Ten starting questions for a Mathematics AI exploration

Choose a seed with accessible evidence

These original question seeds are planning prompts. Adapt one to data or measurements you can obtain, and check the mathematical scope with your teacher. A promising idea names a quantity and a decision. Before committing, inspect a small dataset or attempt one calculation. Be clear when observations are real and when a simulation uses assumed inputs.

Choose a context you can explain without spending most of the exploration on background research. Access, consistent definitions and meaningful evaluation matter more than a fashionable topic.

Questions about patterns in data

• Campus journeys: How well does walking distance predict my journey time between a defined set of school locations? Use your own observations, record route conditions and inspect residuals.
• Seasonal daylight: How accurately can a sinusoidal model represent published daylight duration for one city over a year? Define the dates and compare errors across seasons.
• Device discharge: Which simple function best describes battery percentage during one repeatable, ordinary device task? Document the measurement interval and recognize that displayed percentages are rounded estimates.
• Public rainfall: How sensitive is a description of one station's rainfall to the averaging window? Compare the same period and avoid treating missing observations as zero.

Questions about probability and waiting

• Bus headways: How does irregular spacing between arrivals affect an estimated passenger waiting time? Compare a clearly stated arrival assumption with an observed or published timetable.
• Repeated sports attempts: How well does a constant-probability model describe one player's practice results across sessions? Seek permission where needed and examine whether fatigue or session differences challenge the assumption.
• A refill queue: How does service duration affect the chance of a queue exceeding a chosen length? Use a small, clearly explained simulation and justify input estimates with permitted observations.

Questions about geometry and decisions

• A garden path: How much material would two feasible routes require across a measured space? Compare length or area while respecting access and the site's real constraints.
• A display stand: Which arrangement of rectangular objects fits a fixed shelf most efficiently? Define orientation rules and compare a systematic method with a practical arrangement.
• Event ticket options: Under what attendance conditions do two publicly stated pricing options produce different total costs? Define a piecewise model and test the breakpoints, without inventing demand evidence.

Run a feasibility comparison

Shortlist two ideas and make a small planning table. Include data access, mathematical method, the outcome you expect and the assumption that most needs testing. Give each candidate a pilot task you can finish in one session. The pilot should reveal whether there is enough mathematical work and whether you understand the proposed technique.

For the daylight idea, fit a rough model to a few dates, check its prediction on a different date and identify a likely limitation. That test is more useful than collecting hundreds of rows before deciding how to use them.

Turn the seed into your own question

Specify the population or location, period, variables and purpose. Explain why you chose the method and how you will evaluate the result. Keep a record of changes after the pilot and teacher discussion. Avoid combining several seeds into a project so broad that none receives enough analysis.