Negative Numbers


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There is a bit longer history to the negative numbers than what you will find here - so investigate links on the side if you want to find more.

People thought about the negative numbers for a long time before they accepted them as 'real' numbers. Sometimes they would get negative numbers as solutions to some equations, as well as use them to represent them as 'debts' when there was not enough to be covered by a positive value (for example when subtracting a larger from a smaller number).

But it was only in the 16 th century that they became famous. Girolamo Cardano, a famous Italian mathematician and medical doctor (or physician - that is how they were then called) for the first time described negative numbers as 'fictitious' and accepted the possibility of them being the solutions to equations. He described this in his famous book Ars Magna which was published in 1545.

Descartes studied further the possible solutions of equations and called the negative solutions 'false' and other solutions, which contained the square root of negative numbers, 'imaginary'. This is where we get our name for imaginary numbers.

The thing is that you can show (or imagine) all real numbers on a number line of a kind - even the irrational numbers can be imagined to slide down the number line, albeit their position is very difficult to pin!

Back to negative numbers - they rose to become accepted members of the numbers community sometime in the 17th century. Now we use them freely and without any confusion.

But the irrational, imaginary, and complex numbers remained something of an enigma for the greatest part of the 18 th century, and even today you don't learn about them until you are about 16. Complex numbers are also very important to understand if you want to understand the Fundamental Theorem of Algebra.



Girolamo Cardano (1501-1576) - a famous Italian mathematician.

Some other pages on negative numbers:

Leo Rogers' page on the history of negative numbers

Anne Boye's page for teachers

and another page - nicely giving the timeline of developments



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