I wanted to see if GPT-3 could explain a mathematical expression for me, as a follow-on from Using GPT-3 to explain how code works. I grabbed an example from this page of the GitHub documentation.
Here's my conversation with GPT-3 as plain text - except I added > to the lines that I entered to differentiate them from the GPT-3 output:
> Explain this:
>
> $$\left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)$$
This is the Cauchy-Schwarz inequality.
> Explain the formula syntax step by step, using $$ wrapped around the formula steps:
$$\left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)$$
This is the Cauchy-Schwarz inequality.
$$\left( \sum_{k=1}^n a_k b_k \right)^2$$
This is the sum of all products of corresponding elements in the vectors a and b, squared.
$$\leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)$$
This is saying that this sum is less than or equal to the product of the sums of the squares of each vector.
The reason I said "using $$ wrapped around the formula steps" was to get the output to be produced in the syntax that GitHub Markdown understands. It worked! Here's the rendered version of my conversation:
Explain this:
$$\left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)$$
This is the Cauchy-Schwarz inequality.
Explain the formula syntax step by step, using $$ wrapped around the formula steps:
This is the Cauchy-Schwarz inequality.
This is the sum of all products of corresponding elements in the vectors a and b, squared.
This is saying that this sum is less than or equal to the product of the sums of the squares of each vector.