somewhere in there we invent a quicker and better way to mine bitcoins. I am taking a wild guess at it but I think we will end mining bitcoin sometime before 2100 comes around I am not sure when that would be though.
Nonsense. Absolute nonsense. Please avoid answering any technical questions about bitcoin until you've taken the time to learn a little bit about how it works. Otherwise you are just going to spread misinformation and cause more confusion.
Inventing a quicker way to mine bitcoins does NOT significantly speed up the release of new bitcoins. It just increases the difficulty.
Every 2016 blocks (approximately every 2 weeks) EVERY node on the Bitcoin network re-calculates the difficulty target.
If it takes less than 20160 minutes to mine those 2016 blocks, then the blocks are happening too fast and the difficulty is adjusted proportionally to slow the block solving back down to 10 minutes average per block.
If it takes more than 20160 minutes to mine those 2016 blocks, then the blocks are happening too slow and the difficulty is adjusted proportionally to speed the block solving back up to 10 minutes average per block.
So, if you suddenly came up with a new technology (and implemented it immediately after a difficulty retarget) that increased everyone's ability to solve blocks so that they could solve them 4 times as fast... The next 2016 blocks would be solved in 5040 minutes (approximately 3.5 days) instead of 2 weeks. Then the difficulty would automatically be increased to be 4 times as difficult, and blocks would go back to being solved once every 10 minutes again. You would only shave, at most, 11 days off of the 100+ years estimate.