Numbers are really interesting. Even usual numbers have extraordinary properties. For example, a year has 365 days. This number can be written as the sum of three consecutive squares: 365 = 10² + 11² + 12². It can also be written as the sum of the next two squares: 365 = 13² + 14².

A very experienced math professor said during a seminar: “A friend of mine, who is also a mathematician, once dreamed he was inside a square root as −1.” It made me think that mathematicians can have unusual and complex dreams.

On The Big Bang Theory, Sheldon Cooper called 73 the best number. It sounds like a joke — but the math behind it is surprisingly beautiful. First, 73 is a prime number. But it also holds a special spot in the list of primes. If you count them one by one, 73 turns out to be the 21st prime number. Now flip the digits of 73 and you get 37 which is the 12th prime number (21 reversed becomes 12). Second, take the number 21 and factor it: 21 = 7 × 3. Those are the exact digits that make 73. And finally, write 73 in binary (the language computers use): 1001001. Read it left to right or right to left — it’s the same. That makes it a binary palindrome.

Carl Friedrich Gauss was a rowdy-dowdy student at elementary school in the late 1700s. In order to hold him, his teacher asked him to count the sum of all numbers from 1 to 100, but in just a few seconds Gauss counted it and shouted 5,050. Without any hesitation, the teacher slapped him. Gauss recognized he had fifty pairs of numbers when he added the first and last number in the series from 1 to 100 and he would have a 101 for each pair. 50 pairs × 101 (the sum of each pair) = 5,050. That was one of the wrongest slaps in the world history.

Zerah Colburn: Entertaining Calculations One of the first lightning calculators to capitalize on his talent was Zerah Colburn (1804–1839), an American farmer’s son from Vermont who learned the multiplication tables up to 100 before he could even read or write. By the age of six, young Zerah’s father took him on the road, where his performances generated enough income to send him to school in Paris and London. By age eight, he was internationally famous, performing lightning calculations in England, and was described in the Annual Register as “the most singular phenomenon in the history of the human mind that perhaps ever existed.” No less than Michael Faraday and Samuel Morse admired him. No matter where he went, Colburn met all challengers with speed and precision. He tells us in his autobiography of one set of problems he was given in New Hampshire in June 1811: “How many days and hours since the Christian Era commenced, 1811 years ago? Answered in twenty seconds: 661,015 days, 15,864,360 hours. How many seconds in eleven years? Answered in four seconds: 346,896,000.” As is often the case with lightning calculators, interest in Colburn’s amazing skills diminished over time, and by the age of twenty he had returned to America and become a Methodist preacher. He died at the youthful age of thirty-five. In summarizing his skills as a lightning calculator, and the advantage such an ability affords, Colburn reflected, “True, the method requires a much larger number of figures than the common rule, but it will be remembered that pen, ink, and paper cost Zerah very little when engaged in a sum.” Source: SECRETS OF MENTAL MATH by Arthur Benjamin and Michael Shermer