The nth Dedekind number is the number of monotonic Boolean functions on n variables, i.e. functions that take in n Boolean variables (which can only take on values of 0 or 1, or some equivalent representation), output one Boolean variable and are non-decreasing in each variable.
Currently, D(0) through D(9) are known, with the ninth one just being discovered this year. Will D(10) be known before 2040?
1,000
1.00@PlasmaBallin Fwiw I was the one to derive the series using differences of powers and the prior dedekind numbers. Worked up to the 7th dedekind and didn't go further mostly because I've been working doubles at work. I'm 100% confident the 8th and 9th can be derived this way, though verification of the results themselves might be another problem. Deriving the 8th, 9th, and then the 10th, and having the 10th fall in the estimated bounds by various people, would be a positive but weak indicator that the method works. If I get more time, I'll share it.