Hey, Historians,
How sure are we that the current year is actually 2,014 years after Jesus's birth? Is it not possible that a couple years somehow 'fell through the cracks' and weren't accounted for. It's not hard to imagine a few years were unaccounted for when the Roman empire fell (let's say in the 400's) since the Barbarian tribes would have had different calendars than the Roman empire did. Wouldn't the collapse of a major empire and a transition from one culture to another be a point of concern for accounting time?
Modern historians date the birth of Jesus to between 2 and 7 BC, so, strictly speaking, no, it's not 2014 years after the birth of Jesus. The medieval scholars who did the original dating weren't accurate, but getting everybody to agree on changing the dates would be pretty much impossible, so the world just stumbles along as usual.
Others have already said that it is in fact not 2014 years after the birth of Jesus.
I'd like to point out that your reasoning that years might be unaccounted for is, at least for this period in history, wrong. Firstly people in Europe didn't really count years a few thousand years ago: they mostly named years after rulers (Greeks after their archons, Romans after their consuls), perhaps counting how many years someone had ruled. Secondly, even if they had lost track of the years that doesn't mean we would. After all, we have more to go by than just their count. When the Western Roman Empire stopped existing, the Eastern Roman Empire went on for another millenium or so. That's 1000 odd years of unbroken records of emperors. And we are not limited to Europe of course. I'm no expert on China, but I believe we can string the various empires and dynasties quite reliably back to well before the year 1. By combining what is known from various regions (X ruled here, Y ruled there) it is possible to work out if any particular list of years has an error or not. (And indeed, this is how we know that Jesus probably was born in some year Before Christ.)
We're sure. Apart from the fact that Jesus wasn't born in 1 AD, but 4 BC or prior, there is the Phantom Time Hypothesis, but it is widely regarded as a conspiracy theory, and the combination of astronomical data, archaeological evidence, and the lack make it patently absurd.