About 150 BC, the Mauryan Empire collapsed. India split up into a lot of small kingdoms. These small kingdoms were weak and so they were often invaded by stronger neighbors. The Greeks under their king Seleucus came back in 150 BC. They conquered the Indus Valley (modern Pakistan) again, but they didn’t stay for long. Taxila (now in eastern Pakistan) may have conquered part of western China, opening up Silk Road trade. In return, Chinese armies, under the strong Han Dynasty, invaded over and over. And the Parthians and Sassanians sometimes attacked India too.
But even though they suffered from all these invasions, India was still rich (like its neighbors) from trading on the Silk Road. Indian traders sold cotton cloth, steel, cinnamon, black pepper, silver and pearls and glass beads and opium, and in exchange they bought horses – it’s too hot to breed good horses in India – silk from Central Asia, glass from the Parthians, and ivory and gold from Africa.
A lot of people in India were Buddhists at this time, and people came from all over – from as far away as China – to study with the botanists, doctors, mathematicians and astronomers at India’s great universities at Taxila and at Nalanda (on the banks of the Ganges River). It was during this time that Indian mathematicians, in cooperation with China, worked out the number system we use today (1,2,3, etc.).
All this trade and exchange of knowledge only increased in 319 AD, when the Guptan Empire reunited all of northern India into one empire again.