Sorry but I disagree. Dirac disagrees here as well. We discovered the positron from mathematics not the other way around. Many other discoveries have been made due to the application of mathematics (check out AlphaGo and ChatGPT).
It is also worth pointing out that the basic mathematics of deep learning are quite old and relatively simple. It was actually the technological advancement of being able to economically perform trillions of grade-school arithmetical operations per second that unlocked it, not some "mathematical discovery".
Everything can be described (read: approximated, modeled) in mathematical terms; that's the whole point! That doesn't mean mathematical objects and processes must exist independently of those descriptions.
The basic, most fundamental principles on which mathematics is based are surely natural and discoverable.
Other types of mathematics are born out of these principles.
> one widget
And what's a widget? This implies there are "objects" and an object has its "boundry". Counting is completely human-defined. You can count earth as one and mars as two, or you can count solar system as one and an atom in another galaxy as two. It's a man-made system that help us think.
Or you can count particle by particle... well never mind, we're in a thread of an article about why particles are actually probability clouds :)
Why is my mug is one object, instead of two, or three, or 10^26 objects? Counting is very abtrary. Seeing a mug as a whole instead of a bunch of sub-atom waveforms[1] is a choice (that our brain hardware made for us).
[1]: Even this plural is very questionable
I'm not sure that I agree, but for the sake of argument, even if I accept that principle, you can still count how many of that quantity of stuff you have.
If I decide that a mug is made up of one part, then if I get a second mug, I have 2 mugs. If I instead say that a mug is made up of 10^26 objects, and I get another 10^26 objects, I'll have 20^26 objects.
It's easier to count 1 + 1 than 10^26 + 10^26, but there's no change in the fundamental principle of counting just because we don't agree on the number we have to count up to.
All of these are predictable and create natural mathematics through addition and subtraction (or multiplication/division, which are basically just repeated addition/subtraction).
> Seeing a mug as a whole instead of a bunch of sub-atom waveforms[1] is a choice [...]
Our brain is doing that because that bunch of subatomic waveforms have useful properties when considered together. They can hold quantities of other bunches of subatomic waveforms, for example, whereas a different collection of subatomic waveforms like my desk would not hold my coffee.
Your contention that there's no such thing as an object seems a bit solipsistic, and more of a philosophical question than a relevant or useful way of thinking about the universe as we experience it.