Even though Calculus is often taught starting only at the college level, mathematicians have shown that it can be taught to kids as young as at the age of 5, suggesting that it should be taught not just to those who pursue higher education, but rather to literally everyone in society.
2. There's a mathematical theorem called the "hairy ball theorem." It states that you can't comb a hairy 3D ball without getting a cowlick. It also dictates that, given at least some wind on Earth, there must at all times be a cyclone somewhere.
3. A Russian mathematician named Grigori Perelman solved a 100 year old math problem. He declined the Fields medal, $1 million in awards, and later retired from math because he hated the recognition the math community gives to people who prove things.
4. One of mathematician John von Neumann's lecturers said "Johnny was the only student I was ever afraid of. If in the course of a lecture I stated an unsolved problem, the chances were he'd come to me at the end of the lecture with the complete solution scribbled on a slip of paper."
5. You can count to 12 on one hand by using your thumb to count the bones of each finger. This might explain the base 12 and base 60 number systems we use for telling time and measuring angles.
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In 1736, a mathematician named Leonhard Euler was trying to find a way to cross every single one of the seven bridges of Königsberg exactly once. He realized that this was, in fact, impossible and based on that created a new area of mathematics called Graph Theory.
7. Belphegor's Prime is a prime number that is also a palindrome. It's named after the Prince of Hell for ingenious inventions because it contains two sets of 13 zeroes with 666 in the center. The palindromic prime number is 1000000000000066600000000000001.
8. There are prime numbers (Illegal prime) that are illegal to possess or distribute. One of the first ones, found in 2001, was used to bypass copyright protection on DVDs.
9. A Chinese mathematician named Yitang Zhang could not get an academic job upon graduating, having to work as an accountant and a delivery worker for a New York City restaurant. He later went on to solve a math problem that had been unsolved for 150 years and won a MacArthur Genius Grant.
10. The sum of all numbers on a roulette wheel is 666.
Mathematicians have jokingly proposed a standard unit of measurement for beauty called the “millihelen.” Inspired by Helen of Troy, a millihelen is defined as “the amount of beauty required to launch one ship.”
12. The Dunbar's number is a theoretical upper limit of the people one can maintain stable relationships with. It is suggested between 100 and 250. So if a town's population is below the Dunbar's number, it is more likely to have harmony and peace than a larger town or city.
13. The sum of odd numbers starting at 1 is always a square number.
14. I, V, X, L, C, D, M aren't the only letters used in Roman numerals; "S" is used to represent ½ along with dots for other fractions.
15. The number 142,857, when multiplied by 1,2,3,4,5, or 6, is an anagram of itself. The fractions 1/7 through 6/7 also are forms of 142857, and the right six digits of any higher multiple plus the remaining left digits will equal an anagram of 142857.
The inverse of 999,999,999,999,999,999,999,998,999,999,999,999,999,999,999,999 gives the fibonacci sequence in 24 digit strings.
17. The percent symbol (%) is supposed to be a fraction of zero over zero. There are higher symbols such as the permille sign (‰) and others for smaller percentages.
18. Tree(3) is a number so large that Graham's number of people wouldn't be able to begin calculating it. The only thing we know about Tree(3) is that it is finite. We do not know what it is or even how many digits there are.
19. The number 8 is such a lucky number in China that the Chinese government scheduled the Beijing Olympics to begin 8 seconds after 8:08 on 8/8/2008.
20. Trigonometry was invented by Muslim mathematicians as a way for worshippers to calculate the direction to Mecca for prayer.
6174 is Kaprekar's constant. If you have a 4 digit number with at least 2 distinct digits, order the numbers within it in ascending and descending order, subtract the smaller number from the larger, and repeat with the result, you'll eventually always end up with 6174.
22. 73939133 is the largest known prime number that, if you keep removing digits from the right, will always leave a prime number.
23. Abū al-Wafā' Būzjānī was a Persian mathematician and astronomer who worked in Baghdad and made important innovations in spherical trigonometry.
24. In 1887, a mathematician named Henri Poincaré received a prize for his work on the stability of the solar system. A year later, after finding an error in his own work, he published a paper contradicting it, which led to the development of chaos theory.
25. The longest mathematical proof is 15,000 pages long, involved more than 100 mathematicians and took 30 years just to complete it.