that the attitude of mathematicians towards the way mathematics should be written is almost moralistic. There is a de?nition often quoted, 'A mathematician is a person who proves theorems', and a similar, more alchemistic one, credited to Paul Erd? os, but more likely going back to Alfr' ed R' enyi,statingthat'Amathematicianisamachinethattransformsco?eeinto 1 theorems '. Therefore it seems to be the form, not the content, that char- terizes mathematics, similarly to what happens in any formal moralistic code wherein form takes precedence over content. This book is deliberately written in a very di?erent manner, without a single theorem or proof. Since morality has its subjective component, to pa- phrase Manuel Vasquez Montalban, we could call it Ten Immoral Mathemat- 2 ical Recipes . Does the lack of theorems and proofs mean that the book is more inaccurate than traditional books of mathematics? Or is it possibly just a sign of lack of co?ee? This is our ?rst open question. Exactness is an interesting concept.