AI or a human tutor?

The mathematician George Polya said:

“To teach effectively a teacher must develop a feeling for his subject; he cannot make his students sense its vitality if he does not sense it himself. He cannot share his enthusiasm when he has no enthusiasm to share. How he makes his point may be as important as the point he makes; he must personally feel it to be important.”

This is a true point; a good tutor should make you feel maths is important.

The mathematician Alexander Paulin said:

‘What is algebra? If you ask someone on the street this question, the most likely response will be: “Something horrible to do with x, y and z”. If you’re lucky enough to bump into a mathematician then you might get something along the lines of: “Algebra is the abstract encapsulation of our intuition for composition”. By composition, we mean the concept of two objects coming together to form a new one. For example adding two numbers, or composing real valued single variable functions. As we shall discover, this seemingly simple idea of composition hides vast hidden depth.’

We’re constrained by the requirements of the school maths syllabus (so the above level of abstraction is not specifically aimed for) but there is still plenty to get excited about; again a good tutor should make you aware of something of the excitement of studying maths.

“Any fool can know. The point is to understand.” Albert Einstein (quoted in a George F Simmons book)

Could an AI tutor transmit to its tutees the interest and excitement of learning maths? ChatGPT claims that it can:

“While I don’t have personal experiences or emotions, I can simulate them to some extent to create engaging and informative interactions on the topic of mathematics or any other subject.”

Does an AI language model understand mathematics? ChatGPT says:

“While I don’t “understand” mathematics in the same way a human mathematician does, I have been trained on a vast amount of text data, including mathematical concepts, formulas, and problem-solving techniques.

I can perform various mathematical tasks such as arithmetic calculations, solving equations, explaining mathematical concepts, and providing examples. However, my understanding is limited to the patterns and relationships present in the data I’ve been trained on. For complex or specialized mathematical topics, my responses may vary in accuracy and depth, depending on the specific query and the extent of my training data.

Overall, while AI language models like me can provide assistance with mathematical tasks and explanations, consulting with a human expert for complex or specialized mathematics is often advisable.”

The mathematician William Thurston said:

“Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding.”