Line a baking sheet with waxed paper. In a large heavy saucepan, combine the sugar, corn syrup, and water. Bring to a boil over moderately high heat, stirring constantly with a wooden spoon to dissolve sugar. (Avoid splashing mixture onto side of the pan.) Boil for 3 minutes. If using a candy thermometer, carefully clip to side of pan, making sure the bulb is immersed but not touching the bottom of the pan.
Cook over moderate heat, without stirring, to 260° on candy thermometer, hard-ball stage (15 to 18 minutes). (Or, use this cold water test. Using a spoon, drop a small amount of hot mixture into very cold, not icy, water. Dip your fingers into the water and form the mixture into a ball. Remove the ball from the water; it should not flatten but can be deformed by pressure.)
Remove pan from heat; remove the thermometer from saucepan. In a large bowl, with very clean beaters and an electric mixer on medium to high, beat the egg whites until stiff peaks form. Slowly pour hot syrup mixture in a fine stream over egg whites, beating with electric mixer on high for 3 minutes and scraping the side of the bowl occasionally.
Add the vanilla. Continue beating with the electric mixer on high just until candy starts to lose its gloss and holds soft peaks (5 to 6 minutes), scraping the side of the bowl occasionally. Stir in nuts (if using).
Working quickly, drop by teaspoonfuls onto waxed paper. If the divinity becomes too stiff, beat in very hot water, a few drops at a time, until it is a softer consistency. Cool completely. To store, cover tightly.
Choose a dry day. Because sugar absorbs moisture from the air, divinity may never set up if you try to make it on a humid day.
Start with room temperature egg whites. They heat up to a greater volume than cold egg whites.
Use a heavy-duty, freestanding electric mixer. Beating divinity puts a strain on a mixer's motor. Portable mixers and lightweight, freestanding mixers may not have heavy enough motors.
Follow the recipe directions carefully. Timing is important. Adding the hot syrup too quickly or not beating the candy mixture long enough can cause divinity to fail. Overbeating the divinity will cause it to set up before you can drop it into individual pieces.