Peel the potatoes and carrots. Dice them so each cube is about 1/2 inch. Add the potatoes to a large pot and cover with cold water. Put on the stove over medium high heat. Add the carrots to a regular-sized pot and cover with cold water. Put on the stove over medium high heat. Once the potatoes and carrots begins to boil, give them a stir and place the lids on the pots. You might also want to turn down the heat to just above medium. Let boil for 8-13 minutes. Test with a fork to check if they are done before you turn off the heat.
Drain the potatoes and carrots in a colander, combined, and let them cool for 10-15 minutes. Put in a large bowl, cover with plastic wrap, and put them in the fridge until they are chilled, at least 2 hours.
About 3 hours before serving, get the dressing for the salad ready. In a small bowl, combine the minced garlic, mayo, salt, and pepper.