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Maths History

Maryam Mirzakhani and drawing on surfaces

Introduce creative mathematical drawing, maps and surfaces for curious older children.

Quick answer

Maryam Mirzakhani was a brilliant mathematician who loved drawing on surfaces to solve puzzles and understand shapes. She showed how drawing and geometry can help us understand the world around us.

Learning outcome

By the end of this page, you will understand how mathematicians like Maryam Mirzakhani use drawing on surfaces to explore shapes, patterns, and real-world problems. Success signs:
  • You can draw simple shapes on a surface
  • You can explain how drawing helps solve maths problems
  • You can imagine how a surface might look when it's twisted or folded
  • You can connect drawing to real-life situations like maps or art

Why this matters

Drawing on surfaces helps mathematicians see patterns, solve puzzles, and understand how things work in the world. Maryam Mirzakhani showed that even the most complex problems can be explored by drawing and thinking creatively. This kind of thinking helps you solve problems in maths, art, and everyday life. It also helps you understand how maps, clothing, and even the Earth itself work.

How it works

Think of a surface as any flat or curved area you can draw on. A surface can be:
  • A piece of paper (flat)
  • A ball (curved)
  • A donut (curved with a hole)
  • A pillow (curved on top, flat on bottom)
When mathematicians draw on surfaces, they often:
  1. Draw lines or shapes
  2. Look at how the lines connect or cross
  3. Find patterns or make predictions
  4. Use their drawings to solve problems

Examples you can see

Let’s imagine Maryam is drawing on a donut-shaped surface (called a torus). She might draw:
  • Lines that go around the donut's hole
  • Lines that go around the donut's body
  • Patterns that show how the surface connects
Try this: Take a piece of paper and draw a circle. Now, imagine you can stretch and twist that circle to make a donut shape. What happens to your lines? Real-world example: Think about a map of your town. A map is a flat surface that shows the curved Earth. When you draw roads, rivers, and buildings on a flat map, you are drawing on a surface. Maps help you find your way around, just like Maryam's drawings helped her understand complex maths.

Try it as a mini adventure

Maryam's Map Quest Maryam is on a mission to find the shortest path between two cities on a curved map. She starts at point A and wants to get to point B. But the map is drawn on a donut-shaped surface!
  1. First time: Draw a straight line from A to B on a flat piece of paper
  2. Second time: Draw the same line, but now imagine the paper is a donut
  3. Third time: Draw a curved line that goes around the donut's hole
  4. Fourth time: Compare your lines and decide which one is shortest
  5. Fifth time: Draw your own path from one side of the donut to the other
What you learned: Sometimes the shortest path isn't a straight line, especially when the surface is curved!

Common mistakes

  • Mistake: Thinking that all surfaces are flat
    Why it happens: We usually think of paper and tables as flat, so it's hard to imagine curved surfaces
    Fix: Use a ball, donut, or pillow to see how curved surfaces work
  • Mistake: Drawing lines that don't follow the surface
    Why it happens: It's easy to draw on flat paper without thinking about the shape underneath
    Fix: Try drawing on the surface of a ball or donut and see how lines change
  • Mistake: Believing that drawing can't help with maths
    Why it happens: Some people think maths is only about numbers
    Fix: Watch how Maryam used drawings to solve hard problems

Parent and carer guide

To help your child explore drawing on surfaces:
  • Use everyday objects like balls, donuts, or pillows to show different surfaces
  • Ask your child to draw lines on these objects and describe what happens
  • Play "surface guessing games" - guess what shape a surface is just by looking at it
  • Encourage your child to draw their own maps or patterns on curved surfaces
  • Read books about Maryam Mirzakhani or other female mathematicians
  • Don't worry if your child doesn't get it right away - it's normal to be confused at first

Practice questions

  1. What shape is a donut? Is it flat or curved?
    Answer: A donut is curved with a hole in the middle
  2. How can you draw a line on a ball?
    Answer: You can draw lines that go around the ball's surface
  3. Why might Maryam draw on curved surfaces?
    Answer: To solve problems that are easier to see when the surface is curved
  4. What is a surface in maths?
    Answer: Any flat or curved area you can draw on
  5. Can you name three surfaces you can draw on?
    Answer: Paper, ball, donut

FAQ

Who was Maryam Mirzakhani?

Maryam Mirzakhani was a mathematician who loved to draw and solve puzzles. She was the first woman to win the Fields Medal, which is the highest award in mathematics.

What does "drawing on surfaces" mean?

It means using drawings to explore and understand shapes, patterns, and problems that exist on flat or curved surfaces.

Why is it important to understand surfaces?

Understanding surfaces helps us solve problems in maps, art, engineering, and science. It also helps us see the world more clearly.

Can I draw on surfaces at home?

Yes! You can draw on paper, balls, donuts, or even your pillow to explore different shapes.

What kind of problems did Maryam solve?

She solved problems about geometry, patterns, and how shapes behave on different surfaces. Her work helped us understand complex ideas in maths and science.