In our profession we often come into contact with those who do not understand Pure Mathematics. Some of these are respectful as if entering a shrine; but others, of the baser sort, are contemptuous. These have found the way of progress dark and difficult. Their guides, perhaps, have not inspired them, and symbolism seems far removed from the needs of ordinary human life. They deny that it can have an ideal, that it can have any claim to beauty. They admit that it has some purpose in its application to the practical affairs of life, but that it can have an end in itself is incomprehensible. It is associated in the minds of some with the removing of interminable brackets, and with the chasing of elusive unknowns. Since it deals usually with the variable and not with the particular, and since it is concerned more with deductions from data than with the truth of these data, it has been described as the subject “in which we never know what we are talking about, nor whether what we are saying is true.” It is usually considered unwise to express lack of appreciation of the works of a great painter or sculptor or poet, but there have been men of intellect who not only have expressed ignorance of scientific method, but have also been inclined to exaggerate that ignorance. The questions that such a criticism of the subject naturally raises are: Is this hostility justified? Can it be wholly attributed to feebleness of insight? For it is possible that although Mathematics need not fail to supply the necessary stimulus to intellectual thoughts and aspirations, yet its exponents may fail in the interpretation and expression of its ideals; and it must be admitted that the way of mathematical learning can be, and often is, a dull and cheerless one, especially for him whose aptitude is weak. The inherent beauty of mathematical reasoning may be marred by methods that are brutal, and its outlook warped by unduly insisting on the necessity of the moment.