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Comment by paulpauper | Hacker News Reader

I don't think this is ever making it past the editor of any journal, let alone peer review.

Elementary functions such as exponentiation, logarithms and trigonometric functions are the standard vocabulary of STEM education. Each comes with its own rules and a dedicated button on a scientific calculator;

What?

and No comparable primitive has been known for continuous mathematics: computing elementary functions such as sin, cos, √ , and log has always required multiple distinct operations. Here we show that a single binary operator

Yeah, this is done by using tables and series. His method does not actually facilitate the computation of these functions.

There is no such things as "continuous mathematics". Maybe he meant to say continuous function?

Looking at page 14, it looks like he reinvented the concept of the vector valued function or something. The whole thing is rediscovering something that already exists.

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This preprint was written by a researcher at an accredited university with a PhD in physics. I'm sure they know what a vector valued function is.

The point of this paper is not to revolutionize how a scientific calculator functions overnight, its to establish a single binary operation that can reproduce the rest of the typical continuous elementary operations via repeated application, analogous to how a NAND or NOR gate creates all of the discrete logic gates. Hence, "continuous mathematics" as opposed to discrete mathematics. It seems to me you're being overly negative without solid reasoning.

its to establish a single binary operation that can reproduce the rest of the typical continuous elementary operations via repeated application,

But he didn't show this though. I skimmed the paper many times. He creates multiple branches of these trees in the last page, so it's not truly a single nested operation.

Well, it is still the case, even if not explicitly shown. Personally I think it almost boils down to school math, with some details around complex logarithms; the rest seems to be simpler.

The formulas are provided in the supplementary information file, as mentioned in the paper. https://arxiv.org/src/2603.21852v2/anc/SupplementaryInformat... You want page 9.

> so it's not truly a single nested operation.

Some of us had the wondrous epiphany as children that we could build any digital device we could dream of (yes, up to and including a full computer, CPU, RAM, peripherals, and all) out of SN7400 NAND gates that we could buy down at the local Radio Shack, if only we could scrape together enough change to buy the requisite number of parts and sockets and Tefzel wire.

Obviously, I can't speak for all of us who had that epiphany, but I strongly suspect that most of us who had that epiphany would find this result joyous.

The principal result is "all elementary functions can be represented by this function and constant 1". I'm not sure if this was known before. Applications are another matter, but I suspect interesting ones do exist.

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