AOK Mathematics

  1. History of Mathematics
  2. Should Mathematics be ethical?
  3. The Man Who Knew Infinity
  4. Is Mathematics discovered or invented?
  5. Fermat’s Last Theorem
  6. Resources

History of Mathematics

Should Mathematics be ethical?

The Guardian view on ethics for mathematicians: an essential addition

Maths and tech specialists need Hippocratic oath, says academic

Does maths make you moral?

The Man who Knew Infinity

Mathematical proof reveals magic of Ramanujan’s genius

The Man Who Knew Infinity: inspiration, rigour and the art of mathematics

For more understanding of Ramanujan, watch the following.

It is recommended that you use one of the resources above to help you answer these questions.

a. Why did people not trust Ramanujan as a mathematician? Were they right to do so?

b. Can only educated people be trusted? Are they valued more?

c. Were his mathematical theories discovered or invented?

d. What is proof? Can there ever be 100% proof? How do you know something is proven?

e. Why is mathematics important? How do you know it is important? Who tells you that it is? How do you know their perspective can be trusted?

Is Mathematics discovered or invented?

Daniel Tammet is perhaps similar to Ramanujan. Could his explanations explain the origins of Ramanujan’s knowledge?

Watch Daniel’s explanation of how he develops knowledge.

  • Is it the same for everybody? Why, why not?
  • Does he discover maths or has he invented a new way of inventing?
  • How do you develop your knowledge of mathematics?
  • If you arrive at the same answer but in different ways, is it the same knowledge?

Is Maths just a game?

Fermat’s Last Theorem

This is a fascinating documentary, if rather long, about how a maths professor solved the centuries-old problem of Fermat’s Last Theorem.

  1. How did Professor Andrew Wiles solve the problem?
  2. Which WOK did he use?
  3. What were the difficulties in proving his solution (his knowledge)?
  4. Can his knowledge be trusted? How can it be used outside of mathematics?

Resources

Two excellent websites with Maths resources are below, kudos to the teachers who developed them.

TOK and Mathematics

TOK2022

Choose one of the articles below and explain how it links to the issue of proof in mathematics.

Proof and Evidence in maths

Controversial Maths Problems

How do we know how to teach mathematics?

Is Mayan maths better?

Why study maths? Does it have the answers?

2020 Student Presentations

Student Presentation – September 2020