1. Bring a large pot of water to a boil. Add the potatoes and cook over moderate heat for 15 to 20 minutes, or until tender. Drain and let cool.
2. In a serving bowl, mix the Dijon mustard, lemon juice, and salt and pepper; stir in mayonnaise. Cut the potatoes into chunks and add to serving bowl. Gently mix in celery and carrots. Taste for seasoning, adding more mayo, salt, or pepper as desired.