Hi. I'm Steve Jones, and I'm going to tell you something about mathematical symbols.
Now, obviously if you were going to count, then you can do it verbally: one, two, three,
four, five, six. It's very easy. But if you want to convey that information to somebody
else, you need some way of doing it. And fairly obviously, also, the Greeks and Romans came
up with similar systems. Not altogether surprising since most Romans also spoke Greek, or educated
Romans spoke Greek. So here the symbols are simple representations. One is a single stroke.
Two is two strokes. Three is three strokes. Four is four strokes. The trouble is when
we get to 596, we have a big problem in deciding what the number is, because 596 strokes does
not make a sensible thing to work with. So we have to convey a meaning without actually
putting all of the counting in it. So the meaning, so we get to five, and we have a
single digit for five, in both forms. The problem with the Greeks was they couldn't
agree on what the form should be. So each different state had its own form and, therefore,
the Greeks were in a confusion over counting. The Romans didn't have a problem. Although
you probably are aware that often where the Roman four is, you will see four vertical
lines like the Greek one. And also, the nine also can be represented in the same way. So
that's a similarity. These systems were very effective for doing what the Romans and the
Greeks wanted. Unfortunately, later on, things were developing so rapidly that you needed
a quicker number system. And therefore, to create a set of individual digits from actually
from zero to nine, but I've just done here one up to ten. So from zero to nine are the
individual digits. This again, makes representing big numbers much easier. Big Roman numbers
were quite cumbersome, would involve lots and lots of digits. Whereas modern Arabic
numbers involve just four, five, six, seven digits. A big number will contain many more,
of course, but they are reasonable numbers. But these aren't the only symbols that we
used. Obviously, we needed symbols to tell us what to do. And some of the important ones
are these, which you are probably familiar with. These are the operations symbols, or
operators. We have minus, plus, divide, and multiply. And these came quite late. These
were not early developments. Once we have these, we can operate on our counting numbers.
But still we can't actually do mathematics. And for that, we need developments like those
of Leibnitz and at the same time, Newton and people in Britain were doing the same thing,
where we develop the calculus notation. Each time, we need new symbols to represent new
things, new operations. These are objects. This is an operation. So we need special symbols
all the time to develop our mathematics. And some of the most interesting ones are things
like this, which we know is infinity. Nobody has ever been able to define what infinity
is, but we have a symbol for it. In other words, we can write a symbol for something
that is impossible to imagine, like most of mathematics.