JT:
The (absurd) math to get to 1914 is in the current daniel book (and i think the bible teach book too), I believe. Basically it goes like this:
the 7 times fortold the 7 years of Nebuchadnezzar's maddness, but it was to also have a second fulfillment
To calculate the time of the second fulfillment, they take the 2520 days (since apparently they used 360 day lunar years at the time, and because there's some random stuff in revelation about 3 1/2 times being 1260 days) and instead make it 2520 years. The basis for this is two random scriptures that cite the concept of a 'day for a year.' These scriptures have nothing prophetic in them, and it's just a complete leap to make the math work.
So, counting 2520 years from 607 (the contrived date of the destruction of jerusalem, which is wrong) you get to 1914.
Now for the problems with their accounting:
First off, the second fulfillment is assumed because daniel was a bit grandious with his "prophecy" (which was really an accounting of historical events to the person that wrote the book) and said that the time of the nations trampling on Jehovah's kingdom would end at the end of the 7 times (or something like that). Since that didn't happen (and since there's no way anyone in the bible could've gotten something wrong) there has to be a second fulfillment that actually happens like daniel said.
Next, there's no basis for the assumption that the 7 times should mean 360 day years just because of some random thing in revelation. If the prophecy was really for us, as they assert, wouldn't god have used a measurement for time that we recognize today? Especially considering it's more accurate? He is the "great timekeeper" afterall, so did he not know how long a year was when the bible was written?
So we've already got two questionable leaps, but now we've got 2520 days. So lets pick a random scripture that says "a day for a year" and use it as justification for the math that we've already put the end date on! Did daniel put a footnote in the origonal text pointing the reader to Numbers and Ezekiel to figure out how to interpret it? Why couldn't we use the scripture that a thousand years is as a day for Jehovah? That would put the end somewhere in the year 2519393 AD.
Continuing on, we've now got 2520 years. What is the length of these years? Well to get to 2520 we had to assume a 360 day year, so where does that put us? We've now got 907200 days, or just shy of 2484 365.25 day years. So, even assuming the date of 607 is accurate (it isn't) that'd put us at the end of 1877 or beginning of 1878 depending on what time of the year in 607 you start counting (BTW, does 1878 ring any bells? It wouldn't for a JW, but we know it was a "marked year" for CTR! He must've been just a hair better at math than the current GB) The only way to get to 1914 is to assume that god meant 360 day years for the 7 times, and 365.25 day years when he said "a day for a year." It's like god didn't want anyone to figure out what he meant!