Such is a very brief résumé of the evidence showing that the numerals of the Punjab and of other parts of India as well, and indeed those of China and farther Persia, of Ceylon and the Malay peninsula, might well have been known to the merchants of Alexandria, and even to those of any other seaport of the Mediterranean, in the time of Boethius. The Brāhmī numerals would not have attracted the attention of scholars, for they had no zero so far as we know, and therefore they were no better and no worse than those of dozens of other systems. If Boethius was attracted to them it was probably exactly as any one is naturally attracted to the bizarre or the mystic, and he would have mentioned them in his works only incidentally, as indeed they are mentioned in the manuscripts in which they occur.
In answer therefore to the second question, Could Boethius have known the Hindu numerals? the reply must be, without the slightest doubt, that he could easily have known them, and that it would have been strange if a man of his inquiring mind did not pick up many curious bits of information of this kind even though he never thought of making use of them.
Let us now consider the third question, Is there any positive or strong circumstantial evidence that Boethius did know these numerals? The question is not new,
nor is it much nearer being answered than it was over two centuries ago when Wallis (1693) expressed his doubts about it[[333]] soon after Vossius (1658) had called attention to the matter.[[334]] Stated briefly, there are three works on mathematics attributed to Boethius:[[335]] (1) the arithmetic, (2) a work on music, and (3) the geometry.[[336]]
The genuineness of the arithmetic and the treatise on music is generally recognized, but the geometry, which contains the Hindu numerals with the zero, is under suspicion.[[337]] There are plenty of supporters of the idea that Boethius knew the numerals and included them in this book,[[338]] and on the other hand there are as many who
feel that the geometry, or at least the part mentioning the numerals, is spurious.[[339]] The argument of those who deny the authenticity of the particular passage in question may briefly be stated thus:
1. The falsification of texts has always been the subject of complaint. It was so with the Romans,[[340]] it was common in the Middle Ages,[[341]] and it is much more prevalent
to-day than we commonly think. We have but to see how every hymn-book compiler feels himself authorized to change at will the classics of our language, and how unknown editors have mutilated Shakespeare, to see how much more easy it was for medieval scribes to insert or eliminate paragraphs without any protest from critics.[[342]]
2. If Boethius had known these numerals he would have mentioned them in his arithmetic, but he does not do so.[[343]]
3. If he had known them, and had mentioned them in any of his works, his contemporaries, disciples, and successors would have known and mentioned them. But neither Capella (c. 475)[[344]] nor any of the numerous medieval writers who knew the works of Boethius makes any reference to the system.[[345]]