‘You mean you can’t take less,’ said the Hatter: ‘It’s very easy to take more than nothing’. The Mad Hatter said no to negative numbers.

Sometimes we withdraw more cash from the bank than is in our bank account. Where is the negative money? We then use the cash for shopping. The money given to the shopkeepers is real. It now belongs to the shopkeepers. We do not have any negative money, the shopkeeper does not have any negative money and the bank does not have any negative money but wants real money back, with a bit extra for their troubles. There is no negative money because negative numbers are not real. This is why accountants use debits and credits and avoid negative numbers.

I struggled with the square root of -1 at school. Not finding the square root was frustrating because I rather liked square roots. The teacher told me that the square root of -1 is ‘i’ and it is a complex or imaginary number. During the pandemic lockdown, I thought about this. It is not fair to the square root function. Why should you be surprised that you get an imaginary number from a function when the input is imaginary? Yes, I believe that negative numbers are imaginary to start with and I am not sure that they are worth the trouble they cause. It is no wonder that children have much more difficult learning negative numbers than other math.

Mathematicians discovered many constants but the √-1 is the only one that is somewhat negative. Physicists describe the quantum world in terms of particles and antiparticles. There is no place for negative particles or negative waves.

In this blog, I will explore the case for negative numbers by looking at them from many perspectives, including the natural world, history, education, accounting, physics, quantum computing and tennis. The blog will question whether negative numbers are fit for purpose.

If the temperature is at -3 degrees and it goes down by -8 degrees, what is the new temperature?

-11 degrees

Yes, but in math when you subtract -8 from -3 you get -8 -(-3) = 5. This shows a difficulty children can have learning negative numbers.