One of my favorite stories from the history of math is about Madhava of Sangamagrama. Know who he is, reader? Of course you do, for you are like all my readers, full of worldly knowledge, insight and wit! But just in case you’d like a brief refresher, Madhava is among those who invented calculus.
Now, I know what you may be thinking, reader – hold up, smart ass, that isn’t true, calculus was invented by Newton! And I concede the point because this is true, or maybe also true, for you may have insisted Leibniz invented calculus. Again, I acknowledge the rebuttals but emphasize that it is also true that Leibniz invented calculus. The point is that they all invented calculus, them and possibly a few other folks, each contributing in some way or the other to humanity's accumulating knowledge about what we know today as everyone's least favorite high school subject.
The big difference between Madhava and his European counterparts was their backgrounds. Newton and Leibniz were born in Europe to well-off families. They attended prestigious schools from young ages and eventually became educated enough to regularly collaborate with the world’s leading scholars on all the important subject matters of the day. Their lifetimes of study led to the insights and inspirations into big ideas that changed the world. All of this investment in these two men over the course of their lifetimes led to their crowning achievement – the invention of calculus, a title that remains in dispute in the present day.
On the other hand, Madhava likely came from distinctly humbler origins. I'm guessing he was born to a relatively poorer family than Newton's or Leibniz's for three reasons. First, he was born hundreds of years earlier than either man. Second, I assume the average Indian of the time was almost always materially worse off than a European counterpart. Finally, since I couldn't dig up anything about his background, upbringing, or adult life, I assumed that the lack of detailed records about him suggested the circumstances into which he was born were not as materially secure as those of Newton or Leibniz. Although I cannot definitely say for sure that my guesswork is reliable, I'm confident that the investment in his educational upbringing and the resulting resources and contacts that became available to him during his working years were nowhere near the level enjoyed by Newton or Leibniz.
All of this leads me to one big question - what does it take to prepare someone to come up with a great idea? The story of Madhava leaves me with some hunches about the relative value of natural ability and education in the context of idea generation but I'll leave calculating the exact proportion to smarter folks than me. Instead, I'll focus on something I know for sure after learning about the backgrounds of calculus's many inventors - a great idea can come from anyone, living anywhere, doing anything. It reminds me that no matter what we think we know about coming up with a great idea, there is always someone out there just waiting to prove everyone wrong.
Why is it important to understand where great ideas come from? Well, coming up with great ideas is how people create value. If the process of generating great ideas was perfectly understood, we would essentially be able to generate value on-demand and humanity would make massive strides forward. I’m not sure we are quite ready for this today but we can still do pretty well by seeking to understand the next best thing – how to reduce the time we spend waiting for the next person to generate the next great idea.
There are a lot of very well established beliefs about idea generation. Most suggest that great ideas come from great thinkers. These thinkers combine their brilliance with some mix of education and resources to maximize their natural intellect. But such beliefs don’t account much for the case of Madhava or for many others like him whose accomplishments rival those of the far better educated and connected. If Madhava could come up with his ideas despite lacking some of the advantages enjoyed by Newton or Leibniz, then surely education and resources aren't as important as some believe. At the very least, Madhava suggests the attempt to predict who will come up with a great idea based on education and resources alone is a fruitless exercise.
If we can’t predict the next person who is going to come up with a great idea, then what should we do? My humble suggestion is that we maximize the number of people who potentially might come up with the next great idea. I think a lot of folks share this idea and I see the manifestation of their beliefs every time society finds a way to extend or expand access to education. However, I look at this challenge from the other side because I believe people are perfectly capable of coming up with good ideas regardless of their background, education, or resources. So, I think we should consider what might have stopped someone like Madhava from inventing calculus.
Death, I think, is an obvious first choice. If Madhava had died at the age of twelve from an airborne infection or malnutrition or starvation, then he probably wouldn’t have made it into this post. Time wasting is another good candidate – if Madhava had walked six hours everyday to get water, for example, he probably would not have had enough time left in the day to invent calculus (though I suppose I can’t be fully sure - long walks are considered by some who voluntarily take them to be invaluable thinking time).
I’ll cut my speculations off here, reader, because I think the point is clear – the only thing that could have stopped Madhava from inventing calculus was the thing that probably should have stopped him in the first place – poverty. Now, Madhava might not have been impoverished in the relative terms of his day and perhaps that is all that he needed to power his intellectual accomplishments. However, this leads me to wonder how many other people just like him lived during his time that did not maximize their intellectual potential due to the restraints of poverty.
This detail is never pointed out in stories about improbable accomplishments. For every 'so and so' who overcomes the odds, how many others fell by the wayside just because they lacked some basic essential that many others take for granted? I shudder to think of all the great ideas that have probably disappeared into history’s black hole of irrelevance and obscurity thanks to solvable problems of resource distribution. Is the name of the person with the cure to cancer already etched onto a gravestone? Or perhaps crawling around in a junkyard somewhere, applying his or her considerable brainpower to identifying value in what others have tossed aside? Could the person with the potential to invent a solution for global warming be spending his or her day pulling scraps together for dinner? There’s no way to know the answer to such questions but I’m confident at the very least that we’ve wasted the potential of countless lives over the years by so casually accepting poverty as a poor person's problem.
It brings me to the lesson I draw every time I hear about someone who changes the world despite being born into poverty – allowing people to remain in poverty limits the potential for the entire human race. We currently have somewhere north of seven billion people on our little blue planet. In theory, any one of us could come up with the next great idea and move our entire species forward another step. In practice, though, with so many still shackled to needless poverty, the number of potential idea generators is far less than seven billion. When people in malaria-infested regions spend all day thinking about mosquitoes or people in the richest country in human history spend a couple hours a week standing in line at the food bank, we are asking some subset of our seven billion idea generators to spend their time coming up with solutions for problems like sleeping safely or affording dinner. This, of course, means a subset of our seven billion is not able to contribute to solving problems that we haven’t already solved.
There are far better arguments out there for why ending poverty is humanity’s most important collective goal. These arguments approach the goal from moral, ethical, or pacifist grounds. I’ll leave these arguments to those who can make the case with the passion, energy, or commitment that I feel such arguments deserve. I’ll instead conclude with my own relatively subdued point of view – since the next great idea can come from anywhere, we should make sure as many people as possible are secure enough to spend their time working on ideas. When we allow so many to remain in poverty, we reduce the number of people who are able to work on ideas, make it much less likely for great ideas to emerge, and ultimately limit the potential of the human race.
