A universal way to solve problems, from a mathematical genius

By Zat Rana | August 25, 2018

It took Claude Shannon about a decade to fully formulate his seminal theory of information.

He first flirted with the idea of establishing a common foundation for the many information technologies of his day (like the telephone, the radio, and the television) in graduate school.

It wasn’t until 1948, however, that he published A Mathematical Theory of Communication.

This wasn’t his only big contribution, though. As a student at MIT, at the humble age of 21, he published a thesis that many consider possibly the most important master’s thesis of the century.

To the average person, this may not mean much. He’s not exactly a household name. But if it wasn’t for Shannon’s work, what we think of as the modern computer may not exist. His influence is enormous not just in computer science, but also in physics and engineering.

The word genius is thrown around casually, but there are very few people who actually deserve the moniker like Claude Shannon. He thought differently, and he thought playfully.

One of the subtle causes behind what manifested as such genius, however, was the way he attacked problems. He didn’t just formulate a question and then look for answers, but he was methodological in developing a process to help him see beyond what was in sight.

His problems were different from many of the problems we are likely to deal with, but the template and its reasoning can be generalized to some degree, and when it is, it may just help us think sharper, too.

All problems have a shape and a form. To solve them, we have to first understand them.

Build a core before filling the details

The importance of getting to an answer isn’t lost on any of us, but many of us do neglect how important it is to ask a question in such a way that an answer is actually available to us.

We are quick to jump around from one detail to another, hoping that they eventually connect, rather than focusing our energy on developing an intuition for what it is we are working with.

This is where Shannon did the opposite. In fact, as his biographers note in A Mind at Play, he did this to the point that some contemporary mathematicians thought that he wasn’t as rigorous as he could be in the steps he was taking to build a coherent picture. They, naturally, wanted the details.

Shannon’s reasoning, however, was that it isn’t until you eliminate the inessential from the problem you are working on that you can see the core that will guide you to an answer.

In fact, often, when you get to such a core, you may not even recognize the problem anymore, which illustrates how important it is to get the bigger picture right before you go chasing after the details. Otherwise, you start by pointing yourself in the wrong direction.

Details are important and useful. Many details are actually disproportionately important and useful relative to their representation. But there are equally as many details that are useless.

If you don’t find the core of a problem, you start off with all of the wrong details, which is then going to encourage you to add many more of the wrong kinds of details until you’re stuck.

Starting by pruning away at what is unimportant is how you discipline yourself to see behind the fog created by the inessential. That’s when you’ll find the foundation you are looking for.

Finding the true form of the problem is almost as important as the answer that comes after.

Continue reading at: https://qz.com/1365059/a-universal-way-to-solve-problems-from-a-mathematical-genius/