Peel and quarter potatoes. In a kettle cover potatoes with salted cold water by 2 inches and simmer until just tender, about 25 minutes. Add tomatoes and simmer 5 minutes. Drain vegetables in a colander and transfer potatoes to a large bowl and tomatoes to a cutting board. With a potato masher mash potatoes and keep warm, covered. Cut tomatoes into thin julienne strips.
Using largest holes of a 4-sided grater, grate zucchini. Pit olives and cut into thin julienne strips. Mince garlic. In a large nonstick skillet heat oil over moderately high heat until hot but not smoking and sauté garlic, stirring, until golden. Add tomatoes, zucchini, olives, and salt and pepper to taste and sauté, stirring, until zucchini is just tender, about 3 minutes.
Stir zucchini mixture into potatoes until combined well and season with salt and pepper. Potatoes may be made 1 day ahead and chilled, covered. Reheat potatoes, covered, in a 350°F oven about 30 minutes.