After reading the explanations in the previous section, a skeptic asked the author what the difference is between the previous argument that the Collatz 3n+1 Conjecture
is unprovable and the following argument that Fermat's Last Theorem is unprovable (which cannot possibly be valid, since Fermat's Last Theorem was proven by Wiles and Taylor in the last decade of the twentieth century ):
This systematic approach can be seen as testing series of conjectures
or as a deliberate search for a pattern, which, indeed, is found and explained as a result of a successful input.
case where the two conjectures
are identical, the verifying process is
Important as they are, these larger themes of transatlantic and modernist thought in Conjectures
are but the most prominent of this study's achievements.
She then paired children and told them they needed to agree on which nets formed which polyhedra and on their conjectures
about matching nets and polyhedra.
Graffiti has motivated many graph theoreticians, including its designer, to try to refute or prove the generated conjectures
which are broadcast on an email list.
But according to Popper's epistemology, since a presupposition is only a conjecture
or conclusion used to help spawn other conjectures
, there is no reason why presuppositions cannot be debated and criticized.
n] [is less than or equal to] n - 1, the response to i's output that firm i conjectures
for its rival firms.
His major contributions include several work on conjectures
, such as Calabi conjecture
, positive mass conjecture
and existence of black holes, Smith conjecture
, Hermitian Yang-Mills connection and stable vector bundles, Frankel conjecture
and Mirror conjecture
, as well as new methods and concepts of gradient estimates and Harnack inequalities, uniformization of complex manifolds, harmonic maps and rigidity, minimal submanifolds, and also open problems in geometry, covering harmonic functions with controlled growth, rank rigidity of nonpositively curved manifolds, Kahler-Einstein metrics and stability of manifolds and Mirror symmetry.
The 13 papers comprising the proceedings discuss such aspects as conjectures
about p-adic groups and their noncommutative geometry, affinoids in Lubin-Tate surfaces with exponential full level two, an automorphic variant of a conjecture
of Deligne, proof of the Aubert-Baum-Plymen-Solleveld conjecture
for split classical groups, and the geometry and combinatorics of Springer fibers.
The starting point are the prominent conjectures
of Farrell-Jones on the algebraic K- and L-theory of group rings, of Baum-Connes on the topological K-theory of reduced group C^*-algebras, and of Atiyah on the integrality of L^-Betti numbers.
were later generalised to the corresponding Fuss-Catalan objects by Armstrong [Arm09, Conjecture
Among specific topics are Harold Stark revealing where his conjectures
came from, special values of L-functions at negative integers, introduction to elliptic curves, complex multiplication, root numbers, and Euler systems and Kolyvagin systems.
Finding patterns, and making and justifying conjectures
are considered the building blocks of mathematical reasoning and proof.
The good book; thirty years of comments, conjectures
, and conclusions by I.