Snow-on-the-mountain (Aegopodium podagraria) was introduced in English gardens during the Middle Ages by the Romans, and was used as an herb. Due to its vigor, it escaped to the wild where it made itself at home on the edge of woodlands and in waste places. Historically it has been used medicinally as a treatment for gout, bee stings, burns, wounds, etc. In his book The Herbal, John Gerard made this comment in 1633: “… it groweth of it selfe in gardens without setting or sowing, and is so fruitful in his increase, that where it once hath taken root, it will be hardly got out againe, spoiling and getting every year more ground, to the annoying of better herbs.” (Nearly 400 years later, we are still battling this plant!)
A few people love it as a groundcover, but most people have grown to thoroughly dislike it, to say the least. It can take over a garden so aggressively that some people even consider bulldozing the entire garden. It spreads like wildfire, by rhizomes and by seed. Under the right conditions, 3 little starter plants can spread 30 feet in two years! This is a serious pest for any climate that gets regular rainfall or moisture. It smothers other plants up to 12 inches tall. Roots break off (especially in hard, packed soil) and sprout, even a year or more later.
There are several ways to try to get rid of it. In loose soil, you can pull/sift it out of the soil by hand, with lots coming back from parts you missed. Even the smallest piece of root left behind will start a new patch. You can try multiple applications of Roundup: spray, wait until new growth starts, then spray again. You’ll have to repeat this process multiple times, for several years. You can also try a combination of Roundup and covering the area with black plastic or carpet. You would have to leave that on for 2 years at least, and still monitor for any shoots coming up. A possible biological control: groundhogs. They love it. They, however, have their own downsides in the garden.