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To what extent can we use intuition to evaluate mathematical claims?

Is it possible to ‘experience’ mathematics?

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How has the development of technology impacted mathematics?

Does mathematics progress cumulatively, or does new knowledge violently destroy old knowledge?

Is mathematics invented or discovered – or created in some other way?

Why is it so difficult to produce mathematical proof?

Does mathematics develop in the same way as other areas of knowledge?

Is mathematical knowledge driven forward by individual thinkers?

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Is mathematics ever aligned to a particular culture or tradition?

How easy is it to establish consensus in mathematics?

Is it a paradox that mathematics is both a human construct, and objectively true about the world?

To what extent do assumptions underpin our understanding of mathematics?

Can we draw on personal experiences to help produce and understand mathematical knowledge?

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Does mathematics provide us with the most objective form of language?

How can data visualizations be manipulated in order to spin the knowledge they communicate?

Do mathematical symbols convey the same type of meaning as ordinary words?

How can the intention behind statistics interfere with its objectivity?

How can statistics be used to manipulate people?

Is it possible to present data objectively?

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Are there special ethical responsibilities regarding how mathematical knowledge is produced and used?

Does basing decisions on algorithms create solid ethical knowledge?

Can ethical knowledge be objectively calculated via mathematics?

How different are mathematics and ethics in terms of the evidence used to justify knowledge claims?

Who should create the ethical framework used to produce and use mathematical knowledge?

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Is mathematics the most ‘fundamental’ of all the areas of knowledge?

Does mathematics provide us with certain knowledge?

Are mathematical axioms the same as truth?

Is the term ‘mathematical proof’ different from other types of proof?

Is mathematics defined by its content or method?

How does mathematical reasoning differ from other forms of reasoning?

Is mathematical knowledge always abstract?

Why is mathematics so highly esteemed?

Is mathematics based on ‘unproven truths’?

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Good KQs ask how we know about the world (second-order knowledge), rather than what we know about the world (first-order knowledge). Being able to tell the difference between first and second-order knowledge can be difficult, but it is the most important attribute of successful TOK thinking - and will form the basis of your essay and exhibition.

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Use our other free padlets on this area of knowledge - the quotes, real-world issues, and key thinkers - to explore and answer these KQs, trying to identify and challenge your assumptions as you do so.

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Although the KQs you see here relate primarily to mathematics, many of them link to other AOKs and themes, so bear this in mind as you consider them.

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Knowledge questions (KQs) form the heart of TOK, providing us with the opportunity to discuss, explore, and sometimes argue about the way we acquire and use our knowledge about the world.