India has more mathematical, scientific, and engineering geniuses to drive its economic growth than other countries. In absolute terms, this may be true; after all, India has a population of more than 1.2 billion people. But a population this big will have more people at either end of the distribution of economic ability: more geniuses, and more people with serious challenges to their cognitive capacity. The question is whether the extra geniuses will have a positive effect that is disproportionate to India's population. If this were true more generally, populous countries like Germany and France would have higher living standards than smaller countries with similar advantages, like Switzerland and Denmark. Clearly, this is not the case.
As a democracy, India is more conducive to free-market capitalism. The links between democracy and economic growth have interested economists for decades, and the rise of state capitalism in non-democratic countries like China and Saudi Arabia has posed an ideological challenge. India is often touted as the world's biggest democracy; the World Bank's Worldwide Governance Indicators rank it in the 59th percentile for "voice and accountability" of citizens and government, just shy of several members of the European Union. Still, India's markets are far from free. The Heritage Foundation's Index of Economic Freedom calls India "mostly unfree" with a ranking of 119 out of 177 countries, as a result of heavy government involvement in the economy, from regulatory requirements to trade barriers. It's also one of the toughest places in the world to start a business.
The British legacy of a strong legal system gives India an edge. If it does, it's not a very big edge. Geographical factors like coastline, rainfall, and temperature can explain a big share of the differences in living standards between countries today. Controlling for these factors, former British colonies tend to do better than the average among all countries. But among the former colonies, India is one of the worst performers. Indeed, its living standards are worse than you might have expected given its geography. That may be because the vast majority of India's workers operate outside the strictures and protections of the legal system, in an environment more reminiscent of London's 19th century slums than Canary Wharf.
To sum up, there's little basis for any sort of mystique surrounding India's economic growth. On its current path, India shows no obvious signs of rewriting the textbooks; on the contrary, it has confirmed much of what economists already understood about urbanization, industrialization, trade, and institutions. Don't get me wrong -- India is undoubtedly a fascinating country for many other reasons. But to an economist, it's just another poor country that happens to be very, very big.