Fill a large pot with water. Fill a smaller pot with water. Turn both on high heat.
Scrub potatoes. Add to large pot. Bring to a boil.
While potatoes are cooking, you're going to cook the eggs in the small pot. Bring to a boil. Lower to a simmer. Slowly lower eggs into water. Cook for 15 minutes. Drain water and run cold water over eggs. Place eggs in refrigerator.
Cook potatoes 20-25 minutes or until potatoes are crisp tender.
When potatoes are done, drain water. Add cold water. Repeat. The skins should easily come off with a little peeling. Remove as much skin as possible (you don't have to get all of it).
Place potatoes in refrigerator with eggs.
While eggs and potatoes are cooling, chop celery, dice onion, and grate radish. Place in a large bowl.