What is truth?

I know nothing of maths but this is a fun question I posed to readers: 'if two people are on a desert island and an observor claims one is 'mad', whose reality is the true one?' The best explanation of any kind of 'truth' is the one accepted by the majority in that particular society; it would not apply to every society.

ps I envy you maths genii! I find it hard balancing my bank account, let alone complex calculations. I wish there were a microchip you could insert, to make you expert in a chosen field.

Yes, good point.

All Godel was saying is if a rule based system avoids contradicting itself, it admits that some things are outside of its known rules and cannot be answered.and cannot be proven.

If it tries, then it will inevitably contradict itself because it will have to break its own rules and therefore be inconsistent.

So a system of rules can either be consistent but incomplete or complete but inconsistent. And no matter how much you enhance the rules there will still be further truths the system can't handle

This is why there can be no "final truth" since there are always going to be truths that cannot be proven by any rules based system.

There's a jump somewhat from the first two paragraphs. Gödel is referring to a particular aspect of mathematics. Applying this to broader questions is making a leap that requires substantial justification.

That isn't Gödel. 

"No formal system capable of addressing arithmetic will ever be able to prove all mathematical truths. There will always be propositions that elude proof."

Gödel's Incompleteness Theorems Made Simple - Andrea Minini

Can you share where Gödel expresses the "idea hat there will always be some truths that cannot be mathematically expressed, at least in the foreseeable future"?

You wouldn’t, no. But my point is that while it might be true for the person in love, it’s purely a subjective experience and not something that can be captured by any mathematical model. 

This goes to show that "truth" can have different meanings for different people. And in a way, it supports Godel's idea that there will always be some truths that cannot be mathematically expressed, at least in the foreseeable future.

You wouldn’t, no. But my point is that while it might be true for the person in love, it’s purely a subjective experience and not something that can be captured by any mathematical model. 

This goes to show that "truth" can have different meanings for different people. And in a way, it supports Godel's idea that there will always be some truths that cannot be mathematically expressed, at least in the foreseeable future.

That isn't Gödel. 

"No formal system capable of addressing arithmetic will ever be able to prove all mathematical truths. There will always be propositions that elude proof."

Gödel's Incompleteness Theorems Made Simple - Andrea Minini

Can you share where Gödel expresses the "idea hat there will always be some truths that cannot be mathematically expressed, at least in the foreseeable future"?