How Computers Score at Maths
As calculators they score high.
They do lightning, precise numerical calculations and symbolic transformations better than people.
Get the picture from the Guide to Available Mathematical Software.

But they have technique rather than knowledge, they do not understand, and their general problem solving skills are weak for this reason.
On the scale of mathematical sophistication computers are 2500 years behind people.


Abstraction and Reuse
Abstraction is the very essence of mathematics, and the purpose of abstraction is reuse.
For 2500 years since classical Greece, mathematicians have constantly sought the right concepts, notations and theories to underpin applications in commerce, science and engineering.
Chosing the right concepts and notations is essential to effective reuse and until computing builds upon mathematics it will fail to realise the true potential for reuse.


Computer Programming
You need people to decide what a computer should do.
Once that is settled it should be up to the computer to sort out the details.
Precise communication of requirements by dialogue with the computer should mark the end of human involvement, the computer will program itself.
Most people won't even think about programs, they will just have problems which computers help them to solve.


Do it Right?
Its no use idealising about how things should be done, its won't happen that way in the real world.
Or will it? 

Integration, Representation, Logic
When computing power is piped into the home like electricity, there will be coherent global standards for representation of information.

A universal lingua characteristica based in pure logic will dissolve many of today's integration problems.

