You know, I'm sort of split on what to think of the click-bait-y article title.

The guy's a PhD at Princeton, he clearly knows the Fourier Transform is more than just a trick - he even mentions that he wants to bring science/math to a wider audience at the end. From what I can tell, this article's more aimed at the nerdy middle/high schooler who likes math than engineers and computer scientists (the main target audience of this site). So while the article's title sort of tricks you into learning about this "trick", as long as people who normally can't be bothered to look at math (because for some reason it's popular to be "bad at math", ie not want to do math) are learning about the applications of mathematics in the real world, I don't see anything particularly wrong with trying to reach a wider audience.

trick |trɪk|

noun

• a clever or particular way of doing something: the trick is to put one ski forward and kneel.

Synonyms: [tricks]: art, skills, techniques; secrets, shortcuts.

... and I wish people would stop this witch hunt for "clickbait". It seems any headline that includes trace amounts of creativity, imagination, or suspense is seen as illegitimate, usually with an allusion to some mythical past where every book was apparently called "It was the Gardener: A Murder-Mystery".

I agree. I didn't like the original title, but changing it to "The Fourier transform, a widely applicable mathematical discovery" is ridiculous.

But I kind of feel like it might give the wrong impression that these things are "tricks" (whatever that even means). I do agree with you though, the guy probably knows what he's talking about.

Yes, I was a bit surprised at the way the title hinted that this was a new 'trick' thing, when I have been familiar with Fast Fourier Transforms since forever when it comes to audio processing and reverb convolution etc., but then I realised that this is domain specific knowledge that is entirely due to me working in this capacity for so long. To someone in another industry or engineering capacity, FFTs may be an unknown entity, and indeed be an 'interesting discovery'.

I think "trick" here was referring to what is sometimes called "Fourier's trick" for getting the Fourier coefficients, than calling Fourier analysis itself a trick.