I like the Kronecker quote, "Natural numbers were created by god, everything else is the work of men" (translated). I figure that (like programming) it turns out that putting our problems and solutions into precise reusable generalizable language helps us use and reuse them better, and that (like programming language evolution) we're always finding new ways to express problems precisely. Reusability of ideas and solutions is great, but sometimes the "language" gets in the way, whether that's a programming language or a particular shape of the formal expression of something.

More like 1 = 0 + 1.

Read about Lisp, the Computational Beauty of Nature, 64k Lisp from https://t3x.org and how all numbers can be composed of counting nested lists all down.

List of a single item:

     (cons '1 nil)

Nil it's an empty atom, thus, this reads as:

[ 1 | nil ]

List of three items:

    (cons '1 (cons 2 (cons 3 nil)))

Which is the same as

    (list '1 '2 '3)

Internally, it's composed as is, imagine these are domino pieces chained. The right part of the first one points to the second one and so on.

[ 1 | --> [ 2 | -> [ 3 | nil ]

A function is a list, it applies the operation over the rest of the items:

     (plus '1 '2 3') 

Returns '6

Which is like saying:

  (eval '(+ '1 '2 '3))

'(+ '1 '2 '3) it's just a list, not a function, with 4 items.

Eval will just apply the '+' operation to the rest of the list, recursively.

Whis is the the default for every list written in parentheses without the leading ' .

    (+ 1 (+ 2 3))

Will evaluate to 6, while

    (+ '1 '(+ '2 '3)) 

will give you an error as you are adding a number and a list and they are distinct items themselves.

How arithmetic is made from 'nothing':

https://t3x.org/lisp64k/numbers.html

Table of contents:

https://t3x.org/lisp64k/toc.html

Logic, too:

https://t3x.org/lisp64k/logic.html

You don’t really have to believe Wittgenstein; any logician will tell you that if your proof is not logically equivalent to 1=1 then it’s not a proof.

Sure, I just personally like his distinction between a “true” statement like “I am typing right now” and a “tautological” statement like “3+5=8”.

In other words, declarative statements relate to objects in the world, but mathematical statements categorize possible declarative statements and do not relate directly to the world.

If you look from far enough, it becomes "Current world ⊨ I am typing right now" which becomes tautological again.

In my view mathematics builds tools that help solve problems in science.

This is known as “applied mathematics”.

Sounds lame and boring to me.