EXTRAS
* * SPOILER ALERT * *
Items below that appear in red contain spoilers.
DOMINIK HAYES SERIES
THE MILLENNIUM PROBLEMS
The Millennium Problems were inspired by 23 problems organized by German mathematician David Hilbert in 1900. To date only one of these, the Poincaré conjecture, has been solved.
Click here to find more information on the problems and the Clay Mathematics Institute.
See “The Millennium Problems” by Professor Emeritus Bernard Russo of the University of California, Irvine, for a more history and learn why the problems are so difficult.
INTERESTING MATH PROBLEMS/FACTS
The Collatz conjecture, set forth in 1937, is one of mathematic’s most famous problems. It’s simplicity is a trap that can burn up untold hours with no meaningful results to the extent that math professors warn their students not to succumb to its spell.
The conjecture begins by picking any positive integer, x. If x is even, divide it by 2 to get the next number. If the initial x is an odd number, multiply it by 3 and add 1. Then repeat the process. The ultimate result is the number 1.
Here’s an example. Let’s start with 13. The next number is 40 (13 times 3 plus 1). The following numbers are: 20, 10, 5, 16, 8, 4, 2, and 1.
Mathematicians have proven this is true for numbers with up to 19 digits, but is it true for all positive integers?
In an earlier draft of A Rude Awakening, I had a scene where Jazz had a little brother who was incessantly annoying. So she told him she would give him $100 if he could find a number that didn’t follow the pattern.
The Goldbach conjecture was developed in 1742 by Christian Goldberg and states that every even natural number greater than 2, is the sum of two prime numbers.
Start with 44. It is the sum of 3 and 41, or 7 and 37, or 13 and 31.
It has been shown to be true for numbers up to four quintillion (1018), but is it true for larger numbers?