Mathematical Thinking

Pythagoras said “Everything is Number” – in Greek – when letters differed from numbers only by an apostrophe: alpha was the letter “a” and alpha’ was the number “1”.

Since the introduction of Latin and Roman numerals in the West, the ‘sound of letters’ was separated from the ‘quantity of numbers’.

In mathematics, algebra deals with letters, geometry with measuring, arithmetic with numbers.

Number theory, as the queen of mathematics, is of such a high degree of abstraction that it touches the realm of philosophical thinking.

My study of alphabets and number representation has made me conclude that the use of Arab numbers stems from the fact that the Arabic language has the best consistency between representing sound with letters and quantity with numbers.

We use symbols when we study mathematics. We also use symbols when we write instructions to computers.

But nowadays, we don’t communicate with computers any more: we use software packages that talk to computers via all sorts of intermediaries.

My mathematical concepts are based on number theory on one hand and on the principles of computing on the other. Where number theory has to do with the intricate discoveries that numbers can surprise us with, computing has to do with rigorous logic: a computer is always more consistent than the thinking of any human being.

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