>I assume that when Jonathan says that the Greeks >were "bad" at arithmetic he means that large number >arithmetic was difficult considering their numeral >system.
What Greeks are we talking about, exactly? Let's not elide this point too quickly. Jonathan writes,
"I made my own times table the way Euclid, Pythagorus Nicomachus learned their's and it's very hard to learn."
So, Euclid, Pythoagorus, and Nicomachus had a very difficult system of arithmetic yet were able to produce wondrous mathematics. Was every Greek a Euclid, or a Pythagorus, or a Nicomachus? Of course, we shall never know for sure, but I doubt it. Euclid et al were giants of the intellect and I suspect that not every Greek, however worthy an individual he may have been, could think at that level. So, Jonathan is comparing Euclid and Pythagorus to your neighbor's 10 yr old struggling with fractions. Not a useful comparison, I think.
My point generalizes. For example, the Ancient Egyptians had a very difficult system of fractions, and a very difficult system of writing. Egyptian boys spent years in the temple schools learning both. One can marvel at just how much they could calculate, building palaces, temples, surveying land, etc., but the people who could make these calculations were very few in number. A temple education was reserved to a select few who were ultimately initiated into the mystery cults.
In them days, most people could neither read nor calculate. Not enough has changed since, I think. So, to suppose that good arithmetic is not necessary to good mathematics, because Euclid managed, beggars the imagination.