Unprovable Goldbach’s conjecture

[AntonioLao]

It is almost 275 years since the amateur German mathematician Christian Goldbach hypothesized that each and every even whole number can be expressed as the sum of two prime numbers.

In light of Godel’s proof concerning the shortcoming of mathematical logic, certainty is mounting for mathematical truths requiring no logical proofs.

Maybe we still cannot say that all math theorems do not necessarily need logical proofs for their truthfulness. That every kind of proofs is just window dressing made to attract the attention to the specific math assertion.

But for those who possess certain deep-seated mathematical faith in what they do, certainly no proof is required to affirm that what they are doing is correct.

In this sense, mathematical faith is equivalent to religious faith. The question is whether this is absolute faith? Can there be absolute faith knowing that human mental logic and reasoning and physical senses are not infallible?

In light of the principle of relativity for two key physical theories, can mathematical faith or for that matter religious faith being relative as well?

[Guille]

Very good thread theme, Antonio, I wonder why other's haven't posted, but let us two give it light and force.

Well, I believe that all knowledge is, actually, believe. Knowledge, thought, idea, opinion...are all believes of our mind. We just differentiate them, because our mind gives different grade of what I call "factuallity" of each of the beleifs. For example, the beleif that there is an organisation that controls each of our acts and behaviour, without us knowing, is a believe of "factuality" 1, not to give it a 0. Whereas the my belief that the capital of Spain is Madrid, what we call knowledge, has a grade of factuallity 9, not to say ten. There can be NO zero or ten factuality, for they would not be belief, and for we are subjective, and there is always an uncertainity. The grading is from 0-10. So, If I tell you the capital of spain is madrid, even if you don't know if it is, you will accept it and add it to your knowledge container (memory). This is because it makes sense. Why? Maybe because you know Spain, and, let's say, you have been told that neither Seville, Barcelona, Bilbao or Zaragoza is the capital of Spain, and you know that Madrid is the biggest city in Spain, so, you deduce, that it is the capital. Of course it's a belief, but a very-well background belief. There cna be other ways you deduce madrid to be the capital spain, for example, that you know that the US embassy is in Madrid, and that the embassies are always in the capitals, so, by logic, madrid is the capital of Spain. Now, if I tell you that there is an organisation that controls our behaviour and acts, but of which we cannot knwo about, you will definatelly send me to a psychiatric center. First, the statements themselves are a contradictory: if you cannot know about them, how do you know?... Second, I have no background for it, or at least haven't given it to you, or maybe the background I give are fallacies...There are thousands of possibilities.

From this paragraph, the conclusion is that a mathematical belief, or knowledge, let's say Godbach's conjecture, has more background than a, let's say, religious belief, or astrological (ATENTION! NOT astronomical, not the science), we might say that ther eis no differnece for all are belliefs, and that a religious belief is a good as a math belief because for religion, a relgiious belief is as correct as for math a math belief. But we must analize the beliefs not by the manner of itself, but by an overall intuitional-rational way. Intuiton or logic alone can't, but together, it is the basis of our thinking. So, let's say:
We know (please, remember that these knowledges are rational-intuitional-empirical, so they have a 89/10 of factuality) that the definition of virgin is someone that has NOT have sex. We know that to have a baby, a woman must be inseminated, either way (actually, both are artificial, if you think about it). We know that artificial insemination DIDN'T EXIST, AND WASN'T POSSIBLE until, I don't know, the second half of the 20th century? We know that according to the christian religion, the mother of the prophet Jesus Christ was the so-called "Virgin" Marry. We know that they lived 2000 years before medical (let's call it like this) insemination. So she must have had sex, with a man, in order to have a son. Thus, she must be non-virgin. Thus, the religious belief that the virgin marry is virgin is a fallacy bellief, non-rational, non-intuitional, non-empirical... Whereas Godbach's conjecture is not proofed, but I am sure that hundreds or thousands of mathematicians have tried to find an even integer that can't be obtained by the sum of two primes, and they've tried hundreds of numbers, high numbers, also computers, and none is find. This is well background for this belief.

Now, another interesting topic to discuss in this thread, is if Mathematical truths can be find without Pythagoras's invention/discoverment (whatever you belief) of the logical proof. I must say that I came to what the logical proof is, for the first time in my life, a few days ago. I am reading a book called "Fermat's Enigma" by Simon Singh. It is the mathematical book that I am most enjoying in my life. A good collection of math hist, math work and math talk, is done,in correct percentages.

By the way, I know that maybe NOBODY here will believe me, but I thought Fermat's last theorem, which is actually a conjecture, mcuh before knowing about it, Fermat, the logical proof, or knowing about Algebra! I thought about it 3.5 years ago, when I first was tought Pythagoras's theorem, I derived, and saw it was impossible for higher numbers.

Anyway, as this post is already long enough, I will start a thread in philosophy to discuss about logical and mathematical truths/proofs.