what math can teach us about how to live

from your fav gen z philosopher x nerd

I've always found math to be quite poetic and philosophical. It has taught me about patterns, relationships, and the hidden structures that govern how things change over time. The same principles that describe the motion of planets, the spread of epidemics, and the growth of populations also describe the arc of a life, the development of relationships, and the accumulation of meaning.

Turns out, the universe has been giving us life advice all along.

the arithmetic of recovery

If something decreases by 1/5, in order for it to get back to its original state, you have to increase it by 1/4. If something decreases by 1/4, in order for it to get back to its original state, you have to increase it by 1/3. If something decreases by 1/3, in order for it to get back to its original state, you have to increase it by 1/2.

When I first learned this, it took me a minute to process it. But watching this principle play out in human lives? That took years to understand, and even longer to accept. When you're operating from a diminished base, matching the energy that caused the damage isn't enough. The math demands disproportionate effort; not because the universe is cruel, but because that's simply how fractions work when you're building upward from loss.

This pattern stalks every corner of human experience. Your bank account drops 30% in a market crash but needs a 43% gain to break even. Trust crumbles in an afternoon but takes seasons to reconstruct. One careless word can slice through years of carefully built intimacy.

This is why "I'm sorry" followed by business as usual feels so inadequate. If your actions decreased someone's sense of security by a third, you can't restore it with proportional niceness. The mathematics of healing demands disproportionately more…more consistency, more vulnerability, more proof that change is real.

To heal from losing a third of something precious, you can't just patch the hole. You have to build something 50% stronger than what existed before the damage.

The couples who survive betrayal, the friendships that weather deep hurt, the people who rebuild after devastating loss… they all understand this arithmetic of recovery. They know that coming back means becoming more generous, more patient, more intentionally loving than they ever were in the easy times.

the asymptote of perfection

In calculus, an asymptote is a line that a curve approaches infinitely but never quite touches. It is a ghost line: invisible, untouchable, but somehow governing everything. Your curve chases it with mathematical desperation, getting closer and closer: 0.1, 0.01, 0.001, forever halving the distance but never arriving. It's the most elegant torture device mathematics ever invented.

Watch someone in the grip of perfectionism and you're watching human calculus in real time. The novelist who has rewritten chapter one forty-seven times, each draft 0.01% better than the last. The entrepreneur whose business plan has become a gleaming monument to procrastination, polished to mirror perfection but never launched into the messy reality of actual customers.

Their effort follows a hyperbolic curve… dramatic gains at first, then smaller and smaller improvements that require exponentially more work. Draft two was transformative! Draft thirty-two changed some commas. They're spending infinite energy to traverse infinitesimal distances.

But perfectionism isn't the only thing haunting us.

I think social media has turned everyone else into asymptotes. Your college sorority sister's Tuscany honeymoon, your ex-colleauge's startup acquisition, the girl from high school who became a lifestyle influencer. They're all horizontal lines now, floating just out of reach.

You scroll and calculate the distance between your Tuesday afternoon and their apparent enlightenment. The gap never closes.

The math is merciless: you can get 99.99% of the way to that impossible standard and still feel so far from it. The asymptote doesn't care about your effort, your intention, or your exhaustion. You renovate your kitchen to 99.8% of Pinterest perfection and still feel like you're living in a cardboard box. You optimize your dating profile to 99.9% of whatever algorithm determines attractiveness and still get ghosted. The asymptote hovers there, smug and untouchable, one decimal place away from whatever you think will finally make you happy.

While you're obsessing over that unreachable line, you're missing the fact that your curve is telling a story the asymptote never could. That perfect horizontal line? It's static, lifeless, mathematically boring. It just sits there in theoretical space, never changing, never learning, never failing spectacularly and getting back up with grass stains and new wisdom.

Your messy trajectory has actual plot. It has that semester you almost dropped out because organic chemistry felt like witchcraft, the soul-crushing job that taught you exactly what you didn't want to become, the relationship that ended so badly you had to relearn how to trust your own judgment.

The asymptote has never experienced any of this. It's never been heartbroken or euphoric or confused or transformed. It's never had a breakdown in a grocery store parking lot or felt the wild joy of finally understanding something beautiful. It just hovers there in mathematical purgatory… perfect, pristine, and completely dead inside.

We've got it all backwards. The asymptote is museum rope: flawless, untouchable, designed to keep life at a safe distance. Your curve is a lightning bolt; unpredictable, electric, scarred by every storm it's weathered and illuminated by every moment it's touched the ground.

The asymptote exists nowhere except in equations and other people's carefully curated feeds. The curve? At least it exists. At least it moves. At least it's yours.

the topology of influence

In graph theory, human relationships form networks of nodes and edges: people connected by lines of friendship, collaboration, professional overlap, shared experience. Not all connections are created equal, and the people with the most influence aren't necessarily the ones with the most friends.

Most people optimize for degree centrality; accumulating the highest raw number of connections possible. It's the LinkedIn strategy, the networking event approach, the collect-business-cards mentality. But graph theory suggests a different path to influence!

Betweenness centrality measures how often you serve as a bridge between different clusters of the network. A consultant who also knows musicians. A teacher who has friends in tech. An artist with connections in finance. These people occupy positions of disproportionate influence not because they know the most people, but because they connect worlds that don't usually touch.

Think of them as the human equivalent of airport hubs. Not the biggest cities, but the places that make everything else possible.

You might think the internet age would eliminate this clustering effect! After all, we're all theoretically one click away from anyone. But the opposite has happened. Digital platforms have actually intensified clustering by creating algorithmic echo chambers. Your Twitter feed shows you people who think like you. Your LinkedIn network skews toward your industry. Your Instagram algorithm serves you content similar to what you already engage with. We're more connected than ever, yet more isolated in our intellectual and cultural silos.

This makes bridge-builders even more valuable than before. While the platforms divide us into marketable demographics, these connectors create the serendipitous encounters that algorithms actively prevent.

I often think about how many breakthroughs happen at the intersection of different fields. Steve Jobs reinvented the computer and the phone, but he also occupied the rare position between technology and design thinking which changed both industries forever. Martha Stewart didn't invent cooking or decorating, but she bridged the domestic arts with media production, creating a pathway between homemaking culture and the entertainment industry, making homemaking become a marketable identity. Lin-Manuel Miranda connected hip-hop culture to Broadway theater while simultaneously bridging communities of color with elite cultural institutions, creating unprecedented opportunities for Black and Latino performers to inhabit and redefine foundational American narratives. Oprah Winfrey became the critical bridge between mass media entertainment and personal development culture, connecting daytime TV audiences to spiritual exploration and self-improvement in ways that created entirely new categories of content and influence. These people were, of course, creative successes, but are also examples of betweenness centrality creating exponential value.

Perhaps the algorithm for meaningful connection isn't about knowing the most people. Maybe it's about knowing different kinds of people, about building bridges between communities that rarely intersect, about becoming the person who makes things possible by connecting dots that others can't even see.

the mechanics of momentum

In physics, momentum describes how objects in motion tend to stay in motion. The fascinating kind of momentum to me is the kind that governs your daily habits. Each small action doesn't just happen in isolation; it changes the probability of what happens next, creating cascades that can completely redirect your life's trajectory.

I like to think of my life as a collection of invisible spirals, each one either pulling me up or dragging me down. And it’s hard, because you often don't realize you’re on these spirals until they've been spinning for months…

Here’s an example (sounds dramatic, but hear me out). Take Sarah, who decides to go for a thirty-minute walk after lunch. Nothing crazy; just because she's tired of feeling sluggish at 2pm. The walk makes her feel slightly more alert, so tomorrow she walks again. After a week, she's sleeping better. After two weeks, her mental health starts to improve. Two months later, she's signed up for a weekend hiking group. Six months later, she has friends who enjoy being active on weekends.

She didn't set out to become a "fitness person." She just got caught in an upward spiral where each small choice made the next small choice easier. The walk led to better sleep, which led to more energy, which led to more walks, which led to meeting new people, which led to new activities, which led to better sleep. Round and round, up and up.

Meanwhile, her colleague Marcus is caught in the opposite spiral. He skips lunch to finish a project, so he's starving by 4 PM and grabs vending machine cookies. The sugar crash makes him feel terrible, so he orders takeout for dinner because he's too tired to cook. He stays up late doom-scrolling because he feels guilty about his food choices and needs to decompress. He wakes up exhausted, so he skips breakfast and grabs coffee and a muffin. By lunch, he's crashed again, and the cycle continues.

Marcus isn't weak or undisciplined. He's trapped in a perfectly logical system where each choice creates conditions that make the next bad choice feel inevitable. His spiral isn't broken; it's working exactly as designed, just in the wrong direction.

Both spirals started with tiny decisions that felt almost meaningless in the moment. A ten-minute walk. Skipping one meal. But small changes compound in ways that can completely reshape your life within months.

The smartest people I know don't rely on willpower. They're system designers. They understand that if you have to fight yourself every day to make good choices, you're playing a losing game. Instead, they set up their environment so that good choices feel easy and bad choices feel harder.