Exploring the Future of Math Education: Intuition, Algorithms, and Engaging Content
Welcome to my first ever blog post! I'm honestly not sure where this blogging journey will take me, but I'm excited to explore ideas about math education, content creation, and how we can make mathematics more intuitive and engaging. I'm particularly passionate about creating math videos and educational content in areas like probability and mathematical finance, and I'd love to hear your thoughts and suggestions as I figure out what direction to take this.
Math education has a storytelling problem. We've forgotten that behind every theorem, every formula, every seemingly abstract concept lies a compelling reason—something from the natural world that sparked curiosity and demanded exploration. Instead, we've built a system that hands students definitions first and asks them to find meaning later.
This backwards approach is exactly what I want to tackle through the content I'm creating. But first, let's dig into why our current system isn't working and what we can learn from unexpected places.
The Problem: Definitions Before Understanding
Walk into most math classrooms today, and you'll witness the same pattern: teacher presents a formula, works through practice problems, and expects students to develop intuition through repetition. Take AP Calculus BC, for example. Students get thrown the formal definition of a limit, then immediately learn that derivatives are "just limits we talked about."
But what if we flipped this? What if we started by exploring the idea of finding a tangent line to a curvy function? Students could discover that taking two points and approximating a line gets more accurate as those points get closer together. The challenge becomes: how do we calculate this when the distance approaches zero? Now the concept of limits becomes necessary, meaningful, and intuitive.
This approach transforms abstract definitions into tools students actually want to use.
Learning from Computer Science: Algorithms That Make Sense
Here's where things get interesting. Computer science has mastered something math education hasn't: making algorithms feel essential by connecting them to real problems we actually face. Brian Christian's excellent book "Algorithms to Live By" brilliantly demonstrates this with examples that show how mathematical thinking applies to everyday decisions.
Take the simple question of organizing files in a drawer. After using a file, where should you put it back? Most of us intuitively place recently-used items at the front, and computer science proves this is nearly optimal. There's elegant mathematics behind this everyday decision, but the math emerges from the problem, not the other way around.
Or consider the exploration versus exploitation dilemma: imagine you're faced with multiple slot machines, each with unknown success rates. How much should you explore new options versus sticking with what seems to work? This isn't just a gambling problem—it's how we decide whether to try new restaurants, career paths, or investment strategies.
Computer science shows us that when you're new to any situation, exploration is optimal. Even when you find something that works 50% of the time, it's often worth exploring more. But there's a mathematical threshold where sticking with what you know becomes the better strategy.
These examples work because they solve real problems. The mathematics serves the story, not the reverse.
Why I Had a Bad Time with Real Analysis (And Why That Matters)
I'll be honest: real analysis nearly killed my love for mathematics. Everything reduced to plugging in definitions—what's a limit, what's a derivative, what makes a set closed or open. My professor treated boundaries and continuity as abstract entities rather than intuitive concepts.
But a closed set is intuitive—it's a set with its boundaries included, like a room with its walls. An open set excludes its boundaries, like all numbers between 0 and 2, but not 0 or 2 themselves. Simple diagrams could have made this crystal clear, but instead we got definitions divorced from understanding.
This isn't unique to real analysis. Across mathematics education, we're starting from the wrong end. We need intuition first, then formalization to support and refine that intuition.
The Power of Probability: Math That Feels Alive
This is why I'm drawn to probability and mathematical finance for my content. These fields naturally connect to experiences we all have—chance, uncertainty, decision-making under incomplete information.
Consider the birthday problem: in a room of people, what's the probability that no two share a birthday? Or card-drawing problems that mirror real decisions about risk and strategy. These aren't just academic exercises—they're mathematical models of how we navigate uncertainty every day.
When I explain Brownian motion, I start with the intuitive idea: a random process that goes up and down, like a coin flip repeated infinitely often in smaller and smaller time intervals. Once that picture clicks, the mathematical details—why the expected value is zero, why it follows a normal distribution—become natural consequences rather than arbitrary rules.
The animations I create help visualize why Brownian motion produces its characteristic bell curve. You see many paths clustering around the center, with few wandering far from the starting point. The mathematics explains what the animation reveals.
Stock Prices and Geometric Brownian Motion: A Case Study
Here's how intuition-first teaching works in practice. In my undergraduate math finance course, my professor beautifully explained why stock prices follow geometric Brownian motion—before we even knew what Brownian motion was.
What do we know about stock prices? They jump around randomly—we've all seen those jagged graphs. So they probably depend on some kind of noise. Different stocks have different volatilities, so this noise gets multiplied by a volatility parameter.
But good stocks generally trend upward over time. Look at the S&P 500's long-term exponential growth. And here's the key insight: a $1 change means something very different for a $500 stock versus a $50 stock. So both the growth and the noise should be proportional to the current stock price.
Put this together and you get: change in stock price = (return rate × current price × time change) + (volatility × current price × noise).
That's exactly the formula for geometric Brownian motion. The mathematics formalizes what our intuition already understood about how stock prices behave.
The Role of Animation and Storytelling
This is where content creation becomes crucial. Mathematical intuition often requires visualization that traditional textbooks can't provide. Animations can show why concepts work, not just that they work.
I'm inspired by creators like 3Blue1Brown, who've mastered the art of mathematical storytelling through animation. But I see gaps, especially in mathematical finance and probability, where engaging visual content could make these topics accessible to broader audiences.
My goal is to fill that gap—to create content that starts with problems people care about, builds intuition through visualization, and only then dives into the formal mathematics that makes it all work.
Where We Go From Here
The future of math education isn't about abandoning rigor—we absolutely need formal definitions and proofs for the hardest problems. But for most people trying to understand the mathematical world around them, intuition is the better starting point.
We need more educators willing to begin with high-level understanding, to use creative approaches that foster intuition, and to show students why mathematics matters before asking them to memorize how it works.
This is what I'm hoping to achieve with my content: math education that tells stories, builds understanding, and makes the abstract feel concrete. I'm particularly excited about exploring probability, mathematical finance, and other areas where mathematics directly connects to real-world decision-making.
But this is just the beginning. I'd love to hear your thoughts on what mathematical topics deserve better storytelling, what concepts you've always found confusing, or what areas you think need more intuitive explanations. What mathematical stories do you think are worth telling?
The conversation starts here, but where it goes depends on what resonates with you. What would you like to see explored next?
