Let egg whites stand at room temperature for 30 minutes.
Meanwhile, in a heavy 2-quart saucepan, stir together sugar, corn syrup, and water. Cook and stir over medium heat until mixture comes to boiling. Clip a candy thermometer to the side of the pan. Cook mixture, without stirring, to 234 degrees F (soft-ball stage).
In a large mixing bowl, beat egg whites with a sturdy free-standing electric mixer on medium speed until stiff peaks form (tips stand straight). Gradually pour about half of hot syrup in a thin stream over whites, beating on high for about 3 minutes, scraping sides of bowl occasionally.
Meanwhile, cook remaining syrup to 260 degrees F (hard-ball stage). Gradually pour remaining syrup in a thin stream over whites, beating on high speed for 5 to 6 minutes or until candy just starts to lose its gloss. Beat in vanilla. Drop a spoonful of candy mixture onto waxed paper. If it stays mounded, it's been beaten enough. If not, continue beating until the mixture mounds. Immediately stir in chopped nuts, if you like.
Quickly drop remaining mixture from a teaspoon onto waxed paper. If mixture flattens out, beat 1/2 to 1 minute more; check again. If mixture is too stiff to spoon, beat in a few drops of hot water until candy is a softer consistency. Store in a tightly covered container. Makes about 1-1/2 pounds (48 servings).