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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
Grothendieck's connectedness theorem (algebraic geometry) Haboush's theorem (algebraic groups, representation theory, invariant theory) Harnack's curve theorem (real algebraic geometry) Hasse's theorem on elliptic curves (number theory) Hilbert's Nullstellensatz (theorem of zeroes) (commutative algebra, algebraic geometry)
The fundamental theorem of algebra, also called d'Alembert's theorem [1] or the d'Alembert–Gauss theorem, [2] states that every non-constant single-variable polynomial with complex coefficients has at least one complex root.
The proof takes about 500 pages spread over about 20 papers. 2005 Kepler conjecture. Hales's proof of this involves several hundred pages of published arguments, together with several gigabytes of computer calculations. 2006 the strong perfect graph theorem, by Maria Chudnovsky, Neil Robertson, Paul Seymour, and Robin Thomas.
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.
A mnemonic is a memory aid used to improve long-term memory and make the process of consolidation easier. Many chemistry aspects, rules, names of compounds, sequences of elements, their reactivity, etc., can be easily and efficiently memorized with the help of mnemonics.
Mathematical chemistry [1] is the area of research engaged in novel applications of mathematics to chemistry; it concerns itself principally with the mathematical modeling of chemical phenomena. [2] Mathematical chemistry has also sometimes been called computer chemistry , but should not be confused with computational chemistry .
The fact that a complex solution always exists is the fundamental theorem of algebra, which was proved only at the beginning of the 19th century and does not have a purely algebraic proof. Nevertheless, the main concern of the algebraists was to solve in terms of radicals , that is to express the solutions by a formula which is built with the ...