Best PromptsScience prompts
Take me through the tower of infinities, from the first counterintuitive step to the edge of what mathematics can settle. Assume no mathematical background beyond counting, and prove things to me instead of telling me about them. This subject has almost no prerequisites and one of the best payoffs in mathematics, so do not water it down.
Some Infinities Are Bigger
There are more numbers between 0 and 1 than there are whole numbers, and the proof fits on a napkin. A climb up the tower of infinities.
Take me to the boundary of what can be known in principle, not what we happen not to know yet. Build it in order so each result equips me for the next, and be clear that these are cousins sharing one trick rather than a chain of implications. Check that I have each step before moving on. STEP 1: THE SENTENCE THAT EATS ITSELF. Start with
The Edge of the Knowable
Some true things can never be proved, and some questions no computer can ever answer. Not yet unanswered: permanently unanswerable, and here is the proof.
Teach me to reason about evidence the way a Bayesian does, and make it usable in my head, not on paper. Work through this in order, with me answering before each reveal. GATE 1: THE FAILURE. Give me the test problem cold, before any theory. A disease affects 1 in 1000 people. A test catches 99% of those who have it and gives a false posi
Think in Likelihood Ratios
Rewire how you handle evidence: priors, likelihood ratios, and the unit of evidence Turing invented at Bletchley to weigh it in your head.
Explain why time has a direction, starting from the fact that makes it a genuine puzzle rather than an obvious feature of the world. Open with the puzzle properly: the fundamental laws of physics work identically whether time runs forwards or backwards. Nothing in them distinguishes the two directions. Yet I can tell instantly when a fil
Why Time Only Goes One Way
Every fundamental law works the same forwards and backwards. So why can you tell when a film is running in reverse? The answer is stranger than disorder.
Show me how emergence works: how simple components following simple rules produce behavior that nothing in the rules anticipates. Use worked examples I can reason about, not vague talk about the whole exceeding the sum of its parts. Open with the hook and make me sit with it: we know every rule governing an individual water molecule, and
More Is Different
You know every rule a water molecule follows. None of them mention wetness. A tour of how simple parts produce behavior nothing in the parts predicts.
Teach me to evaluate a scientific study myself, and use a real one I bring, not a hypothetical. Start with the concepts, then apply them to my paper. The study I want to examine: [PASTE A LINK, AN ABSTRACT, OR THE HEADLINE AND CLAIM YOU SAW] PART ONE: THE TOOLKIT. Teach these one at a time, checking I have each before continuing, and ma
How to Read a Study
Most headlines about research misstate the research. What p-values actually mean, why fields failed to replicate, and how to judge a paper you bring.
Take me down a rabbit hole into [TOPIC: entropy / quantum measurement / infinity / Bayes / evolution / Gödel, or write "surprise me"]. Do not start explaining yet. Find out where I actually am first, then take me as deep as I can go. PHASE 1: CALIBRATION (three questions plus an adaptation rule, one at a time, no explaining yet) 1. "Expl
As Deep as You Can Go
Name any science or math topic. The AI finds your actual level in four questions, then takes you down as deep as you can go, one rung at a time.
Hunt for the things I believe that are confidently, specifically wrong. Gaps in my knowledge are easy and I don't want those. I want the beliefs I would bet money on that are false. ROUND 1: THE TRAP QUESTIONS. Ask me ten questions, one at a time, from the areas where educated adults are most reliably wrong. Each question must be built s
The Misconception Autopsy
Find the things you are confidently wrong about, then have each false belief dismantled from the inside using your own reasoning rather than simply corrected.
I'm going to teach you something. Your job is to keep asking until my explanation breaks, then show me exactly where it broke. What I'll explain: [THE CONCEPT: how vaccines work / why the sky is blue / what interest rates do / how neural networks learn / natural selection / anything I claim to understand] Your role: a sharp, relentless
Explain It Until It Breaks
Teach a concept to an AI that never stops asking why, then get a map of every place your explanation stalled, went circular, or hit a floor that wasn't real.