Over the span of human history there are certain ideas that humans have had a very difficult time accepting.

Ideas that no one has any problem with today and are even grasped by children actually took centuries to take root.

And perhaps this is no more true than with the concept of negative numbers.

Learn more about negative numbers and how they went from being absurd to commonplace

on this episode of Everything Everywhere Daily. I've previously done episodes on the number zero, infinity, and complex or imaginary numbers.

All of these mathematical concepts were difficult for people at first to grasp,

because they aren't things that we deal with in everyday life.

Mathematics had its origin in

counting simple objects. If you had two sheep you could count one two sheep. You

couldn't count zero sheep. You couldn't count an infinite number of sheep and there certainly

can't be a negative number of sheep. The first instance of negative numbers which

is mentioned in historical accounts come from the Greek mathematician Diophantus of Alexandria.

In the third century he wrote a book titled Arithmetica, which was a series of solutions to algebraic

equations.

One such equation which he encountered was the simple equation 4X plus 20

equals 4. If you do the math and rearrange the terms you'll find the solution of this

equation is negative 4. solution of this equation is negative four.

Solving this equation isn't really controversial, but Diophantus just considered the result

to be absurd because he couldn't see how you could have a negative amount to something.

Much of this had to do with the fact that algebra, as a separate abstract discipline,

didn't really exist yet at the time. It was intrinsically tied up with geometry, and in geometry you can't have a negative length of something.

The Diophantine view of negative numbers ended up becoming the predominant view of negative numbers in European mathematics for centuries.

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