How many asteroids have been discovered since 1980? A lot of asteroids. This video, by Scott Manley, shows them all as they were discovered over time. You can see new discoveries in white, with their color changing to show where they are in relation to the inner solar system.
Here's some more info on it from Manley himself:
Notice now the pattern of discovery follows the Earth around its orbit, most discoveries are made in the region directly opposite the Sun. You'll also notice some clusters of discoveries on the line between Earth and Jupiter, these are the result of surveys looking for Jovian moons. Similar clusters of discoveries can be tied to the other outer planets, but those are not visible in this video.Space: no matter how cool you think it is, you can always be surprised it.
As the video moves into the mid 1990's we see much higher discovery rates as automated sky scanning systems come online. Most of the surveys are imaging the sky directly opposite the sun and you'll see a region of high discovery rates aligned in this manner.
At the beginning of 2010 a new discovery pattern becomes evident, with discovery zones in a line perpendicular to the Sun-Earth vector. These new observations are the result of the WISE (Widefield Infrared Survey Explorer) which is a space mission that's tasked with imaging the entire sky in infrared wavelengths.