Novice AI interactions for coding yield poor results. However, when experienced coders use AI and provide it with specific technical context about their existing project, it becomes an immense force multiplier, producing highly impressive and useful code that accounts for the project's limitations.

When working on complex or unconventional problems, an AI might initially claim the task is impossible. Prefacing your prompt with a phrase like "I know this is possible" can give the model more confidence to persist and attempt more creative, fringe solutions instead of giving up.

The key AI skill is evolving from crafting individual prompts to "loop engineering." This means defining goals and feedback systems that enable an agent to generate, self-review, and autonomously refine its output to meet a specific objective, minimizing the need for constant human-in-the-loop intervention.

Unlike human mathematicians who give up on ideas after weeks of tedious work, AI models are relentlessly dogged. They will execute on a given approach without the human bias of judging it as unlikely or not worth the time, leading to breakthroughs in problems where the solution required immense, finicky detail work.

The solution to the Erdős unit distance problem stands out not for its computational power, but for its creativity. The AI imported classical techniques from an entirely different mathematical field, a hallmark of human ingenuity, and produced a fruitful result that sparked further human research.

When an AI model initially claims it cannot perform a task, it may not be a true capability limit. Simply insisting with prompts like "just do it though" or "try harder" can sometimes brute-force the model past its own hesitancy and successfully complete the request.

Instead of immediately asking an AI to perform a complex task, first prompt it to create a functional spec or a sequential plan. Go back and forth to align on this plan before instructing it to execute, which significantly improves the final output's quality and relevance.

For advanced AI models, providing a high-level goal rather than a detailed, prescriptive list of instructions often produces better outcomes. Over-prompting can constrain the model's intelligence, while a simpler prompt allows it to leverage its own planning capabilities for a more effective execution.

While AI models are highly effective at accelerating research by implementing existing papers or ideas, they currently lack the 'taste' for true innovation. They tend to explore incremental improvements rather than rethinking concepts from first principles, meaning human creativity remains critical for paradigm shifts.