Jetlag and a problem that would not leave

I looked up conjectures. Not with a research plan. With restlessness. Curiosity, creativity, perseverance: the words sound noble when you write them later. In the moment they felt more like itch. The Collatz problem showed up and sat down in the chair across from me. Halve if even. Triple and add one if odd. Repeat. A child can run the rule. Adults have failed to prove what the rule always does.

I tried numbers the way you try a lock with spare keys. 1 is already home. 2 goes to 1. 3 goes 10, 5, 16, 8, 4, 2, 1. 5 is short. 6 is short. 7 climbs and climbs and then crashes through powers of two into 1. 9, 11, 13, 15. I kept going because every trial walked home, and the walking had a mood to it. Rise, thrash, collapse. Rise again. Then the quiet of 4, 2, 1. It looked like weather. It looked like a parable someone had accidentally written in arithmetic.

I am not going to dress that night as destiny. Plenty of people meet Collatz in a YouTube thumbnail and forget it by breakfast. What happened to me was narrower and less romantic: the problem stuck. While my sleep was broken, the rule kept replaying. While I was thinking hard about the future and feeling a bit lost inside, here was a future-question that was not about revenue targets or hiring plans. It was about whether a simple motion always returns. That question fit the hole in my chest better than another strategy deck.

Las Vegas at New Year is neon and noise even when you stay home. Outside, the Strip was preparing its annual performance. Inside, I had a notebook forming, not as a brand, not as a launch, as a place to put the itch so it would stop chewing the furniture of my mind. Private obsession. Not a public claim. That distinction mattered even then, before I had language for why it mattered.

The next morning still had jobs. Someone's AC. Someone's invoice. Someone's Slack thread that thought it was urgent because Slack threads always do. Going Home did not begin as a sabbatical from capitalism. It began as a second track running under the first. The companies fund the hours. That sentence is dull and necessary. If you want to know how a founder ends up with a math notebook, start with cashflow that buys solitude in uneven scraps, not with a myth about leaving the world behind.

I have sat in trucks in July heat that makes the steering wheel punish your hands. I have sat in board-ish conversations that pretend they are not board conversations. I have prayed on days when the numbers looked kind and on days when they did not. Collatz did not replace any of that. It sat beside it like a second climate. When the business day ended and jetlag reopened the night, the rule came back. Even, odd, even, odd. Walk it again. Watch it fall to 1 again. Feel the same stupid satisfaction, then the same stupid question: why does this keep working, and why can nobody seal it.

People who only know me from essays sometimes imagine a life of pure contemplation. People who only know me from HVAC sometimes imagine I should stick to refrigerant. Both reductions are lazy. The night of December 31, 2024, in the sense of worked date, not fireworks, was the night those rooms shared a hallway. I was lost enough to need a clean question. I was grounded enough by bills and faith and family history to know that a clean question is not a personality transplant.

What I did not have that night: a proof, a lemma, a clever energy function, a literature review worthy of the word, a name for look-ahead that I would later overuse and then have to humble. I had trials on paper and screen. I had the sensation that something about return was speaking in a language I could almost hear. I had the decision, quiet and unannounced, to keep a record.

Later the architecture grew. Look-ahead as a technical bet. Energy functions that tried to score descent. Obstructions that killed some of those scores. Essays that tried to keep the human reading without lying about the math. An open notebook that publishes worked dates honestly and publication dates separately. Ugly windows. Mersenne streaks that refuse to flatter a fixed flashlight. None of that was in the room on the jetlag night. If I tell the origin as if the later machinery were already humming, I am lying with foreshadowing.

The honest origin is smaller. Tired traveler. Famous open problem. Decision to keep a record. The rest is aftermath and craft and failure and a few small negative results that earned their ink. I will not drag Erdős into this particular night as if he were sitting on the couch. He enters later, when I needed a warning more than a pep talk. Tao enters later too, when almost-all became a mountain I had to stop pretending was a foothill. On December 31 the cast was thin: me, the rule, the numbers walking home, the itch.

One of the wake-ups had a kitchen light and a glass of water that tasted like travel. I ran 27 because everyone who stays with Collatz long enough runs 27. It climbs like it has somewhere important to be. It visits 9,232 before it remembers gravity. Watching that on a phone screen after China is a strange form of prayer, if prayer can mean attention without bargaining. I was not asking God to let me solve it. I was asking my own attention to tell me why this felt like homecoming language.

Faith, for me, is not a proof shortcut. I will not baptize a conjecture and call the water a theorem. What faith does in a night like that is keep the ego from turning curiosity into a coronation. You can love a question without appointing yourself its answer. That sentence is easy to type years later. On the night itself it was more like a bodily refusal: do not announce, do not brand, do not turn the itch into a press release while your circadian rhythm is still in Shanghai.

I started calling the feeling Going Home before I had a site section for it. The name was almost too on the nose. Every tested integer seemed to go home to 1. I was trying to go home inside a life that had become a collection of projects. Brazilian roots, American desert city, companies that need me to be decisive, a mind that needs me to stay porous. The map of Collatz and the map of a person mid-orbit are not the same map. I knew that even then. I also knew metaphors are how humans hold formal objects without dropping them. The danger is when the metaphor starts signing checks the math cannot cash.

So the obsession stayed private. Friends might have heard a sentence. Nobody got a white paper. Nobody got a claim that I had seen the structure professional number theorists missed. I had seen a rule that would not leave my head. That is a psychological fact, not a mathematical contribution. Recording psychological facts carefully is still worth doing if you plan to spend years near a dangerous problem. Tao has said versions of the danger out loud. I had not read the right warnings yet. Instinct still told me to keep the volume low.

There is a version of this story that turns me into a mythic seeker who found his life's work between flights. I dislike that version. The true texture includes unread emails, a body angry about time zones, a scrap about a nice car that sounds like a bit, and a sequence of integers behaving themselves in a way that felt like a dare. Curiosity. Creativity. Perseverance. Fine. Also: avoidance of harder emotional inventory by playing with an infinite toy. I can admit both. The notebook is big enough for mixed motives if it refuses fake purity.

If you read the later entries first, you meet obstruction language and Syracuse steps and fixed windows that fail. You might think the project began as a research program with a roadmap. It did not. The roadmap is a civilizing layer poured over a jetlag infection. I am not ashamed of that. Many real projects begin as infections. The shame would be pretending the infection was already a theorem.

What this night gave the later work was permission to care in public eventually, and discipline to wait. Worked 2024-12-31. Published much later. I am not pretending these notes were online while the fireworks were still theoretical. The honest dating model is part of the point. The work is real. The publication clock is separate. That separation is how you avoid turning a private itch into a performance before the thinking can stand upright.

It also gave me a tone I keep trying to protect. Enjoy the view. Including the ugly windows that came after. Including the days when a promising scorecard dies on a family of odd starts that look like a taunt. Including the admission that I am going to die, and therefore the notebook is not an immortality scheme. It is a way of looking while I am here. Every step is worth the look if the looking stays honest. That ethos can sound dramatic if you say it at a dinner party without context. In a jetlag kitchen at the hinge of a year, it felt plain. Finite life. Infinite-feeling question. Keep a record. Do not lie about what the record contains.

I tried not to call myself a mathematician. I am a student of one problem with borrowed tools and paid tutors in the form of papers I only half understand on the first pass. I tried not to confuse computational luck with insight. Every number I tried walked to 1 because billions of checks by people sharper than me had already walked the same neighborhoods. I tried not to invent a new name for an old neighborhood and then sell the name as discovery. The Terras line of thinking about stopping and density was in the world long before my notebook. Later, when Omega and look-ahead showed up in my notes, the adult move was citation and narrowing, not branding.

I tried not to use the conjecture as an escape hatch from ordinary repentance. If my life needed repair, Collatz would not repair it. If a company needed a hard conversation, a hailstone sequence would not hold it. The problem can teach patience and precision. It cannot baptize avoidance. Holding that line is part of why the night still feels clean in memory even though I was a mess in body.

And I tried not to solve it before sleep. That sounds like a joke. It is also a method. The itch wanted a climax. Jetlag wanted a story that would justify the wakefulness. The adult move was smaller: write the rule down, write a few orbits, write that I do not know, close the notebook, fail at sleeping anyway. No proof that night. No hero. A beginning with the volume set correctly.

Travel rearranges your sense of scale. One week you are moving through cities where the language on the signs is not the language in your dreams. The next week you are back in the valley where the mountains sit like a painted backdrop and the heat will return on schedule. Collatz has its own scale trick. A number that fits in one hand can generate a path that feels longer than a flight. A conjecture that fits in one sentence can outlive careers. Standing between those scales after China, I felt less like a founder with a brand and more like a person who had been given a long hallway and no map, which is sometimes what grace looks like when it is not polite.

I keep that hallway image because it blocks a prettier lie. The prettier lie says I chose Collatz the way you choose a thesis topic. The hallway says Collatz chose a gap in me that was already open. Lost inside. Future humming too loud. Body offline. Mind hunting for a clean object. The object arrived with a two-line rule and a century of unbroken teeth. I put my hand on it. I did not pull away.

If you want the origin without romance, keep it at this temperature. A tired traveler in Las Vegas. A famous open problem. Trials that walked to 1. An itch. A notebook. Private obsession, not a public claim. Everything after is construction, demolition, and the slow ethics of saying only what you can hold.

I almost deleted the nice-car line when these notes became something a stranger might read. It sounds like a bit. It sounds like I am auditioning for a quirky founder documentary. I kept it because the alternative is a cleaned origin story where I sit at a walnut desk with a fountain pen and invent a research program. That desk never existed. What existed was motion, status anxiety, humor as armor, and a sentence that told the truth about my posture: sorry, I am trying to solve this math conjecture, as if apology and ambition could share one breath.

Humor is how Brazilians in my family often touch serious things without drowning in them. I am not claiming a national monopoly on jokes. I am saying the scrap belongs to that reflex. If I sand it off, I sand off the person who actually met the problem. Going Home is not a costume change into Serious Mathematician. It is a record of a whole person colliding with a clean question while still being ridiculous enough to narrate himself in a car.

There were other scraps that night that did not survive. Half calculations. A dumb hope that maybe the pattern after 5 was the whole secret. A list of conjectures I glanced at and did not love. Goldbach got a nod. Riemann felt like a mountain range seen from a plane. Collatz felt like a door with a simple handle and a locked room behind it. I do not need to mythologize the selection process. Preference is allowed. Preference plus years of work becomes a project. Preference alone is a mood.

Jetlag compresses the distance between grand thoughts and petty ones. In the same hour I can invent a ten-year vision for a company and forget where I put my charger. That is relevant because Collatz arrived inside that compression. It did not arrive as a carefully scoped P0. It arrived as something my mind could hold when my mind could not hold sleep. I am suspicious of insights born only in that state. I am also unwilling to throw away a question just because the body was wrong about the clock.

So I gave it a probation period in my own head. If the itch died after a week of normal sleep, it was jetlag theater. If it survived payroll weeks and service-call weeks and ordinary Vegas sun, then it was mine. It survived. That is the least glamorous validation method I know, and the one I trust. Obsession that needs constant romantic lighting is usually vanity. Obsession that still shows up when you are behind on emails might be real work trying to happen.

By early January the China trip was already becoming story instead of sensation. The conjecture was not. It had moved from airport aftertaste into morning coffee. That is when I knew the notebook would not be a holiday souvenir. It would be a second job with no title and no applause, which is the only kind of second job worth keeping near a problem this old.

I want at least one paragraph that is boring in the right way. I wrote 7 and followed it to 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1. I wrote 19 and watched it climb through 58, 29, 88, 44, 22, then join a road I already knew. I wrote 21. I wrote 25. I wrote 27 and felt the path get long enough to humble the phone calculator aesthetic. None of this is research in the professional sense. It is acquaintance. You should not talk about a city if you have never walked a street. Those orbits were streets.

What surprised me was not that they reached 1. The internet had already spoiled the punchline for tested ranges. What surprised me was the emotional shape of waiting through a rise. There is a tiny fear, childish and persistent, that this will be the one that refuses. Then the halvings arrive like a staircase down a dark stadium, and you are back at the cycle everyone knows. That fear-and-relief loop is probably why the problem hooks amateurs. It trains a nerve. Later, when you learn how deep the open core goes, the nerve is already involved, which is both useful and hazardous.