As someone with an MS and BS in mathematics I was intrigued by this story. I read the links and could not discern precisely what Mr. Gidiney claimed to have discovered. If, as reported in the newspaper, "Mr. Gidney claims that by an algebraic calculation he has discovered the exact ratio" then he was mistaken. (The newspaper might have misquoted him on this technical topic.)

Pi is famously an irrational number. That means it cannot be expressed precisely as the ratio of two integers.

Pi is even more famously a transcendental number. That means it is "not the solution of any non-constant polynomial equation with rational coefficients."

So I would like to see Mr. Gideney's "algebraic proof" to better understand its claim.

What a great story. Thanks, Amy, for writing it, and thanks, Andrew, for sharing it.

Thank you Amy and Andrew! I really enjoyed this

https://en.wikipedia.org/wiki/Pi

As someone with an MS and BS in mathematics I was intrigued by this story. I read the links and could not discern precisely what Mr. Gidiney claimed to have discovered. If, as reported in the newspaper, "Mr. Gidney claims that by an algebraic calculation he has discovered the exact ratio" then he was mistaken. (The newspaper might have misquoted him on this technical topic.)

Pi is famously an irrational number. That means it cannot be expressed precisely as the ratio of two integers.

Pi is even more famously a transcendental number. That means it is "not the solution of any non-constant polynomial equation with rational coefficients."

So I would like to see Mr. Gideney's "algebraic proof" to better understand its claim.