### Deductive reasoning

*Are you curious about mathematical reasoning?*

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.*

Proof – deductive reasoning – is a cornerstone 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
amazing, wonderful, and fun!*

### Prooftoys

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.

Here is a sample, a 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, a little mathematical parlor trick.