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.