The Mathematical Gazette has commenced a series of articles, adapted for the use of school-teachers, on the great mathematicians of former days. No series of the kind could be complete were Pythagoras omitted, for it was he who raised mathematics to the rank of a science, made it a part of liberal education, and evolved a scheme on which it continued to be studied in Europe for more than 2000 years. But though his claim to inclusion is indisputable, the materials for describing his work are sadly lacking. We have a treatise by Aristotle on Pythagorean teaching, but the biography by the wife of Pythagoras is lost, and only fragments of the sketches by Aristoxenus, Dikaiarchus, and Philolaus exist, while the memoirs by Laertius Diogenes, Iamblichus, and Porphyry, on which we have mainly to rely for personal details, are late and include much that is palpably untrue. The reputation of Pythagoras far exceeded that of any of his contemporaries, and so great was it that in the credulous ages miracles and magical feats were freely attributed to him; later these additions tended to make men go to the other extreme, and doubt the truth of everything written about him. Within recent years, however, the available materials have been subjected to critical examination, and the researches of T. Gomperz of Vienna, J. Burnet of St. Andrews, G. J. Allman of Dublin, and P. Tannery of Paris enable us to speak with more confidence than was formerly possible.

We meet to-day to inaugurate a London Branch of the Mathematical Association. This is a step in a process of evolution.

The Mathematical Association is a continuation of the Association for the Improvement of Geometrical Teaching, commonly known as the A.I.G.T., founded in 1870.

I did not join the Association till 1883, but some of its earliest reports are in my possession; to thrse I shall refer

It owed its existence to a profound wide-spread dissatisfaction with the lack of geometrical knowledge, and still more the absence of geometrical power, displayed by students who had passcd through the ordinary school course of Euclid.

The list of suggestions issued by the London Mathematical Society is open to several amendments and possibly improvements.

1. The use of small fractions in the midst of letterpress is often open to the objection that such fractions are difficult to read, and, moreover, very often do not come out clearly in printing. It is especially difficult to distinguish 1/3 from 1/8, and the latter sometimes prints exactly like the former if the type does not ink properly or is slightly uneven. For this reason it would be better to confine the use of these fractions to such common forms as ¼, ½, ¾, 1/3 and to use the notation 18/22 for other fractions ; at any rate small fractions should not be used for both thirds and eighths, and as thirds are usually commoner, it would be well to restrict their use to these.