The fact that something such as "nothing" first had to exist as an idea before it was given a place in mathematics is emblematic of what a crucial time it was in the development of maths.
Many – including Al-Khwarizmi – weren’t happy with the idea of zero because they didn’t think it was useful. The same went for negative numbers.
When I was at primary school and first confronted with the symbol 'x', I was consoled by my teacher who explained that algebra and all of maths was really just a language and you needed to learn how to translate it. And like any language it’s designed to express ideas.
Later developments such as the idea of infinity or even the symbols that we recognise as algebraic show that rules have to be established, and once they are established they’re taken on faith. Such as what we now all recognise to be zero. We take it for granted. We now have a common understanding of what is implied by the zero symbol and the idea of zero-ness. But in the early Islamic period that hadn’t been invented.
Under the Abbasid caliphs, who ruled at this time, mathematics was valued partly because of the religious duty to pursue knowledge as set out in the Quran. But this grappling with abstract concepts that we all now recognise as true, shows that mathematics is partly a system of belief.
While the Abbasid empire’s HQ was Baghdad, the discussion and development of maths quickly spread across the Arabic speaking world because paper was readily available in the region. So, while Christian Europe lagged behind, these complex new scientific ideas were being discussed east of modern-day Iraq and as far west as Muslim Spain. Maths, like language, spread across the Islamic world.
Europe overtook the Islamic world in the science stakes thanks to the printing press, although many key Abbasid texts were translated into Latin and helped maths evolve further.
So perhaps we could equate the early Islamic world with the concept of “the maths world”. Just please don’t make me move there.
