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Fermat's little theorem and some proofs; Gödel's completeness theorem and its original proof; Mathematical induction and a proof; Proof that 0.999... equals 1; Proof that 22/7 exceeds π; Proof that e is irrational; Proof that π is irrational; Proof that the sum of the reciprocals of the primes diverges
Unlike the previous ones, it is a constructive proof: the integrating Lie group is built as the quotient of the (infinite-dimensional) Banach Lie group of paths on the Lie algebra by a suitable subgroup. This proof was influential for Lie theory [6] since it paved the way to the generalisation of Lie third theorem for Lie groupoids and Lie ...
6 Sendov's conjecture: complex polynomials: Blagovest Sendov: 77 Serre's multiplicity conjectures: commutative algebra: Jean-Pierre Serre: 221 Singmaster's conjecture: binomial coefficients: David Singmaster: 8 Standard conjectures on algebraic cycles: algebraic geometry: n/a: 234 Tate conjecture: algebraic geometry: John Tate: Toeplitz ...
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It was first conjectured in 1939 by Ott-Heinrich Keller, [1] and widely publicized by Shreeram Abhyankar, as an example of a difficult question in algebraic geometry that can be understood using little beyond a knowledge of calculus. The Jacobian conjecture is notorious for the large number of attempted proofs that turned out to contain subtle ...
An elementary proof is a proof which only uses basic techniques. More specifically, the term is used in number theory to refer to proofs that make no use of complex analysis . For some time it was thought that certain theorems, like the prime number theorem , could only be proved using "higher" mathematics.
This is a list of notable theorems.Lists of theorems and similar statements include: List of algebras; List of algorithms; List of axioms; List of conjectures
Every textbook on elementary number theory (and quite a few on algebraic number theory) has a proof of quadratic reciprocity. Two are especially noteworthy: Lemmermeyer (2000) has many proofs (some in exercises) of both quadratic and higher-power reciprocity laws and a discussion of their history. Its immense bibliography includes literature ...