### Why Learn Mental Math Tricks?

"Why Learn Mental Math Tricks?" is the question author Presh Talwalkar tries to answer in the introduction to his new book "The Best Mental Math Tricks". He gives several reasons, starting with

For one, math skills are needed for regular tasks like calculating the tip in a restaurant or comparison shopping to find the best deal. Second, mental math tricks are one of the few times people enjoy talking about math. Third, mental math methods can help students build confidence with math and numbers.

Mental math tricks are fun to share.

I absolutely agree with all of the above and wish only to remark that his book makes a strong stand against the common meaning of the word "trick" whose connotations include magic, deceit, and disapproval.

The book is not a collection of disparate math facts but rather a textbook of well organized and well explained methods of handling arithmetic operations on classes of numbers grouped by their size, divisibility properties, last digits, etc. A whole section that is devoted to each of the "tricks" contains practice problems with complete solutions to illustrate the method. Every method is accompanied by a mathematical proof that sheds the mystery of why the method works. And this is what places the contents of the book in contraposition with the most likely interpretation of the book's title.

In a recent book "Mathematics without Apologies" Michael Harris devotes a whole chapter to the role played by the so called "math tricks" in the body of mathematics.

While capital-M Mathematics is neatly divided among definitions, axioms, theorems, and proofs, the mathematics of mathematicians blurs taxonomical boundaries. ... A mathematical trick is a notorious crosser of conventional borders.

While it is most unlikely that Michael Harris was ever thinking of tricks described and explained by Presh Talwalkar I have no qualms of making this association. Presh Talwalkar has included in his book

... tricks that are relatively easy to learn, are fun, or have educational value.

I'd go further as I strongly believe that those tricks are more than anything else convey to the early learners the essence of practicing mathematics. Presh Talwalkar's book may also open the eyes of an older generation on what they missed in the early grades.