George Boolos has since sketched an alternative proof of the first incompleteness theorem that uses Berry's paradox rather than the liar paradox to construct a true but unprovable formula.

In these papers he sketched a proof of the Poincaré conjecture and a more general conjecture, Thurston's geometrization conjecture, completing the Ricci flow program outlined earlier by Richard Hamilton.

Grigori Perelman sketched a proof of the full geometrization conjecture in 2003 using Ricci flow with surgery.

In 2003 Grigori Perelman sketched a proof of the geometrization conjecture by showing that the Ricci flow can indeed be continued past the singularities, and has the behavior described above.

Haken sketched out a proof of an algorithm to check if two Haken manifolds were homeomorphic or not.

The proof sketched in the previous paragraph that the consistency of ZFC + " there is an inaccessible cardinal " implies the consistency of ZFC + " there is not an inaccessible cardinal " can be formalized in ZFC.

A proof for the homotopy invariance of singular homology groups can be sketched as follows.

A proof can be sketched as follows: Let Ω be the weak *- compact set of positive linear functionals on A with norm ≤ 1, and C ( Ω ) be the continuous functions on Ω.

The consequence ((( A ) B ) C ) = ( AC )(( B ) C ), C7 in LoF, enables an algorithm, sketched in LoFs proof of T14, that transforms an arbitrary pa formula to an equivalent formula whose depth does not exceed two.

The theorem is named after the mathematician Friedrich Engel, who sketched a proof of it in a letter to Wilhelm Killing dated 20 July 1890.

Thurston's geometrization conjecture whose proof was sketched

The date given is usually the publication date of the complete proof of a result, which is sometimes several years later than the proof or first announcement of the result, so some of the items appear in the " wrong " order.

The section requires proof that the announcement is both provably false, and has actual or likely market impact.

In any event, the critical productivity of that time is abundant proof that if he was taking laudanum, it was never in command of him to the extent that it had been during his vagrant years.

Their policy ran counter to the traditional idea that a good fighter was usually a libertine, and that in sex affairs `` God-given passion '' was a proof of manliness.

A credulousness, a distaste for documentation, an uncritical reliance on contemporary accounts, and a proneness to assume a theory as true before adequate proof was provided were all evidences of his failure to comprehend the use of the scientific method or to evaluate the responsibilities of the historian to his reading public.

Both Alfred Harcourt and Donald Brace had written him enthusiastic praise of Elmer Gantry ( any changes could be made in proof, which was already coming from the printer ) and they had ordered 140,000 copies -- the largest first printing of any book in history.

The final proof was a small incident.

It was unlikely that any girl as sharp as Mary Jane Brennan would believe it without proof.

But I had the proof, all documented in a legal agreement which I would show her the moment I was free to do so.

Attorneys for the eight other defendants said only that there was no proof of their clients' guilt.

The absolution of Doaty's last will and testament was proof enough of that ; ;

The axiom of choice was formulated in 1904 by Ernst Zermelo in order to formalize his proof of the well-ordering theorem.

A grant application to build a proof of concept prototype was submitted in March 1939 to the Agronomy department which was also interested in speeding up computation for economic and research analysis.

That was so because it not only was proof of excessive pride, but also resulted in violent acts by or to those involved.

At some point, he was alleged to have accompanied Swein on a pilgrimage to the Holy Land, but proof is lacking.

Mordell's theorem had an ad hoc proof ; Weil began the separation of the infinite descent argument into two types of structural approach, by means of height functions for sizing rational points, and by means of Galois cohomology, which was not to be clearly named as that for two more decades.

Canova in 1817 by George Hayter ( British Embassy, Paris ) There was, however, another proof, which modesty forbade him to mention, an ever-active benevolence, especially towards artists.

It was at this time that ` Abdu ' l-Bahá, in order to provide proof of the falsity of the accusations leveled against him, in tablets to the West, stated that he was to be known as "` Abdu ' l-Bahá " an Arabic phrase meaning the Servant of Bahá to make it clear that he was not a Manifestation of God, and that his station was only servitude.

He had been well educated, and was versed in grammar and rhetoric, and had already, while still a young man, and before reaching the episcopate, given proof to those who dwelt with him of his wisdom and acumen " ( Soz., II, xvii ).

However, others point to the Council of Nicaea as proof in and of itself that Arianism was a real theological ideology.

Also, reserve the right to demand proof of death despite the fact that you'll probably never use it.

This is not a rejection of existence by Gilson, a leading modern metaphysician in the classical tradition: " philosophers are wholly justified in taking existence for granted ... and in never mentioning it again ...." In Gilson's view, the participial being is a given, a primitive of experience, not subject to proof or investigation, as it is the grounds of proof.

Fermat's proof was never found, and the problem of finding a proof for the theorem went unsolved for centuries.

It is important to understand that the outcome of empirical research using statistical hypothesis testing is never proof.

Currently almost all of these are experimental or proof of concept, and as such may never see mass production.

Refraining from these restrictions when there is unequivocal proof that this will lead to the murder of innocents is worse, because movement restricted can later be granted, while dead will never live again.

The second part of the 1st Critique is Kant ’ s examination of the rationalist claims to absolute knowledge, taking on the most famous of these, the ontological proof of God ’ s existence, and showing that he can, through pure, non-experiential logic, both prove the affirmative and the negative of a proposition about a “ noumenal object ” ( i. e. an object like “ God ” which can never be an object of direct experience for a contingent being ).

Boehm claimed to have cured gay people in the fourth part of his series on homosexuality, but presented as proof a case in which “ the homosexuality never became conscious for the patient and had never expressed itself in manifest activity .” This patient does not appear to have been homosexual.

He proposed that the argument from design does not take into consideration future events which may serve to undermine the proof of God's existence: the argument would never finish proving God's existence.

Despite the fact that there has never been proof that Wharton's Hellfire Club ever did more than hold mock religious ceremonies and drink excessively, Wharton's political opposition used his membership as a way to pit him against his political allies, thus removing him from parliament.

The MPAA's R rating is definitive proof that the organization either will never give the NC-17 rating for violence alone, or was intimidated by the subject matter.

: For my part, I was never an admirer of Uncle Tom, nor of his type of goodness ; but I believe that there were lots of old Negroes as foolishly good as he ; the proof of which is that they knowingly stayed and worked on the plantations that furnished sinews for the army which was fighting to keep them enslaved .”

The existence of the Mississippi panther is accepted by many natives, even though there has never been any scientific proof to support this belief.

He had several times tried to send it to different mathematicians to get it acknowledged, amongst them, French mathematician Augustin-Louis Cauchy, but it was never acknowledged, possibly because the proof was spanning 500 pages.

Fulk, or his supporters, were commonly believed responsible, though direct proof never surfaced.

The fact that Duse was just coming out of a relationship with rebellious young lesbian feminist Lina Poletti fueled speculation as to the nature of Duncan and Duse's relationship, but there has never been definite proof that the two were involved romantically.

Gödel's second incompleteness theorem establishes that logical systems of arithmetic can never contain a valid proof of their own consistency.

Since God is absolutely self-sufficient ( a result from the cosmological " proof " of His existence ), all-knowing, and all-powerful, He is categorically free from any type of need and, consequently, He never does anything that is ridiculous, unwise, ugly, or evil.

Eloptic emanations have never been detected by instruments designed to measure electromagnetic energies, and no other evidence or mathematical proof for their existence have been produced, so the theory is considered pseudoscientific and is not accepted by mainstream science.

Cohen took part in various Israeli covert operations in the country during the 1950s, though the Egyptian government could never verify and provide proof of his involvement in Operation Goshen, an Israeli operation to smuggle Egyptian Jews out of the country and resettle them in Israel due to increasing antisemitism there.

Young Simon was educated at King's College, Aberdeen, and his correspondence afterwards gives proof, not only of a command of good English and idiomatic French, but of such an acquaintance with the Latin classics as to leave him never at a loss for an apt quotation from Virgil or Horace.