Richard M. Nixon once used a subtle idea from calculus in a political argument during his campaign for re-election. He claimed that the rate of increase of inflation was decreasing, a statement often described as the first time a sitting U.S. president implicitly invoked the third derivative to support a policy claim. Inflation itself measures how the purchasing power of money changes over time, so it can be viewed as a derivative. The rate at which inflation increases is therefore the derivative of inflation, which corresponds to the second derivative of purchasing power with respect to time. Saying that this rate is decreasing means its derivative is negative. In effect, Nixon’s claim implied that the second derivative of inflation, or equivalently the third derivative of purchasing power, was negative.

A famous formula for π: π/4 = 1 − 1/3 + 1/5 − 1/7 + … This comes from a trigonometry formula: arctan(x) = x − x³/3 + x⁵/5 − x⁷/7 + … Putting x = 1 gives the series for π/4. This result was discovered independently by: Gottfried Wilhelm Leibniz (1673), James Gregory (1671), Nilakantha Somayaji (around 1500, in Tantrasangraha).

If you start counting from 1 and say one number every second, it would take you about 30 years to reach 1 billion (1,000,000,000). Long ago, the word billion meant a million million (that is, 1,000,000,000,000 or 12 zeros). This was the meaning used in countries like England and Germany. The word comes from “bi”, meaning two, because it was thought of as two “millions” written together: 1,000,000 1,000,000 making 1,000,000,000,000 (12 zeros). Later, Americans started using the word billion for a smaller number: 1,000,000,000 (9 zeros). Today, this 9-zero meaning is used almost everywhere in the world, especially in science and mathematics. The word billion itself is not very old. It became common only after the 1500s, and one early American use was recorded in 1729.

Ernst Eduard Kummer, one of the great algebraists of the nineteenth century, had a strange weakness that made his students both amused and bewildered — he was terrible at arithmetic. In the classroom, where one would expect flawless calculations, Kummer often found himself pausing mid-problem, turning to his students for help with even the simplest numbers. One day, while teaching, he arrived at what seemed like an easy step. “Seven times nine,” he began confidently. Then his voice faltered. “Seven times nine is… er… ah… ah… seven times nine is…” The room grew quiet. Students exchanged glances. Finally, a voice from the front row broke the silence. “Sixty-one,” the student said. Relieved, Kummer nodded and wrote 61 on the blackboard. But before the chalk could settle, another student quickly stood up. “Sir, it should be sixty-nine.” Kummer turned, slightly puzzled but entirely serious. “Come, come, gentlemen,” he said, raising his hand. “It can’t be both. It must be one or the other.” He tried to reason it out logically. “The product cannot be 61,” he said, “because 61 is a prime number. It cannot be 65, because 65 is divisible by 5. It cannot be 67, for it too is prime. And 69 is clearly too large…” He paused, thinking carefully, then concluded with quiet satisfaction: “Only 63 is left.” And just like that, through pure reasoning rather than calculation, Kummer arrived at the correct answer — reminding everyone in the room that while arithmetic may fail you, deep mathematical thinking rarely does.

This was the famous maths puzzle that took about 358 years to be solved. In 1637, the mathematician Pierre de Fermat wrote a statement in the margin of his book. The statement was that the equation aⁿ + bⁿ = cⁿ has no solutions in whole positive numbers when the value of n > 2. Fermat also claimed that he had a proof, but the margin was too small to write it. However, he never revealed this proof during his lifetime. Because of this, the statement became a major puzzle for mathematicians. For more than three centuries, many of the greatest mathematicians tried to prove it, but no one succeeded. Then, in 1994, the British mathematician Andrew Wiles, after working on it for about 10 years, finally proved the theorem.

Sir Srinivasa Ramanujan invented a very interesting magic square. Take a look at it. If you add the numbers horizontally, vertically, or diagonally, you always get the same total, which is 139. That is why it is called a magic square. Now, what is truly magical about it? He created this square using his birth date. If you observe the starting numbers carefully, they represent 22 December 1887. This shows how deeply he used to think and analyze.

An infinite number of mathematicians walk into a bar. The first one orders a beer. The second one, half a beer. The third, a quarter of a beer. And so on... The bar man says "you're all idiots" and pours two beers.