Here’s a very interesting philosophical question: How can our brain understand mathematics? Is it like a computer, or, does it work in a different way? Understanding the answer will give you the most effective way to learn mathematics, because if you know how your brain works, you know the most optimal way to teach it. …

Read article →

If I asked you to understand a mathematical proof, you would approach it in 1 of 2 completely different ways. That’s because mathematicians Poincare and Hadamard discovered that there are 2 kinds of mathematical minds: let’s see which one you have, and which one is better at helping you learn mathematics. Let’s take a really…

Read article →

We often think that you have to be a genius to make great mathematical discoveries, and sure, genius probably plays a role, but did you know that there’s actually a pattern to making mathematical discoveries? And most likely, you’ve experienced this pattern yourself when studying mathematics. This pattern was found in a research done by…

Read article →

When you’re asked to consider a non-orientable hyper-dodeca-almost-icosa-oids in the 16 dimensional space with a metric nobody remembers defining, well, you’ll be in the world of pure mathematics. But when someone suddenly asks you to add 57 to 89, and then divide that by 7.5 in your head, you’ll probably panic for a second. And…

Read article →

The general public has literally no idea what pure mathematics is. I mean zero. And in my opinion, that’s a problem, because not only does pure mathematics itself end up being super misunderstood and unappreciated, but the people who study it are looked at as weird, when they’re actually some of the most intelligent people…

Read article →

Quitting my PhD was one the BEST decisions I ever made in my life. I’ve never been happier since. But, why would someone leave a PhD in pure mathematics? I mean, isn’t it the pinnacle of knowledge and prestige? I’m gonna share 3 reasons for why I did it, and my hunch tells me that…

Read article →

Today, I will share with you my favorite strategy for problem-solving. Just think about it: When we sit down to solve a mathematical problem, especially one that is difficult we usually tend to find ourselves looking through our huge, mental world of logic, symmetries, definitions, theorems, and so on. But our brains have two ways…

Read article →

If you’ve studied math or physics (or if you’ve ever done serious research in these areas) there’s a pretty high chance that, at some point, you’ve sat in front of a page full of symbols, completely lost, just thinking to yourself: “Maybe I’m just not smart enough for this. Maybe this is too much for…

Read article →

Taking pride in mathematics is a force that is very subtle. It’s something that can drive you forward if you use it to build your personal sense of identity as a mathematician and it’s something that gives you self-confidence. But, if you take it to the extreme, it can become the very thing that actually…

Read article →

If we look back at the biggest breakthroughs in science or math, they tend to come from people who are willing to challenge current beliefs. And this isn’t done out of pure arrogance (although that does play a role sometimes), but mostly because this person is thinking outside of the box.  In my Bachelor’s I…

Read article →