Why the need for Roman numeral system?

Answer 1

We don't need it today. But it was needed back then because it is thought to derive from an Etruscan tally-stick method of counting. This is backed up by the method used to convert a tally (a series of notches) to a number that could be easily recorded. Tally-sticks would be carved with a series of notches, such as:

IIIIVIIIIXIIIIVIIIIXIIIIVIIIIXIIIIVIIIIXIIIIVIIIILIIIIVIIIIXIIIIVIIIIXIIIIVIIIIXIIIIVIIIIXIIIIVIIIIC

The tally-man would run his finger along these notches to keep a count (of sheep, for instance). When he'd finished counting, he would need to record the total. Let us suppose he stopped counting at this point on the stick:

IIIIVIIIIXIIIIVIIIIXIIIIVIIIIXIIIIVIIIIXIIIIVIIIILIIIIVIIIIXIIIIVIIIIXIIIIVIIIIXIIII

If we physically count the marks, we can see there are 84. However, there's an easy way to convert this tally to a Roman numeral. First, locate the largest value, which is L in this case, and there's just the one. Now locate the next highest mark from the L. That would be X and there are three. The next highest value after the last X is I and there are four. Thus the tally can be recorded as:

LXXXIIII

It is not known when the subtractive system was introduced. Nowadays we say IV means -1+5, or 5-1, which is 4, thus making a subtractive pair, but it's just as likely that a tally of IIII became IV because the symbol following the 4th I is a V (which would be present on the tally stick, even though it was not counted). Thus IV, together, implies III precedes it, and the III can therefore be ignored. Thus the tally becomes:

LXXXIV

The tally stick theory also holds up because a Roman numeral often refers to an ordinal linguistic (first, second, third, etc). As in King Louis XIV, which is read as "King Louis the 14th", and MM, which is read as "20th century", and a.d. MCMLXVII is read as "1967th year of the Lord".

Although some early mathematicians may have used Roman numerals to record numbers, it was not suitable for complex mathematics (although some tried, with some success, such as Dionysius Exiguus in the mid 1st century). But by that time there were many positional numbering systems available to perform mathematics, even as early as 1,500BC (albeit sexagesimal, base-60). Roman numerals were introduced around 4th century BC but were still in use up until the 14th century, by which time Hindu-Arabic became the norm. However, the decimal system first came into being during the 5th century and the number 0 (as opposed to the positional 0) was in common use by mathematicians by the 9th century. So quite how Roman numerals lasted so long is not clear, but there was obviously a need for them or they'd have died out by the 5th century, if not long before.