Understanding and Doing Math

It is not a story of brilliant achievement, heroic deeds, or noble sacrifice. It is a story of blind stumbling and chance discovery, of groping in the dark and refusing to admit the light. It is a story replete with obscurantism and prejudice, of sound judgment, often eclipsed by loyalty to tradition, and of reason long-held subservient to custom. In short, it is a human story.

Tobias Dantzig, about the development of the notion of number,
in Number: The Language of Science, Macmillan, 1930.

We will start our journey with the numbers. Numbers are the oldest mathematical idea, yet the most important one. Not only will we go through the basics of numbers in a way that will give you the confidence to really understand numbers and really know how to apply them, but you will also learn all the essential elements of mathematics on the example of the world of numbers. The example of numbers will be used to illustrate what mathematical objects are and how they are applied, and what mathematical tools we use in their description and application.

Humanity needed millennia to develop the world of numbers and methods of their description and application. While growing up you are expected to pass through this history briefly in a dozen or so years of education. On the basis of experience of the entire human civilisation and your education, we are now in the position to acquire knowledge about numbers at a more mature level in several weeks.

In Preface to Circle 1, various reasons why people engage in mathematics are given. At the same time, the Preface uncovers common misconceptions that prevent people from practicing mathematics.

You can read the introductory theme Introduction to Numbers, On the example of numbers, we can discover all the weirdness of mathematical objects.

You can read one topic from the book, Equations, Equalities and the Laws of Nature, to get a better sense of whether you would like to have this book with you on your journey to math. But be careful – pirate Giorgio lives in this topic. A list of the full Content is also provided.

And of course, here is the inevitable list of detected errors that will be corrected in the next edition: Math Circle 1 Errors.