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Theorem: a general proposition not self-evident but proved by a chain of reasoning; a truth established by means of accepted truths.  

In mathematics, the Pythagorean theorem, relation of the three sides of a right triangle.

It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

The theorem can be written as an equation relating the lengths of the sides a, b and c, where c represents the length of the hypotenuse and a and b the lengths of the triangle's other two sides.

a^2+b^2=c^2

There are over 350 proofs to how to prove that this is true for all conditions

Fermat's last theorem  

Pierre de Fermat, (born August 17, 1601, Beaumont-de-Lomagne, France—died January 12, 1665, Castres), French mathematician who is often called the founder of the modern theory of numbers. Together with René Descartes, Fermat was one of the two leading mathematicians of the first half of the 17th century.

Andrew Wiles spent 7 years in secrecy working on the theorem 

First heard about the theorem when he was 10 years old

In 1986, when he was 33 years old he was a professor at Princeton and spent the next 7 years of his life working in secret trying to prove this theorem

In June 1993, he presented his proof to the public for the first time at a conference in Cambridge.

He gave a lecture a day on Monday, Tuesday and Wednesday with the title "Modular Forms, Elliptic Curves and Galois Representations". There was no hint in the title that Fermat's last theorem would be discussed, Dr. Ribet said. ... Finally, at the end of his third lecture, Dr. Wiles concluded that he had proved a general case of the Taniyama conjecture. Then, seemingly as an afterthought, he noted that that meant that Fermat's last theorem was true. Q.E.D.[17]

In August 1993, it was discovered that the proof contained a flaw in one area. Wiles tried and failed for over a year to repair his proof. According to Wiles, the crucial idea for circumventing, rather than closing, this area came to him on 19 September 1994, when he was on the verge of giving up. Together with his former student Richard Taylor, he published a second paper which circumvented the problem and thus completed the proof. Both papers were published in May 1995 in a dedicated issue of the Annals of Mathematics.[18][19]

https://en.wikipedia.org/wiki/Andrew_Wiles

[9:109] Is one who establishes his building on the basis of reverencing GOD and to gain His approval better, or one who establishes his building on the brink of a crumbling cliff, that falls down with him into the fire of Hell? GOD does not guide the transgressing people.

[59:29] If we revealed this Quran to a mountain, you would see it trembling, crumbling, out of reverence for GOD. We cite these examples for the people, that they may reflect.

[4:82] Why do they not study the Quran carefully? If it were from other than GOD, they would have found in it numerous contradictions.

Treat the Quran like a theorem

If there is a contradiction then it is our understanding that needs to be redefined

Quran is consistent no contradiction 

[39:23] GOD has revealed herein the best Hadith; a book that is consistent, and points out both ways (to Heaven and Hell). The skins of those who reverence their Lord cringe therefrom, then their skins and their hearts soften up for GOD's message. Such is GOD's guidance; He bestows it upon whoever wills (to be guided). As for those sent astray by GOD, nothing can guide them.

[39:27] We have cited for the people every kind of example in this Quran, that they may take heed. [39:28] An Arabic Quran, without any ambiguity, that they may be righteous. [39:29] GOD cites the example of a man who deals with disputing partners (Hadith), compared to a man who deals with only one consistent source (Quran). Are they the same? Praise be to GOD; most of them do not know.

[3:7] He sent down to you this scripture, containing straightforward verses—which constitute the essence of the scripture—as well as multiple-meaning (ambiguous) or allegorical verses. Those who harbor doubts in their hearts will pursue the multiple-meaning verses to create confusion, and to extricate a certain meaning. None knows the true meaning thereof except GOD and those well founded in knowledge. They say, "We believe in this—all of it comes from our Lord." Only those who possess intelligence will take heed.

Abrogation indicate that there is a contradiction

[2:106] When we abrogate any miracle, or cause it to be forgotten, we produce a better miracle, or at least an equal one. Do you not recognize the fact that GOD is Omnipotent?

[10:20] They say, "How come no miracle came down to him from his Lord?" Say, "The future belongs to GOD; so wait, and I am waiting along with you."

[6:115] The word of your Lord is complete, in truth and justice. Nothing shall abrogate (change/substitute) His words. He is the Hearer, the Omniscient.

[18:27] You shall recite what is revealed to you of your Lord's scripture. Nothing shall abrogate (change/substitute) His words, and you shall not find any other source beside it.

[78:37] Lord of the heavens and the earth, and everything between them. The Most Gracious. No one can abrogate (object) His decisions.

[67:3] He created seven universes in layers. You do not see any imperfection in the creation by the Most Gracious. Keep looking; do you see any flaw? [67:4] Look again and again; your eyes will come back stumped and conquered.

Intoxicants

[4:43] O you who believe, do not observe the Contact Prayers (Salat) while intoxicated, so that you know what you are saying. Nor after sexual orgasm without bathing, unless you are on the road, traveling; if you are ill or traveling, or you had urinary or fecal-related excretion (such as gas), or contacted the women (sexually), and you cannot find water, you shall observe Tayammum (dry ablution) by touching clean dry soil, then wiping your faces and hands therewith. GOD is Pardoner, Forgiver.

[5:90] O you who believe, intoxicants, and gambling, and the altars of idols, and the games of chance are abominations of the devil; you shall avoid them, that you may succeed.

Violence towards others

[33:61] They have incurred condemnation wherever they go; (unless they stop attacking you,) they may be taken and killed.

[2:190] You may fight in the cause of GOD against those who attack you, but do not aggress. GOD does not love the aggressors. [2:191] You may kill those who wage war against you, and you may evict them whence they evicted you. Oppression is worse than murder. Do not fight them at the Sacred Mosque (Masjid), unless they attack you therein. If they attack you, you may kill them. This is the just retribution for those disbelievers. [2:192] If they refrain, then GOD is Forgiver, Most Merciful. [2:193] You may also fight them to eliminate oppression, and to worship GOD freely. If they refrain, you shall not aggress; aggression is permitted only against the aggressors.

Inheritance laws 

One of the worst offenses is to attribute lies to God

[29:68] Who is more evil than one who fabricates lies and attributes them to GOD, or rejects the truth when it comes to him? Is Hell not a just retribution for the disbelievers?

[39:32] Who is more evil than one who attributes lies to GOD, while disbelieving in the truth that has come to him? Is Hell not a just requital for the disbelievers?

[6:144] Regarding the two kinds of camels, and the two kinds of cattle, say, "Is it the two males that He prohibited, or the two females, or the contents of the wombs of the two females? Were you witnesses when GOD decreed such prohibitions for you? Who is more evil than those who invent such lies and attribute them to GOD? They thus mislead the people without knowledge. GOD does not guide such evil people.”

[5:101] O you who believe, do not ask about matters which, if revealed to you prematurely, would hurt you. If you ask about them in light of the Quran, they will become obvious to you. GOD has deliberately overlooked them. GOD is Forgiver, Clement. [5:102] Others before you have asked the same questions, then became disbelievers therein.

[20:114] Most Exalted is GOD, the only true King. Do not rush into uttering the Quran before it is revealed to you, and say, "My Lord, increase my knowledge."