With the decline of ancient Greece, the development of maths stagnated in Europe. However the progress of mathematics continued in the East. Du Sautoy describes both the Chinese use of maths in engineering projects and their belief in the mystical powers of numbers. He mentions Qin Jiushao.
He describes Indian mathematicians’ invention of trigonometry; their introduction of a symbol for the number zero and their contribution to the new concepts of infinity and negative numbers. It shows Gwalior Fort where zero is inscribed on its walls. It mentions the work of Brahmagupta and Bhāskara II on the subject of zero. He mentions Madhava of Sangamagrama and Aryabhata.
Du Sautoy then considers the Middle East: the invention of the new language of algebra and the evolution of a solution to cubic equations. He talks about the House of Wisdom with Muhammad ibn Mūsā al-Khwārizmī and he visits University of Al-Karaouine. He mentions Omar Khayyám.
Finally he examines the spread of Eastern knowledge to the West through mathematicians such as Leonardo Fibonacci, famous for the Fibonacci sequence. He mentions Niccolò Fontana Tartaglia.