The book of nature, according to Galilei, is written in the language of mathematics. The nature of mathematics is being exact, and its exactness is underlined by the formalism used by mathematicians to write it. This formalism, characterized by theorems and proofs, and syncopated with occasional lemmas, remarks and corollaries, is so deeply ingrained that mathematicians feel uncomfortable when the pattern is broken, to the point of giving the impression that the attitude of mathematicians towards the way mathematics should be written is almost moralistic. There is a definition 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, stating that “A mathematician is a machine that transforms coffee into theorems1”. Therefore it seems to be the form, not the content, that characterizes mathematics, similarly to what happens in any formal moralistic code wherein form takes precedence over content.
This book is deliberately written in a very different manner, without a single theorem or proof. Since morality has its subjective component, to paraphrase Manuel Vasquez Montalban, we could call it Ten Immoral Mathematical Recipes2. 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 coffee? This is our first open question.
This book has been written for undergraduate and graduate students in various areas of mathematics and its applications. It is for students who are willing to get acquainted with Bayesian approach to computational science but not necessarily to go through the full immersion into the statistical analysis. It has also been written for researchers working in areas where mathematical and statistical modeling are of central importance, such as biology and engineering.