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In a new preprint paper—which, for context, is not peer reviewed, and is more of an editorial or set of observations than a theory or study—mathematician Kevin Buzzard is grappling with a simple idea from coding that becomes a “thornier concept” when translated into math: what does the equal sign actually mean? And what does it not mean?
Buzzard has been in the news for his efforts to turn classic math proofs into code that can be verified by a computer, including Fermat’s Last Theorem. For him, as a classically trained mathematician, the world of computer code includes some surprises.
“Six years ago, I thought I understood mathematical equality,” Buzzard wrote in his paper. “I thought that it was one well-defined term, and that there was nothing which could be said about it which was of any interest to me as a working mathematician with a knowledge of, but no real interest in, the foundations of my subject. Then I started to try and do masters level mathematics in a computer theorem prover, and I discovered that equality was a rather thornier concept than I had appreciated.”
Before any “keyboard warriors” start trying to alert the world that this is overcomplicating things or somehow undermining tradition, it’s important to remember that just because something is an edge case, that doesn’t mean it isn’t important and worth discussing. And there’s actually a lot of nuance to be addressed in this particular discussion: should the same equal sign account for terms you’ve rounded up or down? Does the equal sign cover all of the necessary bases if we imply the passage of time between one side and the other (like, for example, how two chickens eventually become three)?
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