In number theory, the modularity theorem states that elliptic curves over the field of rational numbers are related to modular forms in a particular way...

known as the modularity theorem, and opened up entire new approaches to numerous other problems and mathematically powerful modularity lifting techniques...

Together with Ribet's theorem, it provides a proof for Fermat's Last Theorem. Both Fermat's Last Theorem and the modularity theorem were believed to be...

Hilbert modular forms. In 1986, upon reading Ken Ribet's seminal work on Fermat's Last Theorem, Wiles set out to prove the modularity theorem for semistable...

elliptic curve, something that could be called an elliptic modular curve. The modularity theorem, also known as the Taniyama–Shimura conjecture, asserts...

of number theory and the formulation of the modularity theorem in particular made it clear that modular forms are deeply implicated. Taniyama and Shimura...

them Fermat's Last Theorem and the now-proven Taniyama–Weil (or Taniyama–Shimura) conjecture, now known as the modularity theorem (although this implies...

module or modular in Wiktionary, the free dictionary. Module, modular and modularity may refer to the concept of modularity. They may also refer to: Modular design...

that the Modularity theorem implied FLT. The origin of the name is from the ε part of "Taniyama-Shimura conjecture + ε ⇒ Fermat's last theorem". Suppose...

modularity theorem is a theorem about modular tensor categories. It asserts that two different formulations of the modularity condition of a modular tensor...

important theorems relating to modular arithmetic: Carmichael's theorem Chinese remainder theorem Euler's theorem Fermat's little theorem (a special...

century. Manin–Drinfeld theorem Moduli stack of elliptic curves Modularity theorem Shimura variety, a generalization of modular curves to higher dimensions...

and modular forms. The resulting modularity theorem (at the time known as the Taniyama–Shimura conjecture) states that every elliptic curve is modular, meaning...

theory) Modularity theorem (number theory) Mordell–Weil theorem (number theory) Multiplicity-one theorem (group representations) Nagell–Lutz theorem (elliptic...

little theorem states that if p is a prime number, then for any integer a, the number ap − a is an integer multiple of p. In the notation of modular arithmetic...

conjecture (now known as the modularity theorem), which states that every elliptic curve over the rational numbers is modular. This conjecture became central...

conjecture (later known as the modularity theorem) in the 1950s played a key role in the proof of Fermat's Last Theorem by Andrew Wiles in 1995. In 1990...

universal algebra. Modular lattices arise naturally in algebra and in many other areas of mathematics. In these scenarios, modularity is an abstraction...

to be true for all elliptic curves over Q, as a consequence of the modularity theorem in 2001. Finding rational points on a general elliptic curve is a...

19th century, and the proof of the modularity theorem in the 20th century. It is among the most notable theorems in the history of mathematics, and prior...

as the modularity theorem. This is an important theorem in number theory. It was part of Andrew Wiles' proof (1995) of Fermat's Last Theorem. The addition...

mathematician, known for his role in proving the modularity theorem for elliptic curves. His research interest is in modular forms and Galois representations. Diamond...

In number theory, Euler's theorem (also known as the Fermat–Euler theorem or Euler's totient theorem) states that, if n and a are coprime positive integers...

little theorem, which states that a p ≡ a ( mod p ) {\displaystyle a^{p}\equiv a{\pmod {p}}} for every prime number p and every integer a (see modular arithmetic)...

the modularity theorem) relating elliptic curves to modular forms. This connection would ultimately lead to the first proof of Fermat's Last Theorem in...

curves over rationals is called the Taniyama–Shimura conjecture or the modularity theorem whose statement he subsequently refined in collaboration with Goro...

several theorems of Helmut Hasse that are sometimes called Hasse's theorem: Hasse norm theorem Hasse's theorem on elliptic curves Hasse–Arf theorem Hasse–Minkowski...

program modularity theorem Pythagorean triple Pell's equation Elliptic curve Nagell–Lutz theorem Mordell–Weil theorem Mazur's torsion theorem Congruent...

geometry) Modularity theorem Moduli stack of elliptic curves Nagell–Lutz theorem Riemann–Hurwitz formula Wiles's proof of Fermat's Last Theorem Sarli, J...

Generalized Riemann hypothesis Dirichlet L-function Automorphic L-function Modularity theorem Artin conjecture Special values of L-functions Explicit formulae for...