My fellow blogger and friend, Layman, kindly picked up on the question of zero that I mentioned a while back. I was looking for evidence about whether or not zero was banned by the church in the Middle Ages. My feeling is that this is another anti-Catholic myth. Layman is reading a book called 1491 on pre-Columbian American civilisations by Charles Mann. Mann mentions the church ban on zero in passing and Layman emailed him to ask about it. Mann’s reply is on the ChristianCadre blog. The rest of my post refers to Mann’s email.
I would firstly say that I have studied a manuscript written by the Cambridge University maths lecturer in 1508 and it uses zero as a matter of course. So do all 16th century maths textbooks. I've looked at the collected letters of Gerbert (that’s Sylvester II) already and not found anything related to zero. However, he is credited with being one of the first to introduce Arabic numerals into Western Europe. I'll also check Sacrobosco's Algorismus as that was the main medieval textbook on arithmetic. The earliest version I've seen was printed in 1488 and I think that uses zero (I wasn't looking but it covers normal adding up and multiplying that is impossible without zero). I might dig back to look at some of the manuscripts which date from the thirteenth century.
An important question here is whether we are talking about a naked zero or zero used as part of another number (ie. 490 is not zero but we use zero to write it). For most kinds of arithmetic, you don’t need a naked zero and this might be what is rare in medieval sources. Merchants certainly don’t use it unless they are giving their goods away for free. However, the use of zero as part of other numbers is common from at least the early thirteenth century and it doesn’t appear to be controversial. Contrary to what Mann says, all medieval accounting records that I have seen use Roman rather than Arabic numerals. This is what we would expect as merchants continued to use the abacus to add up rather than arithmetic. Hence, they didn’t need a zero.
Dick Teresi's Lost Discoveries only refers back to Kaplan and Joseph so it is not much help. I’ll try and look at Kaplan and Dantzig’s books in the library on Tuesday and see if they shed any further light. The one thing we are missing is any kind of primary documentation.
Thank you to Layman and Charles Mann for helping make some progress with this.
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