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 first is the strictly scientific, which demands concrete proof and therefore may err on the conservative side by waiting for evidence in the flesh.

We shall show that the polynomials Af behave in the manner described in the first paragraph of the proof.

Stilicho is alleged by some to have wanted control of both Emperors, and is supposed to have had Rufinus assassinated by Gothic mercenaries in 395 ; though definite proof of Stilicho's involvement in the assassination is lacking, the intense competition and political jealousies engendered by the two figures compose the main thread of the first part of Arcadius ' reign.

The first proof was given by (), where the formulation of the problem was attributed to Ulam.

Following Desargues ' thinking, the sixteen-year-old Pascal produced, as a means of proof, a short treatise on what was called the " Mystic Hexagram ", Essai pour les coniques (" Essay on Conics ") and sent it — his first serious work of mathematics — to Père Mersenne in Paris ; it is known still today as Pascal's theorem.

Major public proof of the Soviet program, called Biopreparat, came when Dr. Kanatjan Alibekov, its first deputy director, defected to the U. S. in 1992.

SAT was the first known NP-complete problem, as proved by Stephen Cook in 1971 ( see Cook's theorem for the proof ).

The role of Q in the first proof is played by η in this proof.

The first proof relies on a theorem about products of limits to show that the derivative exists.

In his 1799 doctorate in absentia, A new proof of the theorem that every integral rational algebraic function of one variable can be resolved into real factors of the first or second degree, Gauss proved the fundamental theorem of algebra which states that every non-constant single-variable polynomial with complex coefficients has at least one complex root.

* 1799: Doctoral dissertation on the Fundamental theorem of algebra, with the title: Demonstratio nova theorematis omnem functionem algebraicam rationalem integram unius variabilis in factores reales primi vel secundi gradus resolvi posse (" New proof of the theorem that every integral algebraic function of one variable can be resolved into real factors ( i. e., polynomials ) of the first or second degree ")

The proof of this fact relies on an algorithm which, given the first n digits of Ω, solves Turing's halting problem for programs of length up to n. Since the halting problem is undecidable, Ω can not be computed.

As an example of a conditional proof in symbolic logic, suppose we want to prove A → C ( if A, then C ) from the first two premises below:

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.

Hilbert is known as one of the founders of proof theory and mathematical logic, as well as for being among the first to distinguish between mathematics and metamathematics.

The original versions of his papers contained " many technical errors of varying degree "; when the collection was first published, the errors were corrected and it was found that this could be done without major changes in the statements of the theorems, with one exception — a claimed proof of the Continuum hypothesis.

The engraving may also be the first visual proof of cricket being played in the United States.

The Clay Mathematics Institute has offered a $ 1 million USD prize for the first correct proof, along with prizes for six other mathematical problems.

The Elements begins with plane geometry, still taught in secondary school as the first axiomatic system and the first examples of formal proof.

The very first geometric proof in the Elements, shown in the figure above, is that any line segment is part of a triangle ; Euclid constructs this in the usual way, by drawing circles around both endpoints and taking their intersection as the third vertex.

The prevailing opinion at the time was that one should first write a program and then provide a mathematical proof of correctness.

But her prettiness was what he had noticed first, and all the other things had come afterward: cruelty, meanness, self-will.

There was an artificial lake just out of sight in the first stand of trees, fed by a half dozen springs that popped out of the ground above the hillside orchard.

The first part of the road was steep, but it leveled off after the second bend and curled gradually into the valley.

No one was behind it, but in the rear wall of the office I noticed, for the first time, a door which had been left partially open.

The herd was watered and then thrown onto a broad grass flat which was to be the first night's bedground.

Once again, Tom Horn was the first and most likely suspect, and he was brought in for questioning immediately.

For Matilda, it was the first she had known in many a night.

Even the knowledge that she was losing another boy, as a mother always does when a marriage is made, did not prevent her from having the first carefree, dreamless sleep that she had known since they dropped down the canyon and into Bear Valley, way, way back there when they were crossing those other mountains.

Stevens was grunting over the last empty pocket when Russ abruptly rose and lunged toward Carmer's hat, which had tumbled half-a-dozen feet away when he first fell.

The Indian's arm whipped sidewise -- there was a flash of amber and froth, the crash of the bottle shattering against the side of the first car.

It was her first smile.

At first, I thought he was out of his head, talking wildly like this.

Hell, I gave him the first decent job he ever had, six, seven -- how many years ago was it, Rob ''??

Miss Langford ( her first name was Evelyn ) was an attractive girl.

School began in August, the hottest part of the year, and for the first few days Miss Langford was very lenient with the children, letting them play a lot and the new ones sort of get acquainted with one another.

It was just as well that the ignorant Dandy enjoyed himself to the hilt that first evening, for the room was to become his prison cell.

`` Bastards '', he would say, `` all I did was put a beat to that Vivaldi stuff, and the first chair clobbered me ''!!

In 1961 the first important legislative victory of the Kennedy Administration came when the principle of national responsibility for local economic distress won out over a `` state's-responsibility '' proposal -- provision was made for payment for unemployment relief by nation-wide taxation rather than by a levy only on those states afflicted with manpower surplus.

The first systematic thinking about this Pandora's box within Pandora's boxes was done four years ago by Fred Ikle, a frail, meek-mannered Swiss-born sociologist.

The smell at first was more surprising than unpleasant.

His collaboration with Washington, begun when he was the general's aide during the Revolution, was resumed when he entered the first Cabinet as Secretary of the Treasury.