The distances of these points of light is a problem he cannot master, beyond crude conjectures as to the orderings of the planetary orbits viewed outward from earth.

The Langlands program is a far-reaching web of these ideas of ' unifying conjectures ' that link different subfields of mathematics, e. g. number theory and representation theory of Lie groups ; some of these conjectures have since been proved.

These " proofs ", however, would fall apart if it turned out that the hypothesis was false, so there is considerable interest in verifying the truth or falsity of conjectures of this type.

The two conjectures are mathematically independent, as there exist spacetimes for which the weak cosmic censorship is valid but the strong cosmic censorship is violated and, conversely, there exist spacetimes for which the weak cosmic censorship is violated but the strong cosmic censorship is valid.

It is also not known whether infinitely many Mersenne numbers with prime exponents are composite, although this would follow from widely believed conjectures about prime numbers, for example, the infinitude of Sophie Germain primes congruent to 3 ( mod 4 ).

:" Strict uniformitarianism may often be a guarantee against pseudo-scientific phantasies and loose conjectures, but it makes one easily forget that the principle of uniformity is not a law, not a rule established after comparison of facts, but a methodological principle, preceding the observation of facts.

Cook conjectures that there are optimization problems ( with easily checkable solutions ) which cannot be solved by efficient algorithms, i. e., P is not equal to NP.

The strong Goldbach conjecture is in fact very similar to the twin prime conjecture, and the two conjectures are believed to be of roughly comparable difficulty.

Despite some conjectures ( see ), there is no evidence that movable type from the East ever reached Europe.

* 1755 — Drawing on Wright's work, Immanuel Kant conjectures that the galaxy is a rotating disk of stars held together by gravity, and that the nebulae are separate such galaxies ; he calls them Island Universes

Among the many conjectures as to this tree, the most probable is that it is the osher ( Calotropis procera ) of the Arabs, which grows from Jordan to southern Egypt.

Her elusive nature is indicated by the wildly divergent scholarly conjectures she has prompted: " she was considered a chthonic divinity by Wissowa, a lunar goddess by Pettazzoni, a bean-goddess by Latte, and a patroness of digestion by Dumézil.

In this rendering, Cross has restored the missing top of the tablet ( estimated at two lines ) based on the content of the rest of the inscription, as referring to a battle that has been fought and won by general Milkaton, son of Shubna, against the Sardinians at the site of, surely Tarshish ; Cross conjectures that Tarshish here " is most easily understood as the name of a refinery town in Sardinia, presumably Nora or an ancient site nearby.

Wolfram also conjectures that a particular 2-state 3-symbol Turing machine is universal.

Fabricius, however, conjectures that the true reading is Agathyrsides, not Agatharchides.

The Riemann hypothesis is one of the most important conjectures in mathematics.

One of the exceptions is furnished by three conjectures made by André Weil during the late 1940s ( the Weil conjectures ).

Bortkiewicz used it in the sense of making conjectures that the Greek term has borne since the days of the ancient philosophers, and after the title of " Ars Conjectandi " that Jakob Bernoulli gave to his work ( published in 1713 ) on probability theory.

As an editor, while making many false conjectures, he was responsible for clearing many long-standing errors in the traditional texts.

Mainstream Slavists, including Dmitri Likhachev, and Turkologists criticized Az i Ya, characterizing Suleymenov's etymological and paleography conjectures as amateurish.

Whereas John Nichols in his History of Lambeth Parish conjectures that she was the widow of Guy Fawkes, executed in 1606, John Timbs in his 1867 Curiosities of London states for a fact that there was no such connection, and that the Vaux name derives from one Falkes de Breauté, a mercenary working for King John who acquired the land by marriage.

In the fields of algebraic geometry, number theory and the links between the two, the Weil conjectures were very important.

In the 1950s and 1960s, a fruitful collaboration between Serre and the two-years-younger Alexander Grothendieck led to important foundational work, much of it motivated by the Weil conjectures.

In formulating a number of striking conjectures, he pointed out the possible existence of parallels between the Nevanlinna theory of complex analysis, and diophantine analysis.

Felleisen conjectures that these three categories make up the primary legitimate uses of macros in such a system.

According to another historian ( Warmington ), there were three ancients of Carthage called Hanno " given the same nickname ", that is the Great, but he conjectures that it was a family nickname or a term not well understood by the ancient Greek or Roman writers.

In 1919, he gave a lecture on number theory and spoke of three conjectures: the Riemann hypothesis, Fermat's Last Theorem, and the transcendence of 2 < sup >√ 2 </ sup >.

The so-called Weil conjectures were hugely influential from around 1950 ; they were later proved by Bernard Dwork, Alexander Grothendieck, Michael Artin, and Pierre Deligne, who completed the most difficult step in 1973.

Interpretations by these early scholars varied and often, were baseless conjectures of their own contemporary values.

Many of his other conjectures, particularly about hidden sexual themes ( e. g. images of female nudity concealed in drawings of muscles and tree bark, or Batman and Robin as gay partners ), were met with derision within the comics industry.

The ministers were right in their conjectures ; the work not only provoked a great number of replies, but occasioned a formal complaint from the Lower House of Convocation: the Blasphemy Act 1697 still made it an offence for any person, educated in or having made profession of the Christian religion, by writing, preaching, teaching or advised speaking, to deny the Holy Trinity.

kinds of conjectures were made about the essence of the invention and its subsequent fate.

In mathematics, the Weil conjectures were some highly-influential proposals by on the generating functions ( known as local zeta-functions ) derived from counting the number of points on algebraic varieties over finite fields.

The Weil conjectures in the special case of algebraic curves were conjectured by.

At that time the Weil conjectures were an outstanding motivation to research.

The standard conjectures were first formulated in terms of the interplay of algebraic cycles and Weil cohomology theories.

Guglielmo Marconi's conjectures based on his radio work in the early 20th century, which were articulated in his 1909 Nobel Prize address, may have inspired Hungarian author Frigyes Karinthy to write a challenge to find another person to whom he could not be connected through at most five people.

In his initial work on perfect graphs, Berge made two important conjectures on their structure that were only proved later.

It turns out that lying behind monstrous moonshine is a certain string theory having the Monster group as symmetries ; the conjectures made by Conway and Norton were proven by Richard Ewen Borcherds in 1992 using the no-ghost theorem from string theory and the theory of vertex operator algebras and generalized Kac-Moody superalgebras.

" He also conjectures that if these disguised symbols were normal parts of the marriage ritual, then one could not say for sure whether the items were part of a " disguised symbolism " or just social reality.

In 2002 these conjectures were resolved ( positively ) using Stochastic Löwner Evolution.

Eugene Newton Anderson claimed that there was no evidence for any of the conjectures put forward by scholars on the Tanka's origins, citing Chen, who stated that " to what tribe or race they once belonged or were once akin to is still unknown ".

Observing, e. g., that the intercept-Porism is still true if the two fixed points are points on a conic, and the straight lines drawn through them intersect on the conic instead of on a fixed straight line, Zeuthen conjectures that the Porisms were a by-product of a fully developed projective geometry of conics.

As the year progressed, students were expected to relate these functions to the real world, create conjectures through their own research, and begin a classroom discussion about these topics.