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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 ...
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)
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.
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 .
In other words, the cardinality of the set of transcendentals (denoted ) is greater than that of the set of algebraic numbers (). [ 24 ] Bernhard Riemann , at the end of his famous 1859 paper " On the Number of Primes Less Than a Given Magnitude ", stated (based on his results) that the logarithmic integral gives a somewhat too high estimate of ...
[8] [14] The Abel–Ruffini theorem is thus generally credited to Abel, who published a proof compressed into just six pages in 1824. [3] (Abel adopted a very terse style to save paper and money: the proof was printed at his own expense. [9]) A more elaborated version of the proof would be published in 1826. [4]
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.
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.