YSK: To prevent mashed potatoes from being gummy, boil the potatoes whole.
When a potato cooks, the starches contained in each cell are released as the cell walls break down. These starches absorb the potato's internal moisture and swell and soften. These two processes are what transform a raw, hard potato into a cooked, softer potato fit for mashing.
If you cut your potatoes up before boiling them, the starches absorb the internal potato moisture as well as the water in which they're being boiled. If they boil for too long, they absorb too much water and your mashed potatoes will become gummy. The difference between perfectly cooked potato pieces and soggy pieces can sometimes be as little as a minute or two.
An easy workaround is to boil potatoes whole. They'll take a bit longer to cook but you can leave them in the hot water after boiling without undesirable effects, keeping them warm until it's time to mash them. I start my potatoes boiling as soon as I begin cooking and mash them immediately before dinner.
If they need more moisture, you can add a bit of hot potato boiling water or another liquid. This way, you have more control of their moisture content.
I've never had gummy mashed potatoes, and I've been giving them a 1" chop for years. Takes 10 minutes to cook then drain them right away. They come out fine every time. Plus the butter melts right away when you throw everything together.
To be totally transparent, I never had gummy mash until my wife and I got together. She used to boil her potatoes, let them sit in the hot water until closer to dinner, then whip them with beaters. She's from Ireland, I joke that the potato blight was a failed preemptive strike to prevent her from ever touching a potato.
Pretty sure it's the beaters (assuming that's an electric hand mixer type-thing, i've never heard them referred to by that term) that made them gummy. Over mashing will break up the cell walls too much, releasing the starches and ruining the texture. Cooking chopped or whole doesn't matter as much, since the number of cells broken by chopping is negligible. And the skin is water permeable anyway.
You are correct, op has no idea what they are talking about. Potatoes contain two different types of starch, in differing amounts depending on the kind of potato. Amylase, and Amylopectin, the second when overworked will make gummy potatoes. Overworking them is what makes them gummy.
1" dice, fork tender, food mill, ricer, or fork, perfect. If you want them extra smooth simmer in milk or cream (not water), strain and mash, then fold in the drained liquid gently with a spatula.
And the 'hot potato boiling water' contains mostly Amylase. If you add that it will make them more slippery/slimey.
It's not "the only way to avoid gummy mashed potatoes", it's just an easy way to guarantee it if you keep having the problem. If you don't, then do it your way. It's harder, but you already have it nailed, so don't worry about it. Cooking faster can be a good thing if you want it, and are able to deal with them exactly when they need to be dealt with. Some people would very much prefer an easy guarantee even if it takes longer.
You have to select starchy potatoes, not waxy, and let them steam dry (e.g. drain water in metal colander and toss in a warm oven or on the stove for a bit). Mix in the seasoning and milk/butter after they are mostly mashed for better control of consistency.
Edit: was agreeing. Glueyness is not because they are cut up.