Dialogues on Mathematics – what does it mean to build a mathematical model?

Even seasoned data scientists can have a hard time when one asks them what does it mean to build a (mathematical) model of a problem, or how math is able to represent the world around us and how pure and applied mathematics are related to each other. Alfred Rényi’s Dialogues on Mathematics is a beautiful book on those questions and it is written for the general audience.

Alfred Rényi was one of the most successful Hungarian mathematicians in the 20th century. He contributed to graph theory, combinatorics, number theory, information theory and probability theory. Along with his professional work, he wrote popular scientific books on various parts of mathematics which are inspirational for generations of young math lovers. Although Rényi’s popular scientific books needs no knowledge of mathematics beyond high school level, and their language is very colloquial, they don’t lack the scientific rigor.

Dialogues on Mathematics first appeared in 1967 is Rényi’s first popular scientific book which contains three dialogues. The first one is written in the style of Socratic dialogues, actually, it is a discussion between Socrates and Hippocrates and it can be thought of as the sequel to Plato’s Protagoras. Hippocrates asks Socrates if it worth to study higher mathematics and what is the nature of this science. The second dialogue is about the application of mathematics to scientific and engineering problems. During the battle of Syracuse, king Hiero asks Archimedes about his work on optics (the heat rays against the Roman fleet) and its relation to mathematics. Archimedes expresses his sadness, because only his work related to warfare made him famous, but he likes the more peaceful applications of his research. Also, the classic scientists doesn’t see a sharp boundary between applied and theoretical mathematics, because no-one knows when a purely theoretical theorem can be useful. Also, we have a great body of practical knowledge without an exact proof yet, in that case, theoretical work, e.g. a proof, can clarify and even justify certain methods. The last dialogue is between Mrs. Niccollini and Galilei. The story set in the midst of Galilei’s trial. One night young Torricelli visits the old master and expresses his and his friends plan to help escaping Galilei. The old master declines the rescue plan, because he thinks that the Truth will triumph eventually. Torricelli leaves, and Galilei’s host, Mrs. Niccollini starts asking her guest about the nature of science and the role of mathematics in it.

The cover of the third Hungarian edition.

This book won’t make you a mathematician and won’t prepare you to build mathematical models. You won’t come across any equations on its pages! However, this book will help you to understand the nature of mathematics and its role in scientific research. And you will have a lot of fun when you read it!

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