OpenAI recently announced that one of its AI models had solved the Navier-Stokes problem, one of the hardest in modern mathematics. The Navier-Stokes equations describe how fluids such as water and air move, and are essential for understanding ocean currents, blood circulation and airflow over aircraft wings. Mathematicians have struggled for decades to determine whether coherent solutions always exist, and the problem is one of seven Millennium Prize Problems set by the Clay Mathematics Institute. AI solutions to long-standing problems have shaken the field, but experts say humans must still check the work and guide the research.

Hampi is a UNESCO World Heritage Site in Karnataka, India, with more than 1,600 surviving remains spread over 4,100 hectares. It was the capital of the Vijayanagara Empire from 1336 to 1565. Travellers from Persia and Portugal described it as a prosperous, wealthy and grand city with temples, markets and farms along the Tungabhadra River. By 1500 it was estimated to be the world's second-largest city after Beijing, and probably India's richest at the time. In 1565 a coalition of Muslim sultanates defeated the Vijayanagara Empire, its capital was conquered and destroyed, and the city was left in ruins. Hampi remains a religious centre, with the active Virupaksha Temple at its heart.