One of the more dramatic successes of his theory was his prediction of the existence of secondary and tertiary alcohols, a conjecture that was soon confirmed by the synthesis of these substances.

His attitude towards conjectures was that one should not dignify a guess as a conjecture lightly, and in the Taniyama case, the evidence was only there after extensive computational work carried out from the late 1960s.

‘‘ The most prevalent conjecture was that they were some of the German peoples which extended as far as the northern ocean ,</ br >

Although Tiberius was 77 and on his death bed, some ancient historians still conjecture that he was murdered.

The most celebrated single question in the field, the conjecture known as Fermat's Last Theorem, was solved by Andrew Wiles but using tools from algebraic geometry developed during the last century rather than within number theory where the conjecture was originally formulated.

Euler's conjecture is a disproved conjecture in mathematics related to Fermat's last theorem which was proposed by Leonhard Euler in 1769.

The conjecture was disproven by L. J. Lander and T. R. Parkin in 1966 when they found the following counterexample for k

* In the 1960s, EDSAC was used to gather numerical evidence about solutions to elliptic curves, which led to the Birch and Swinnerton-Dyer conjecture.

The conjecture was first proposed in 1852 when Francis Guthrie, while trying to color the map of counties of England, noticed that only four different colors were needed.

This formula, the Heawood conjecture, was conjectured by P. J.

In 1973 the number theorist Hugh Montgomery was visiting the Institute for Advanced Study and had just made his pair correlation conjecture concerning the distribution of the zeros of the Riemann zeta function.

Gin, though, was blamed for various social problems, and it may have been a factor in the higher death rates which stabilized London's previously growing population, although there is no evidence for this and it is merely conjecture.

But Steinschneider will not admit the possibility of this conjecture, while Renan scarcely strengthens it by regarding " Andreas " as a possible northern corruption of " En Duran ," which, he says, may have been the Provençal surname of Anatoli, since Anatoli, in reality, was but the name of his great-grandfather.

In fact, whether one can smooth certain higher dimensional spheres was, until recently, an open problem — known as the smooth Poincaré conjecture.

Yusuf Ali ’ s translation reads " That they said ( in boast ), " We killed Christ Jesus the son of Mary, the Messenger of Allah ";― but they killed him not, nor crucified him, but so it was made to appear to them and those who differ therein are full of doubts, with no ( certain ) knowledge, but only conjecture to follow, for of a surety they killed him not .― ( 157 ) Nay, Allah raised him up unto Himself ; and Allah is Exalted in Power, Wise.

" And while the conjecture may one day be solved, the argument applies to similar unsolved problems ; to Brouwer, the law of the excluded middle was tantamount to assuming that every mathematical problem has a solution.

He was awarded the Bôcher Memorial Prize in mathematical analysis in 1964 for his paper " On a conjecture by Littlewood and idempotent measures ", and lends his name to the Cohen-Hewitt factorization theorem.

The Poincaré conjecture, before being proven, was one of the most important open questions in topology.

* Catalan's conjecture, a theorem conjectured in 1844 and proven in 2002

Not every conjecture ends up being proven true or false.

On the other hand, Fermat's last theorem has always been known by that name, even before it was proven ; it was never known as " Fermat's conjecture ".

This conjecture can be justified ( but not proven ) by assuming that 1 / ln t describes the density function of the prime distribution, an assumption suggested by the prime number theorem.

This formula has been rigorously proven to be asymptotically valid for c ≥ 3 from the work of Vinogradov, but is still only a conjecture when.

The conjecture was later proven by Grigori Perelman, following the program of Richard Hamilton.

Catalan's conjecture ( or Mihăilescu's theorem ) is a theorem in number theory that was conjectured by the mathematician Eugène Charles Catalan in 1844 and proven in 2002 by Preda Mihăilescu.

( Gauss ' conjecture was proven more than one hundred years later by Heegner, Baker and Stark.

Rosen's conjecture was proven in 2008 by P. L.

This conjecture is called " weak " because if Goldbach's strong conjecture ( concerning sums of two primes ) is proven, it would be true.

The conjecture has not yet been proven, but there have been some useful near misses.

* Discusses the Taniyama-Shimura-Weil conjecture 3 years before it was proven for infinitely many cases.

The Taniyama – Shimura conjecture for elliptic curves ( now proven ) establishes a one-to-one correspondence between curves defined as modular forms and elliptic curves defined over the rational numbers.

The Kepler conjecture postulated an optimal solution for packing spheres hundreds of years before it was proven correct by Thomas Callister Hales.

On the assumption of the Elliott – Halberstam conjecture it has been proven recently ( by Daniel Goldston, János Pintz, Cem Yıldırım ) that there are infinitely many primes p such that p + k is prime for some positive even k less than 16.

This conjecture has not been proven or disproven.

Neither conjecture has been proven since their conception.

The Hadwiger conjecture has been proven only for k ≤ 6, but remains unproven in the general case.

In general its properties, such as functional equation, are still conjectural – the Taniyama – Shimura conjecture ( which was proven in 2001 ) was just a special case, so that's hardly surprising.

Because the Möbius function only takes the values − 1, 0, and + 1, the Mertens function moves slowly and there is no n such that | M ( n )| > n. The Mertens conjecture went further, stating that there would be no n where the absolute value of the Mertens function exceeds the square root of n. The Mertens conjecture was proven false in 1985 by Andrew Odlyzko and Herman te Riele.

Milnor K-theory modulo 2 is related to étale ( or Galois ) cohomology of the field by the Milnor conjecture, proven by Voevodsky.

* Schanuel's conjecture ; if proven it would imply both the Gelfond – Schneider theorem and the Lindemann – Weierstrass theorem

* Crank conjecture, a term coined by Freeman Dyson to explain congruence patterns in integer partitions

He may have been married, a conjecture supported by his writings.

Whether this formula produces an infinite quantity of Carmichael numbers is an open question ( though it is implied by Dickson's conjecture ).

At the moment, it is not known how the material is produced or if it remains stable without applied pressure, however, there is conjecture that it is possible to produce a new stable state of matter by compressing ultracold deuterium in a Rydberg state.

Woudhuizen revived a conjecture to the effect that the Tyrsenians came from Anatolia, including Lydia, whence they were driven by the Cimmerians in the early Iron Age, 750 – 675 BC, leaving some colonists on Lemnos.

This conjecture is also supported by other letters Galois later wrote to his friends the night before he died.

Another early published reference by in turn credits the conjecture to De Morgan.

Beyond the Bible, considerable conjecture has been put forward over the centuries in the form of Christian and Rabbinic tradition, but such accounts are dismissed by modern scholars as speculative and apocryphal.

This conjecture, however, is discredited by the Oxford English Dictionary.

If a definite statement is believed plausible by some mathematicians but has been neither proved nor disproved, it is called a conjecture, as opposed to an ultimate goal: a theorem that has been proved.

A conjecture developed by Cumrun Vafa, Amer Iqbal, and Andrew Neitzke in 2001, called " mysterious duality ", concerns a set of mathematical similarities between objects and laws describing M-theory on k-dimensional tori ( i. e. type II superstring theory on T < sup > k − 1 </ sup > for k > 0 ) on one side, and geometry of del Pezzo surfaces ( for example, the cubic surfaces ) on the other side.

This conjecture seems to be confirmed in the introduction of the first volume of the chronicles of Gallus Anonymus concerning the Pomeranians: Although often the leaders of the forces defeated by the Polish duke sought salvation in baptism, as soon as they regained their strength, they repudiated the Christian faith and started the war against Christians anew.

After nearly a century of effort by mathematicians, Grigori Perelman presented a proof of the conjecture in three papers made available in 2002 and 2003 on arXiv.

An exposition of attempts to prove this conjecture can be found in the non-technical book Poincaré's Prize by George Szpiro.

In 1961 Stephen Smale shocked mathematicians by proving the Generalized Poincaré conjecture for dimensions greater than four and extended his techniques to prove the fundamental h-cobordism theorem.

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.