Did Statistical Science Win World War 2?

John Keegan, the famous military historian, wrote an interesting book, Intelligence In War, back in 2003, which apparently he has updated in 2004. In it, he talks about the importance of mathematics and statistics in estimating the likely probability that certain signals meant certain letters or numbers in a code, and what a contribution mathematicians from England, Poland, and the United States made to breaking the supposedly unbreakable "Enigma" code of the Germans at places like Bletchley Park (a mansion in England where mathematicians would work on the problems posed by German encryption). John Keegan points out that unlike today where knowledge of foreign languages is often the key to breaking the code of terrorists, the ability to break the German encryption codes was due entirely to mathematics and the effective use of probability theory applied to vast quantities of recorded German messages sent in code.