" At first I thought, despite everything that I saw with my own eyes, that the Soviet state was a breakthrough into the future, a kind of prototype for all countries ".

It was also the first real breakthrough for sampling, as the bassline of Chic's " Good Times " laid the foundation for the song.

Kelly's first career breakthrough was in the Pulitzer Prize-winning The Time of Your Life, which opened on October 25, 1939, where for the first time on Broadway he danced to his own choreography.

Upon making this breakthrough, Carmack and Hall stayed up late into the night making a replica of the first level of the popular 1988 NES game Super Mario Bros. 3, inserting stock graphics of Romero's Dangerous Dave character in lieu of Mario.

After the year's previous success, King had Brown sign a new recording contract and in June 1965, released " Papa's Got a Brand New Bag ", which became his breakthrough hit single, becoming his first # 1 single on the R & B chart since " Try Me " and his first Top 10 pop single winning Brown his first Grammy.

To be more precise, already before Schrödinger, the young postdoctoral fellow Werner Heisenberg invented his matrix mechanics, which was the first correct quantum mechanics –– the essential breakthrough.

When the votes were counted, the party doubled its federal vote from 1. 9 million ( PDS result in 2002 ) to more than 4 million — including an electoral breakthrough in industrial Saarland where, for the first time in a western state, it surpassed the Greens and FDP due, in large part to Lafontaine's popularity and Saarland roots.

In September 2012 Australian researchers say the world's first quantum computer is just 5 to 10 years away, after announcing a global breakthrough that makes manufacture of its memory building blocks possible.

* 2011: Israeli scientist Inbar Friedrich Ben-Nun led a team which produced the first stem cells from endangered species, a breakthrough that could save animals in danger of extinction.

A major breakthrough in the methodology and popularization of volumetric analysis was due to Karl Friedrich Mohr, who redesigned the burette by placing a clamp and a tip at the bottom, and wrote the first textbook on the topic, Lehrbuch der chemisch-analytischen Titrirmethode ( Textbook of analytical-chemical titration methods ), published in 1855.

Curry first became well known with his breakthrough role as Dr. Frank-N-Furter in the 1975 cult film The Rocky Horror Picture Show, reprising the role he played in the 1973 London and 1974 Los Angeles stage productions of The Rocky Horror Show, then later for his supporting roles as Rooster in the film adaption of Annie ( 1982 ), Lord of Darkness in the film Legend ( 1985 ), Wadsworth in the film Clue ( 1985 ) as well as a starring role as Pennywise the Clown in the horror TV miniseries It ( 1990 ), which is one of Curry's most acclaimed performances aside from Rocky Horror.

The breakthrough year for arabidopsis as the preferred model plant came in 1986, when T-DNA-mediated transformation was first published, and this coincided with the first gene to be cloned and published in Arabidopsis.

* In February 2010, Researchers at the Tyndall National Institute in Cork, Ireland announced a breakthrough in transistors with the design and fabrication of the world's first junctionless transistor.

His first major breakthrough came in 1912 at age eighteen with his first book illustration for Carl H. Claudy's Tell Me Why: Stories about Mother Nature.

His first film appearance was a role in Tony Richardson's The Entertainer ( 1960 ), with Laurence Olivier, but he made his breakthrough with his portrayal of a disillusioned factory worker in Karel Reisz's film version of Alan Sillitoe's Saturday Night and Sunday Morning.

An attack of this nature was not a breakthrough operation ; the German defensive position Flandern I lay 10, 000 – 12, 000 yards behind the front line and would not be attacked on the first day, nonetheless it was more ambitious than Plumer's earlier plan, which had involved an advance of 1, 000 – 1, 750 yards.

Green parties in Belgium first made a breakthrough.

He first publicly announced his " breakthrough " in Ron's Journal 67 ( RJ67 ), a taped lecture Hubbard recorded on September 20, 1967, to be sent to all Scientologists.

There first breakthrough was a demo called the Little Color Demo released in the fall of 1987.

* The set of real algebraic numbers is linearly ordered, countable, densely ordered, and without first or last element, so is order-isomorphic to the set of rational numbers.

This result was his first major achievement in algebraic geometry.

Categories were first introduced by Samuel Eilenberg and Saunders Mac Lane in 1942 – 45, in connection with algebraic topology.

This is a fundamental idea, which first surfaced in algebraic topology.

The subsequent development of category theory was powered first by the computational needs of homological algebra, and later by the axiomatic needs of algebraic geometry, the field most resistant to being grounded in either axiomatic set theory or the Russell-Whitehead view of united foundations.

In his 1799 doctorate in absentia, A new proof of the theorem that every integral rational algebraic function of one variable can be resolved into real factors of the first or second degree, Gauss proved the fundamental theorem of algebra which states that every non-constant single-variable polynomial with complex coefficients has at least one complex root.

* 1799: Doctoral dissertation on the Fundamental theorem of algebra, with the title: Demonstratio nova theorematis omnem functionem algebraicam rationalem integram unius variabilis in factores reales primi vel secundi gradus resolvi posse (" New proof of the theorem that every integral algebraic function of one variable can be resolved into real factors ( i. e., polynomials ) of the first or second degree ")

He was the first person to use algebraic notation and symbolism.

Functors were first considered in algebraic topology, where algebraic objects ( like the fundamental group ) are associated to topological spaces, and algebraic homomorphisms are associated to continuous maps.

His first construction shows how to write the real algebraic numbers as a sequence a < sub > 1 </ sub >, a < sub > 2 </ sub >, a < sub > 3 </ sub >, ....

This was first done in algebraic geometry and algebraic number theory by Alexander Grothendieck to define the étale cohomology of a scheme.

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and ( the first power of ) a single variable.

While studying these languages, Abel published his first notable work in 1824, Mémoire sur les équations algébriques où on démontre l ' impossibilité de la résolution de l ' équation générale du cinquième degré ( Memoir on algebraic equations, in which the impossibility of solving the general equation of the fifth degree is proven ).

Between 1880 and 1887, Heaviside developed the operational calculus ( involving the D notation for the differential operator, which he is credited with creating ), a method of solving differential equations by transforming them into ordinary algebraic equations which caused a great deal of controversy when first introduced, owing to the lack of rigour in his derivation of it.

The name " transcendental " comes from Leibniz in his 1682 paper where he proved sin x is not an algebraic function of x. Euler was probably the first person to define transcendental numbers in the modern sense.

He first showed that e to any nonzero algebraic power is transcendental, and since e < sup > iπ </ sup > = − 1 is algebraic ( see Euler's identity ), iπ and therefore π must be transcendental.

While he is best known for the Kolmogorov – Arnold – Moser theorem regarding the stability of integrable Hamiltonian systems, he made important contributions in several areas including dynamical systems theory, catastrophe theory, topology, algebraic geometry, classical mechanics and singularity theory, including posing the ADE classification problem, since his first main result — the partial solution of Hilbert's thirteenth problem in 1957 at the age of 19.

In connection with his work on function theory, he was one of the first mathematicians to use the emerging ideas of algebraic topology.

In this article, we first survey kernels for some important types of algebraic structures ; then we give general definitions from universal algebra for generic algebraic structures.

He also introduced cyclic cohomology in the early 1980s as a first step in the study of noncommutative differential geometry.

The first approach is to compute the statistical moments by separating the data into bins and then computing the moments from the geometry of the resulting histogram, which effectively becomes a one-pass algorithm for higher moments.

The first book focuses on linear geometry.

Another approach, used by modern hardware graphics adapters with accelerated geometry, can convert exactly all Bézier and conic curves ( or surfaces ) into NURBS, that can be rendered incrementally without first splitting the curve recursively to reach the necessary flatness condition.

The determination of molecular structure by geometry optimization became routine only after efficient methods for calculating the first derivatives of the energy with respect to all atomic coordinates became available.

The invention of Cartesian coordinates in the 17th century by René Descartes ( Latinized name: Cartesius ) revolutionized mathematics by providing the first systematic link between Euclidean geometry and algebra.

Differential topology and differential geometry are first characterized by their similarity.

Riemannian geometry generalizes Euclidean geometry to spaces that are not necessarily flat, although they still resemble the Euclidean space at each point " infinitesimally ", i. e. in the first order of approximation.

The Elements begins with plane geometry, still taught in secondary school as the first axiomatic system and the first examples of formal proof.

Near the beginning of the first book of the Elements, Euclid gives five postulates ( axioms ) for plane geometry, stated in terms of constructions ( as translated by Thomas Heath ):

We know from other references that Euclid ’ s was not the first elementary geometry textbook, but it was so much superior that the others fell into disuse and were lost.

Then he went to hear a Pythagorean philosopher, who demanded that he first learn music, astronomy and geometry, which he did not wish to do.

In fact, his interest in the geometry of differential equations was first motivated by the work of Carl Gustav Jacobi, on the theory of partial differential equations of first order and on the equations of classical mechanics.

He manages to find some rational points on these curves – elliptic curves, as it happens, in what seems to be their first known occurrence — by means of what amounts to a tangent construction: translated into coordinate geometry

The Geometry Engine was the first very-large-scale integration ( VLSI ) implementation of a geometry pipeline, specialized hardware that accelerated the " inner-loop " geometric computations needed to display three-dimensional images.

They used the same graphics subsystem and Ethernet as the 2000s, but could also use up to 12 " geometry engines ", the first widespread use of hardware graphics accelerators.

In general relativity, one often first specifies a plausible distribution of matter and energy, and then finds the geometry of the spacetime associated with it ; but it is also possible to run the Einstein field equations in the other direction, first specifying a metric and then finding the energy-momentum tensor associated with it, and this is what Alcubierre did in building his metric.