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.
2. 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.
3. The sum of all numbers on a roulette wheel is 666.
4. 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.”
5. 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.
The sum of odd numbers starting at 1 is always a square number.
7. 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.
8. 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.
9. 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.
10. 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.
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.
12. 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.
13. Trigonometry was invented by Muslim mathematicians as a way for worshippers to calculate the direction to Mecca for prayer.
14. 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.
15. 73939133 is the largest known prime number that, if you keep removing digits from the right, will always leave a prime number.
16Abū al-Wafā' Būzjānī
Abū al-Wafā' Būzjānī was a Persian mathematician and astronomer who worked in Baghdad and made important innovations in spherical trigonometry.
17. 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.
18. The longest mathematical proof is 15,000 pages long, involved more than 100 mathematicians and took 30 years just to complete it.
19. A mathematician named Per Enflo solved Problem 153 in the "Scottish Book" in 1972 and was awarded a live goose as promised by Polish mathematician named Stanisław Mazur, who posed the problem in 1936.
20. In 2012, a mathematician named Vi Hart sent an open letter to Nickelodeon proving Spongebob's Pineapple was geometrically impossible. Pineapple designer Kenny Pittenger responded on his blog (in video description) by posting a new "mathematically correct" design. This new design is now used on the show.
8675309 is the fourth most common 7-digit password, number one, of course, is 1234567.
22. A Narcissistic number is a number that is the sum of its own digits each raised to the power of the number of digits.
23. The line between the 2 numbers in a fraction is called the Vinculum.
24. A mathematician named Fry Lewis Richardson discovered that it is impossible to measure the length of coastlines in a meaningful manner. This so-called Coastline Paradox later led to the creation of the field of Fractal Geometry.
25. A female English mathematician named Ada Lovelace wrote an algorithm in the mid-1800s designed to be carried out by a machine. As a result, she is often regarded as the first computer programmer.