Reductio ad absurdum… is a subtler move than any in chess: the chess player might sacrifice a pawn, even a piece, for the sake of the game—but the mathematician sacrifices the game itself. — G.H. Hardy
I’ve learned some of the best lessons of my life while studying mathematics. Back when I was a kid, I was captivated by Euclidean geometry and the parallel postulate—which, as I grew older, started to seem like it might never be provable. Later, when I was more dramatic about things, I even calculated the expected value of my first relationship. “Alright, pros: dark hair—weight 3, short height—weight 4… Cons: talks absolute nonsense—weight 30…” But few things have ever delighted me as much as reductio ad absurdum.
There is something deeply humorous at the core of reductio. You say: “I think you’re a fool. But I won’t argue. Go ahead, be a fool. I only hope you crash into a wall.” And then we do everything we can to make sure they crash into that wall. Oddly enough, some of the most famously unsolvable problems in mathematics have been solved with exactly this delightful strategy.
Two things in this approach have always inspired me: comedy and tragedy. You love the problem—but you also want it to vanish.
In my experience, comedy is inseparable from wisdom. I’d even boldly say: they’re two sides of the same coin. Some of the wisest figures I’ve found in history were court jesters. They observed carefully and—with gentle irony—delivered the harshest critiques to the noble lords, who were often the most savage of their age. And the result? Laughter from the whole room. I believe writers should keep two faithful companions close: truth and humor. They should serve truth, and make humor serve them. Then, even the most tangled problems of our time might start to seem solvable.
Second—tragedy. We live in a world where tragedy is unspeakable. The ruling class has explained it all to us: opportunities are equal, success is for the smart and hardworking, and the miserable are lazy, corrupt, or broken. Universities are open to all. Anyone can succeed, no matter where they are, if they just try hard enough. Put in ten thousand hours and you, too, can become a global icon.
They’ve told us this story through democracy, through technology, through a handful of examples. But the truth is—tragedy is still here. Most people don’t succeed. And when they fail, we don’t blame luck or God anymore—we blame ourselves. Failure becomes proof of stupidity, weakness, or unworthiness. That’s why so many people today are sad—fundamentally sad—even while liking each other’s radiant Instagram smiles.
The Greeks developed tragedy. The hero is often noble and decent, but makes small, unavoidable errors—and the result is their downfall. An intelligent, good, hardworking person can still fall into ruin. That, I think, is where comedy returns. Such stories are deeply soothing. Because they help us forgive: ourselves, the world, other people. Suddenly, the pressure lifts.
We need more tragedy. In our lives. To befriend ourselves. To forgive ourselves, and others. To accept that the world is built for tears—and maybe not torment ourselves over every little detail.
Reductio ad absurdum is one of those strange companions that walks with mathematicians. But oddly enough, mathematicians don’t care much about such things. They seek something pure. Flawless. Perhaps that’s why they rarely get entangled in the contradictions and strange astonishments of our flawed existence.