I have no University education but I have undergone the ordinary school course. After leaving school I have been employing the spare time at my disposal to work at Mathematics. I have not trodden through the conventional regular course which is followed in a University course, but I am striking out a new path for myself. I have made a special investigation of divergent series in general and the results I get are termed by the local mathematicians as “startling.”
Let me start off by reiterating something that you’ve surely heard during those Saturday morning cartoons. It sounds pretty obvious, but it really isn’t. Stay in school. Even if we completely ignore the ramifications that school have on our future career prospects, education is intrinsically valuable in and of itself. Learning, even if only for its own sake, is positively invaluable.
When you weigh the struggles of crippling student debt against the income potential that those pieces of paper can provide, it can feel difficult to justify the increasing cost of higher education. I get it. People often cite highly successful individuals, like Matt Damon and Mark Zuckerberg, who dropped out of Harvard and went on to accomplish great things. We also have to recognize, though, that these individuals are the exception, rather than the rule. And they had to be accepted into Harvard in the first place, a feat achieved by a very select few.
For any number of reasons, not everyone can pursue a traditional university degree. This shouldn’t prevent you from pursuing your passion and learning as much as you possibly can about it. That was precisely the case for Indian mathematician Srinivasa Ramanujan. Despite having never received a formal education at the university level, he is widely regarded as one of the more influential mathematicians of his time, contributing to number theory, infinite series and continued fractions.
And yet, despite all of this, he was able to work through and even identify a number of completely original equations and mathematical concepts. There are concepts today that are named after him, like the Ramanujan prime and the Ramanujan theta function. Most of us laypeople don’t know what those are, of course, but most of us don’t understand a lot of things that are important. Just because you don’t use the quadratic equation in your daily life doesn’t mean it is without value.
Many of the things we take for granted are not nearly as simple as we make them out to be. Did you know that there are no solids in the universe? This doesn’t make intuitive sense to us at all, since we can place our hands on our desks or grab our coffee mugs in the morning. It is through education, scientific inquiry, and a fervent curiosity that we can begin to explore these deeper truths. The more you know, the more you realize how little you know.
Sometimes, the correct answer will appear completely illogical. Sometimes, the correct answer is a goat.
Given our unprecedented access to almost the entirety of human knowledge, we have no excuse NOT to keep learning about the world around us. While I don’t think that my university degree was a waste of time and money, I also cannot downplay the value of self-education and self-exploration. With great YouTube channels like Crash Course and Minute Physics, higher level concepts are more approachable than ever before.
To get a sense of the great mind of Srinivasa Ramanujan, consider this story that British mathematician G. H. Hardy shared about their encounter.
I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. “No,” he replied, “it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.”
Discover the remarkable in the mundane. Endeavor to gain a better understanding of the world around you. Never stop learning.
And in case you were wondering, the two different ways you can add a pair of cubes to produce the number 1729 are 1^3 + 12^3 and 9^3 + 10^3. The more you know…