April 14, 2026
Calculator wars ignite
Not all elementary functions can be expressed with exp-minus-log
‘One Math Button to Rule Them All’? Commenters cry goalpost shift
TLDR: A blog pushes back on a hyped “one-button” math trick, saying exp-minus-log can’t make basics like absolute value under standard rules. Commenters split: some accuse goalpost shifting, others note the original paper already narrowed scope—proof that definitions decide whether the “universal” claim holds.
Math internet is at it again. A viral paper claimed one mega-button — the “exp minus log” trick — could re-create every “elementary” calculator function. Enter a spicy rebuttal: a blogger argues that with the usual definitions of exponent and log, you can’t even build plain old absolute value. Translation: this isn’t the math version of a universal remote. The dream of a single super-button? Not so fast. Blog post vs. paper is the showdown of the week.
The comments went full courtroom drama. One camp says the critique is goalpost-shifting — as in, the original author already narrowed the meaning of “elementary” on purpose, and that’s the whole point. Another camp fires back: if “elementary” doesn’t include stuff like taking roots of polynomials, what are we even doing? Meanwhile, confused onlookers begged for simple examples and fewer ten-dollar math words. A deep-cut cameo: a commenter dropped a link about “closed-form numbers,” noting that not even general polynomials live in the exp–log world, so of course the one-button can’t do everything.
Jokes flew: “Absolute value walked in and flipped the table,” “This button is universal, but only if you define ‘universal’ very carefully,” and “Not the NAND of calculus, folks.” The vibe: bold claim, sharp reality check, definitions doing most of the heavy lifting.
Key Points
- •Odrzywołek’s paper claims all elementary functions can be built from E(x,y)=exp x − log y (EML terms), variables, and the constant 1.
- •The paper’s definition of “elementary” is restricted to a specified set of 36 symbols and involves modifications to the conventional logarithm.
- •Smith argues that under broader standard meanings of “elementary,” EML terms are not universally expressive.
- •Smith proves that |x| cannot be represented by any EML term under standard exp/log, because EML terms are real-analytic while |x| is not differentiable at 0.
- •Smith notes the paper’s non-standard or extended-real workarounds and signals a second, more technical complex-domain argument (incomplete in the excerpt).