Why it happens
Lumps usually mean some of the potatoes weren't cooked all the way through, so the firm pieces won't mash down. This happens when potatoes are cut into uneven sizes, or drained before the largest pieces are tender. Mashing potatoes after they've cooled also makes lumps more likely, because cooled starch firms up. Beating hard to get rid of lumps releases too much starch and makes the mash sticky and gluey.