Place the diced potatoes in a pot of salted cold water and bring to a boil over medium-high heat. Cook until the potatoes are fork-tender, about 6-8 minutes. Drain well.
Place the potatoes in a single layer on a plate or baking sheet to allow them to cool more rapidly. Refrigerate to speed up the cooling process.
Once the potatoes are cooled, mix in the onion, celery, carrot, scallions, and mayonnaise; season with salt & pepper to taste, then serve.