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Short Summary
Main recommendation: Learn a few mental math shortcuts, such as squaring numbers and multiplying large numbers by breaking them into parts, to perform calculations faster than a calculator. Art Benjamin, a self-described "mathemagician," demonstrates these techniques live on stage, combining math with magic-style showmanship. The talk also includes memory-based tricks like guessing a missing digit and naming the day of the week for a given date.
Key Points
- Squaring a number means multiplying it by itself (for example, 5 squared is 25), and most calculators can do this by pressing the number, times, then equals.
- Benjamin squares two-digit, three-digit, and even four-digit numbers in his head faster than audience members can on calculators.
- For large products, he splits the problem into parts: (a + b)² = a² + b² + 2ab, computing 57,000 squared, 683 squared, and twice the product of 57,000 and 683, then adding them.
- He uses a phonetic code that converts digits into words, which he stores and later retrieves as numbers to remember intermediate results.
- He guesses a missing digit from a seven-digit product by having a volunteer call out any six digits, with a stated one-in-ten-thousand chance of guessing four cases correctly by random chance.
- He determines the day of the week for a birth date by using a book of calendars covering years back to 1000.
Details Worth Noting
- Concrete instructions: To square a number on most calculators, enter the number, press the multiplication key, then press equals (for example, 5 × 5 = 25). For faster squaring on some older RPN calculators, use the x-squared button. For mental large-number multiplication, break the problem into parts (for example, 57,683² = 57,000² + 683² + 2 × 57,000 × 683) and add the results.
- Benjamin notes that his method involves storing numbers as words through a phonetic code, which he later converts back to digits to track intermediate results.
- In the 57,683 squaring demonstration, he works through 57 × 683 = 38,931, doubles it to 77,862, then computes 57² = 3,249 and 683² = 466,489, combining them into a final answer of 3,328,189,... (the transcript's final answer is spoken as "328,000 189" with partial audio clarity).
- The calculator-based demonstrations involved audience volunteers checking results and confirming correctness, including a ten-digit calculator user.
- The day-of-week trick used a calendar book; he asked volunteers for their birth year, month, and day, then confirmed the weekday shown in the book.
Bottom Line
Mental math tricks like squaring with decomposition and memory techniques can outpace calculators for specific calculations, and they are presented here as entertaining, learnable skills rather than magic.