I've heard of Bourbaki. Iirc it is a collective of mathematicians and not a person?
Meanwhile, I am making serious progress with the Gödel stuff. Last time it was a real issue that the main (greek) uni paper I was focusing on is written in a way which isn't at all directed to people not in university math (I am only a philosophy degree holder :/ ), since it was presenting the logic behind the theorem in a very roundabout way. But now I got to the point and am at the Tarski alternative proof, without being stopped by the use of base 13 instead of the more intuitive for me base 10 (the author uses base 13 so as to make use of 13 being prime, but for obvious reasons this isn't good with myself as the reader when I am focusing on the logic and not some side-practicality in the proofs).
Of course my OCD won't let me shy away from reading Gödel's original proof, but for the time being I am looking at Tarski.
I like everything
Edit: As I mentioned once before, there was one chance I could have gotten into formal logic in my first year in university. I did come across the infamous Tractatus book - but due to Wittgenstein being a jerk I didn't feel like reading much past the first pages.
I think that if I had instead come across the Principia Mathematica, or Turing, or Gödel, it could have gone very differently - though tbh at the time I was roughly one month away from a major mental breakdown, so I wouldn't bet on it.
Principia Mathematica is an awfully dense book. I'd try to find any reasonably readable alternative.
Gödel's Second Incompleteness Theorem Explained in Words of One Syllable
First of all, when I say "proved", what I will mean is "proved with the aid of
the whole of math". Now then: two plus two is four, as you well know. And,
of course, it can be proved that two plus two is four (proved, that is, with the
aid of the whole of math, as I said, though in the case of two plus two, of
course we do not need the whole of math to prove that it is four). And, as
may not be quite so clear, it can be proved that it can be proved that two plus
two is four, as well. And it can be proved that it can be proved that it can be
proved that two plus two is four. And so on. In fact, if a claim can be proved,
then it can be proved that the claim can be proved. And that too can be
proved.
Now, two plus two is not five. And it can be proved that two plus two is not
five. And it can be proved that it can be proved that two plus two is not five,
and so on.
Thus: it can be proved that two plus two is not five. Can it be proved as well
that two plus two is five? It would be a real blow to math, to say the least, if
it could. If it could be proved that two plus two is five, then it could be
proved that five is not five, and then there would be no claim that could not
be proved, and math would be a lot of bunk.
So, we now want to ask, can it be proved that it can't be proved that two plus
two is five? Here's the shock: no, it can't. Or, to hedge a bit: if it can be
proved that it can't be proved that two plus two is five, then it can be proved
as well that two plus two is five, and math is a lot of bunk. In fact, if math is
not a lot of bunk, then no claim of the form "claim X can't be proved" can be
proved.
So, if math is not a lot of bunk, then, though it can't be proved that two plus
two is five, it can't be proved that it can't be proved that two plus two is five.
By the way, in case you'd like to know: yes, it can be proved that if it can be
proved that it can't be proved that two plus two is five, then it can be proved
that two plus two is five.
George Boolos, Mind, Vol. 103, January 1994, pp. 1 - 3.