The mathematical skepticism which such statements may awaken is usually mitigated by reflection, since it soon appears that philosophical difficulties abound in all domains of knowledge, and that mathematical results continue to inspire relatively the highest degrees of confidence. The unknowns in mathematics to which we aim to direct attention here are not of this philosophical type but relate to questions of the most simple nature. It is perhaps unfortunate that in the teaching of elementary mathematics the unknowns receive so little attention. In fact, it seems to be customary to direct no attention whatever to the unsolved mathematical difficulties until the students begin to specialize in mathematics in the colleges or universities. One of the earliest opportunities to impress on the student the fact that mathematical knowledge is very limited in certain directions presents itself in connection with the study of prime numbers. Among the small prime numbers there appear many which differ only by 2. For instance, 3 and 5, 5 and 7, 11 and 13, 17 and 19, 29 and 31, constitute such pairs of prime numbers. The question arises whether there is a limit to such pairs of primes, or whether beyond each such pair of prime numbers there must exist another such pair. This question can be understood by all and might at first appear to be easy to answer, yet no one has succeeded up to the present time in finding which of the two possible answers is correct. It is interesting to note that in 1911 E. Poincare transmitted a note written by M. Merlin to the Paris Academy of Sciences in which a theorem was announced from which its author deduced that there actually is an infinite number of such prime number pairs, but this result has not been accepted because no definite proof of the theorem in question was produced. Another unanswered question which can be understood by all is whether every even number is the sum of two prime numbers. It is very easy to verify that each one of the small even numbers is the sum of a pair of prime numbers, if we include unity among the prime numbers; and, in 1742, C. Goldbach expressed the theorem, without proof, that every possible even number is actually the sum of at least one pair of prime numbers. Hence this theorem is known as Goldbach's theorem, but no one has as yet succeeded in either proving or disproving it.