Mir Books

Mathematics is too often mistaken for nothing more than a jungle of formulas. Yet the story of numbers and ideas is far richer. Ancient cultures counted with objects, carved truths into stone, or sang them in verse, long before symbols dominated the page. Somewhere along the way, the formula — once a tool of clarity — became a burden, turning many away from the subject altogether.

This book takes a different path. It is not a textbook, nor a technical manual for specialists, but a lyrical exploration of mathematics beyond the formulas. It seeks the meaning behind the symbols, the living ideas that have always made mathematics more than syntax. For those who wish to see the subject with fresh eyes — curious readers, students, and teachers alike — it offers an invitation to rediscover mathematics as something human, imaginative, and deeply alive.

Translated from the Russian and

Typeset in LaTeX by Damitr Mazanav

Released on the Web in 2025.

Get the book here

Notes: It was fun to typeset the book, and I am pleased with the results. I think the book has  come out beautifully. Perhaps in the next iteration I will add more pictures to make this even more readable for the intended readers..

Contents

A Lyrical Digression vii

1 Sets 1

2 Infinity Comes in Different Forms 11

3 Operations On Sets 19

4 Correspondences, Mappings, Relations 27

5 Special Relations 35

6 Mathematical Logic (Meaningless Logic) 43

7 Operations On Statements 49

8 Propositional Algebra 55

9 Predicate Logic 61

10 Axiomatic Theories 67

11 Theory Of Algorithms 75

12 Formal Grammars 85

13 Computational Complexity 91