Math is

the ultimate toy

and power tool

Mastering math

Would you like to master the art of mathematical thinking?

Much as mathematics is an essential building material for science, mathematical reasoning is an essential building material for mathematics, that makes it possible to build sturdy mathematical structures that reach all the way “To Infinity and Beyond!"

But math can also be entertainment, the ultimate puzzle and game for your mind.

Mathematical reasoning is at the heart of mathematical thinking. With this website you can see how it is done, building your skills and confidence in solving mathematical problems through proof.

With luck, you might even begin to see how mathematics can be something amazing and wonderful, even fun!


Prooftoys is a computer tool that works with you interactively to solve math problems – or prove mathematical statements. It has correct rules for reasoning built into it, always follows them, and never makes a careless mistake or forgets its rules. You give the orders, and it takes care of the details.

Working problems is a natural way to learn mathematical reasoning, and Prooftoys has been designed especially to do precise reasoning, but in an especially simple way. You can always dig into the solution of any problem and any proof to see exactly how it was done.

Our first problem is from the book “My Best Mathematical and Logic Puzzles” by the legendary Martin Gardner, author of numerous books of entertaining and puzzling mathematics and, for 25 years, the Mathematical Games column in Scientific American magazine.

This is problem 20 in the book, and starts with a little mathematical parlor trick.

The problem of the repetitious number