Given the information above, before what date was the Schoen-Yau conjecture disproved?
1acf346b009d8d02926bf38bcaf6753a
Schoen–Yau conjecture In mathematics, the Schoen–Yau conjecture is a disproved conjecture in hyperbolic geometry, named after the mathematicians Richard Schoen and Shing-Tung Yau.
2182077a683ae93fa498f9555d737973
Shing-Tung Yau Shing-Tung Yau ( ; ; born April 4, 1949) is a Hong Kong and naturalised American mathematician. He was awarded the Fields Medal in 1982. He is currently the William Caspar Graustein Professor of Mathematics at Harvard.
444d0cc4a3828aa6686d130ef987e258
Schottky form In mathematics, the Schottky form or Schottky's invariant is a Siegel cusp form "J" of degree 4 and weight 8, introduced by as a degree 16 polynomial in the Thetanullwerte of genus 4. He showed that it vanished at all Jacobian points (the points of the degree 4 Siegel upper half-space corresponding to 4-dimensional abelian varieties that are the Jacobian varieties of genus 4 curves). showed that it is a multiple of the difference θ("E" ⊕ "E") − θ("E") of the two genus 4 theta functions of the two 16-dimensional even unimodular lattices and that its divisor of zeros is irreducible. showed that it generates the 1-dimensional space of level 1 genus 4 weight 8 Siegel cusp forms.
54b63c960571d7f5f614fbd82c955646
Arthur Moritz Schoenflies Arthur Moritz Schoenflies (] ; 17 April 1853 – 27 May 1928), sometimes written as Schönflies, was a German mathematician, known for his contributions to the application of group theory to crystallography, and for work in topology.
8cd7f35e714f711afc0bfdc31f3e3ebd
Sullivan conjecture In mathematics, Sullivan conjecture can refer to any of several results and conjectures prompted by homotopy theory work of Dennis Sullivan. A basic theme and motivation concerns the fixed point set in group actions of a finite group formula_1. The most elementary formulation, however, is in terms of the classifying space formula_2 of such a group. Roughly speaking, it is difficult to map such a space formula_2 continuously into a finite CW complex formula_4 in a non-trivial manner. Such a version of the Sullivan conjecture was first proved by Haynes Miller. Specifically, in 1984, Miller proved that the function space, carrying the compact-open topology, of base point-preserving mappings from formula_2 to formula_4 is weakly contractible.
93d1724fcac23a84cb7f17dedfc4efce
6P/d'Arrest 6P/d'Arrest (also known as d'Arrest's Comet or Comet d'Arrest) is a periodic Jupiter-family comet in the Solar System, orbiting between Mars and Jupiter. It passed 0.15124 AU from the Earth on August 12, 1976.
a63e638a4ddeca317436d4db0ffb1a0d
Schwarz alternating method In mathematics, the Schwarz alternating method or alternating process is an iterative method introduced in 1869-1870 by Hermann Schwarz in the theory of conformal mapping. Given two overlapping regions in the complex plane in each of which the Dirichlet problem could be solved, Schwarz described an iterative method for solving the Dirichlet problem in their union, provided their intersection was suitably well behaved. This was one of several constructive techniques of conformal mapping developed by Schwarz as a contribution to the problem of uniformization, posed by Riemann in the 1850s and first resolved rigorously by Koebe and Poincaré in 1907. It furnished a scheme for uniformizing the union of two regions knowing how to uniformize each of them separately, provided their intersection was topologically a disk or an annulus. From 1870 onwards Carl Neumann also contributed to this theory.
2226b38491deb5e7e713f89e5871fda1
Bunyakovsky conjecture The Bunyakovsky conjecture (or Bouniakowsky conjecture) stated in 1857 by the Russian mathematician Viktor Bunyakovsky, asserts when a polynomial formula_1 in one variable with positive degree and integer coefficients should have infinitely many prime values for positive integer inputs. Three necessary conditions are
f755d4b81f5a913d3bb8c557285369c7
2017 FZ2 2017 FZ (also written 2017 FZ2) is an Apollo asteroid that was a quasi-satellite of the Earth until March 23, 2017.
cd462f76200f1da454da6e3ae5204797
Fontaine–Mazur conjecture In mathematics, the Fontaine–Mazur conjectures are some conjectures introduced by about when "p"-adic representations of Galois groups of number fields can be constructed from representations on étale cohomology groups of a varieties. Some cases of this conjecture in dimension 2 were already proved by .
1c9f8eec6d2e6d3971e0035444081015
Hilbert's eleventh problem Hilbert's eleventh problem is one of David Hilbert's list of open mathematical problems posed at the Second International Congress of Mathematicians in Paris in 1900. A furthering of the theory of quadratic forms, he stated the problem as follows:
3a63672f39caecdd8d68fcaf4ec394a4
Wang Xianghao Wang Xianghao, Shianghao Wang, or Shianghaw Wang (; 5 May 1915 – 4 May 1993) was a Chinese mathematician who introduced the Grunwald–Wang theorem in , correcting an error in Wilhelm Grunwald's original statement and proof of this. He later changed from mathematics to computer science and control theory, and became a member of the Academia Sinica .
faada3906abaa8e408a01be33c878ac7
Zorich's theorem In mathematical analysis, Zorich's theorem was proved by Vladimir A. Zorich in 1967. The result was conjectured by M. A. Lavrentev in 1938.
4d6e5ac2dcfc20e3a5a9310830553ab0
Two-Micron Sky Survey Two-Micron Sky Survey, or IRC, or Caltech infrared catalog is the astronomical catalogue of the infrared sources published in the 1969 by Neugebauer and Leighton.
b16ff67043b2405e4f0b078619d9865c
Graham's number Graham's number is an enormous number that arises as an upper bound on the answer of a problem in the mathematical field of Ramsey theory. It is named after mathematician Ronald Graham, who used the number as a simplified explanation of the upper bounds of the problem he was working on in conversations with popular science writer Martin Gardner. Gardner later described the number in "Scientific American" in 1977, introducing it to the general public. At the time of its introduction, it was the largest specific positive integer ever to have been used in a published mathematical proof. The number was published in the 1980 "Guinness Book of World Records", adding to its popular interest. Other specific integers (such as TREE(3)) known to be far larger than Graham's number have since appeared in many serious mathematical proofs, for example in connection with Harvey Friedman's various finite forms of Kruskal's theorem. Additionally, smaller upper bounds on the Ramsey theory problem from which Graham's number derived have since been proven to be valid.
48170da4d1a873c8e21bf88b76b893f0
Second Hardy–Littlewood conjecture In number theory, the second Hardy–Littlewood conjecture concerns the number of primes in intervals. The conjecture states that
8f3b6b43a0c172f08c1a80f23ef93b72
Hilbert's third problem The third on Hilbert's list of mathematical problems, presented in 1900, was the first to be solved. The problem is related to the following question: given any two polyhedra of equal volume, is it always possible to cut the first into finitely many polyhedral pieces which can be reassembled to yield the second? Based on earlier writings by Gauss, Hilbert conjectured that this is not always possible. This was confirmed within the year by his student Max Dehn, who proved that the answer in general is "no" by producing a counterexample.
179b9fc0a8c49d83f1e0e1f58783012c
Post correspondence problem The Post correspondence problem is an undecidable decision problem that was introduced by Emil Post in 1946. Because it is simpler than the halting problem and the "Entscheidungsproblem" it is often used in proofs of undecidability.
f5da641821be87b8451c87ea7972724b
List of comets with no meaningful orbit This is a list of comets designated with X/ prefix. The majority of these comets were discovered before the invention of the telescope in 1610, and as such there was nobody to plot the positions of the comets to a high enough precision to generate any meaningful orbit. Later comets, observed in the 17th century or later, either did not have enough observations, sometimes as few as one or two, or the comet disintegrated or moved out of a favorable location in the sky before it was possible to make more observations of it.
1a6e53cd4df5fe0e434c6693fd0d79e3
Age of the universe In physical cosmology, the age of the universe is the time elapsed since the Big Bang. The current measurement of the age of the universe is billion (10) years within the Lambda-CDM concordance model. The uncertainty has been narrowed down to 21 million years, based on a number of projects that all give extremely close figures for the age. These include studies of the microwave background radiation, and measurements by the Planck satellite, the Wilkinson Microwave Anisotropy Probe and other probes. Measurements of the cosmic background radiation give the cooling time of the universe since the Big Bang, and measurements of the expansion rate of the universe can be used to calculate its approximate age by extrapolating backwards in time.
924eb2565f0f98ea5e335ab90e3b811a
Generalized Poincaré conjecture In the mathematical area of topology, the term Generalized Poincaré conjecture refers to a statement that a manifold which is a homotopy sphere 'is' a sphere. More precisely, one fixes a
e416f558c6e19ede307e98bd53d42a6f
16P/Brooks 16P/Brooks, also known as Brooks 2, is a periodic comet discovered by William Robert Brooks on July 7, 1889, but failed to note any motion. He was able to confirm the discovery the next morning, having seen that the comet had moved north. On August 1, 1889, the famous comet hunter Edward Emerson Barnard discovered two fragments of the comet labeled "B" and "C" located 1 and 4.5 arc minutes away. On August 2, he found another four or five, but these were no longer visible the next day. On August 4, he observed two more objects, labeled "D" and "E". "E" disappeared by the next night and "D" was gone by the next week. Around mid-month, "B" grew large and faint, finally disappearing at the beginning of September. "C" managed to survive until mid-November 1889. No new nuclei were discovered before the apparition ended on January 13, 1891.