X-Nico

unusual facts about conjecture



Alternating knot

Morwen Thistlethwaite, Louis Kauffman and K. Murasugi proved the first two Tait conjectures in 1987 and Morwen Thistlethwaite and William Menasco proved the Tait flyping conjecture in 1991.

Andrzej Schinzel

A conjecture of his on the prime values of polynomials, known as Schinzel's hypothesis H, has attracted the attention of many number theorists.

Association of Professional Futurists

The ten 'most important futures works' recognized by the APF in that year included Peter Schwartz's The Art of the Long View, Wendell Bell's Foundations of Futures Studies: Human Science for a New Era, Bertrand de Jouvenel's L'Art de la Conjecture (The Art of Conjecture), and Ray Kurzweil's The Age of Spiritual Machines.

Bateman–Horn conjecture

In number theory, the Bateman–Horn conjecture is a statement concerning the frequency of prime numbers among the values of a system of polynomials, named after mathematicians Paul T. Bateman and Roger A Horn, of The University of Utah, who proposed it in 1962.

Beal's conjecture

Peter Norvig, Director of Research at Google, reported having conducted a series of numerical searches for counterexamples to Beal's conjecture.

Beketaten

She never appears alongside the daughters of Nefertiti, leading to the conjecture that she must be the daughter of Akhenaten by another wife who may be Kiya.

Calabi conjecture

Calabi transformed the Calabi conjecture into a non–linear partial differential equation of complex Monge–Ampere type, and showed that this equation has at most one solution, thus establishing the uniqueness of the required Kähler metric.

Connes embedding problem

In von Neumann algebras, the Connes embedding problem or conjecture, due to Alain Connes, asks whether every free ultrafilter.

Copies by Vincent van Gogh

They also offer the conjecture of some scholars of a resemblance between the Van Gogh and the red-bearded Christ in The Pietà and Lazarus in the copy after Rembrandt.

Dr. Phibes Rises Again

Blees' first idea, which never progressed beyond one-page conjecture, was tentatively titled Phibes II and would have pit Phibes against Robert Quarry's Count Yorga.

Elliptic curve

The Birch and Swinnerton-Dyer conjecture (BSD) is one of the Millennium problems of the Clay Mathematics Institute.

Endre Boros

In 1986, Boros settled (with T. Szőnyi) a conjecture by Beniamino Segre about the cyclic structure of finite projective planes, and in 1988 provided the best known bound for a question posed by Paul Erdős about blocking sets of Galois planes.

Epigenes of Byzantium

It is unclear when Epigenes lived - he may have lived about the time of Augustus; some conjecture that he lived centuries earlier - but he is known to have refined the study of his chosen field, defining Saturn, for example, as "cold and windy." Along with Apollonius of Myndus and Artemidorus of Parium, he boasted of having been instructed by the Chaldean priest-astrologers, many of whom infiltrated Greece when the ports of Egypt opened to Greek ships after 640 BC.

Firoozbakht’s conjecture

The conjecture is named after Farideh Firoozbakht, from the University of Isfahan, who stated it in 1982.

Goldbach's weak conjecture

In 2012 and 2013, Peruvian mathematician Harald Helfgott released a pair of papers claiming to improve major and minor arc estimates sufficiently to unconditionally prove the weak Goldbach conjecture.

In 2013, Harald Helfgott claimed to have fully proved the conjecture for all odd integers greater than 5 (rather than the much larger e^{3100}\approx 2 \times 10^{1346}, implied by previous results).

Grigori Perelman

In 1999, the Clay Mathematics Institute announced the Millennium Prize Problems: $1,000,000 prizes for the proof of any of seven conjectures, including the Poincaré conjecture.

History of manifolds and varieties

In 2003, Grigori Perelman proved the conjecture using Richard Hamilton's Ricci flow, this is after nearly a century of effort by many mathematicians.

Homological mirror symmetry

Following this route, Alexander Polishchuk and Eric Zaslow provided a proof of a version of the conjecture for elliptic curves.

Kenji Fukaya was able to establish elements of the conjecture for abelian varieties.

Honeycomb conjecture

The first record of the conjecture dates back to 36BC, from Marcus Terentius Varro, but is often attributed to Pappus of Alexandria (c. 290 – c. 350).

Italian classical music

Thus, we know that there was a vibrant troubador tradition in the 12th century in the Provence in their language and we know that 1000 miles away on the island of Sicily there was also a vibrant troubador tradition at the Hohenstaufen court of Frederick II, songs sung in the dialect of the people (very much influenced, for example, by Arabic), but it is conjecture as to exactly what either one sounded like.

Ivan M. Niven

This problem, based on a 1770 conjecture by Edward Waring, consists of finding the smallest number g(n) such that every positive integer is the sum of at most g(n) nth powers of positive integers.

Jacobi–Madden equation

Noam Elkies was first to find an infinite series of solutions to Euler's equation with exactly one variable equal to zero, thus disproving Euler's sum of powers conjecture for the fourth power.

Lagaria

Cluverius placed it at Nocara, about 16 km from the sea, and this conjecture (for it is nothing more) has been adopted by Romanelli.

Landau's problems

Deshouillers, Effinger, te Riele and Zinoviev conditionally proved the weak conjecture under the GRH.

Lemoine's conjecture

In number theory, Lemoine's conjecture, named after Émile Lemoine, also known as Levy's conjecture, after Hyman Levy, states that all odd integers greater than 5 can be represented as the sum of an odd prime number and an even semiprime.

LLT polynomial

Ian Grojnowski and Mark Haiman (preprint) proved a positivity conjecture for LLT polynomials that combined with the previous result implies the Macdonald positivity conjecture for Macdonald polynomials, and extended the definition of LLT polynomials to arbitrary finite root systems.

Macdonald polynomials

These conjectures are now proved; the hardest and final step was proving the positivity, which was done by Mark Haiman (2001), by proving the n! conjecture.

The n! conjecture of Adriano Garsia and Mark Haiman states that for each partition μ of n the space

Mahan Mj

This led to the resolution of the conjecture that connected limit sets of finitely generated Kleinian groups are locally connected.

Manuel Kauers

The second conjecture proven by Kauers, Koutschan and Zeilberger was the so-called q-TSPP conjecture, a product formula for the orbit generating function of totally symmetric plane partitions, which was formulated by George Andrews and David Robbins in the early 1980s.

Michael Lacey

This transform was at the time the subject of a conjecture by Alberto Calderón that Lacey and Christoph Thiele solved in 1996, for which they were awarded the Salem Prize.

Mirror symmetry

Homological mirror symmetry, a mathematical conjecture about Calabi-Yau manifolds made by Maxim Kontsevich

Montgomery's pair correlation conjecture

He confirmed that the distribution of the spacings between non-trivial zeros using detail numerical calculation and demonstrated that the Montgomery's conjecture would be true and the distribution would agree with the distribution of spacings of GUE random matrics eigenvalues using Cray X-MP.

Norm residue isomorphism theorem

Its statement was previously known as the Bloch–Kato conjecture, after Spencer Bloch and Kazuya Kato, or more precisely the motivic Bloch–Kato conjecture in some places, since there is another Bloch–Kato conjecture on values of L-functions.

Norte Pequeno

This settlement was originally formed by peoples from the village of Calheta, around 1690; this is conjecture, based on the construction of the village chapel, which was built to evoke São Lázaro.

Oecanthus fultoni

It is a major plot point in the The Big Bang Theory episode "The Jiminy Conjecture", where Sheldon wrongly believes that a common field cricket, Gryllus assimilis, found in the apartment, is a snowy tree cricket.

Pope Pius I

There is some conjecture that he was a martyr in Rome, a conjecture that entered earlier editions of the Breviary.

Razumov

Alternating sign matrix, a mathematical model also called the Razumov–Stroganov conjecture

Regio Patalis

Siltation has caused the Indus to change its course many times since the days of Alexander the Great, and the site of ancient Patala has been subject to much conjecture.

Robbins algebra

William McCune proved the conjecture in 1996, using the automated theorem prover EQP.

Rodney Baxter

In 2005 he used the method of Michio Jimbo, Tetsuji Miwa and Nakayashiki to verify Albertini, McCoy, Perk and Tang's conjecture for the order parameter of the chiral Potts model.

Sujatha Ramdorai

Together with Coates, Fukaya, Kato, and Venjakob she formulated a non-commutative version of the main conjecture of Iwasawa theory, on which much foundation of this important subject is based.

Tait conjectures

For non-alternating knots this conjecture is not true, assuming so lead to the duplication of the Perko pair, because it has two reduced projections with different writhe.

Tarski's exponential function problem

This conjecture states that there is an effective procedure that, given n ≥ 1 and exponential polynomials in n variables with integer coefficients f1,..., fn, g, produces an integer η ≥ 1 that depends on n, f1,..., fn, g, and such that if α ∈ Rn is a non-singular solution of the system

Uncle Petros and Goldbach's Conjecture

Uncle Petros and Goldbach's Conjecture is a 1992 novel by Greek author Apostolos Doxiadis.

Wingrave

Why she built a large house barely two miles from her own home Mentmore Towers (one of the largest mansions in Buckinghamshire) can only be the subject of conjecture.

Yutaka Taniyama

In a 2011 TED talk by English economist Tim Harford titled, "Trial, error and the God complex," Taniyama is referenced as a mathematician who was ultimately unable to prove his conjecture during his lifetime.


see also