The most famous proponent of finitism was Leopold Kronecker, who said:

The historical development of commutative algebra, which was initially called ideal theory, is closely linked to concepts in elimination theory: ideas of Kronecker, who wrote a major paper on the subject, were adapted by Hilbert and effectively ' linearised ' while dropping the explicit constructive content.

Leopold Kronecker ( December 7, 1823 – December 29, 1891 ) was a German mathematician who worked on number theory and algebra.

Other mathematicians such as Hermann Weyl ( who eventually became disenchanted with intuitionism, feeling that it places excessive strictures on mathematical progress ) and Leopold Kronecker also played a role-though they are not cited by Brouwer in his definitive speech.

* The Kronecker delta in mathematics

Then he moved to the Humboldt University of Berlin ( then called the Friedrich William University ) in 1878 where he continued his study of mathematics under Leopold Kronecker and the renowned Karl Weierstrass.

" Kronecker even objected to Cantor's proofs that the algebraic numbers are countable, and that the transcendental numbers are uncountable, results now included in a standard mathematics curriculum.

Kronecker, now seen as one of the founders of the constructive viewpoint in mathematics, disliked much of Cantor's set theory because it asserted the existence of sets satisfying certain properties, without giving specific examples of sets whose members did indeed satisfy those properties.

In mathematics, the Kronecker delta or Kronecker's delta, named after Leopold Kronecker, is a function of two variables, usually integers.

The Kronecker delta is used in many areas of mathematics.

In 1841 Kronecker became a student at the University of Berlin where his interest did not immediately focus on mathematics, but rather spread over several subjects including astronomy and philosophy.

Back in Berlin, Kronecker studied mathematics with Gustav Lejeune Dirichlet and in 1845 defended his dissertation in algebraic number theory written under Dirichlet's supervision.

For several years Kronecker focused on business, and although he continued to study mathematics in his own time as a hobby and kept correspondence with Kummer, he published no mathematical results.

His business activity allowed Kronecker a comfortable financial situation, which made it possible for him to go back to Berlin in 1855 to pursue mathematics as a private scholar.

In 1866, when Riemann died, Kronecker was offered the mathematics chair at the University of Göttingen ( previously held by Carl Gauss and Dirichlet ), but he refused preferring to keep his position at the Academy.

In mathematics, Kronecker's theorem is either of two theorems named after Leopold Kronecker.

In mathematics, the Kronecker product, denoted by ⊗, is an operation on two matrices of arbitrary size resulting in a block matrix.

Hensel studied mathematics in Berlin and Bonn, under mathematicians like Leopold Kronecker and Karl Weierstrass.

Setting aside the animosity Kronecker had displayed towards him, Cantor invited him to address the meeting, but Kronecker was unable to do so because his wife was dying from injuries sustained in a skiing accident at the time.

Due to the characteristic entrywise procedure, this operation is identical to many multiplying ordinary numbers ( mn of them ) all at once-hence the Hadamard product is commutative, associative and distributive over addition, and is a principal submatrix of the Kronecker product.

For example, if a Dirac delta impulse occurs exactly at a sampling point and is ideally lowpass-filtered ( with cutoff at the critical frequency ) per the Nyquist – Shannon sampling theorem, the resulting discrete-time signal will be a Kronecker delta function.

The Kronecker comb thus consists of an infinite series of unit impulses N units apart, and includes the unit impulse at zero.

Hölder first studied at the Polytechnikum ( which today is the University of Stuttgart ) and then in 1877 went to Berlin where he was a student of Leopold Kronecker, Karl Weierstraß, and Ernst Kummer.

Kronecker originally introduced the term arithmetization of analysis, by which he meant its constructivization in the context of the natural numbers ( see quotation at bottom of page ).

His parents, Isidor and Johanna ( née Prausnitzer ), took care of their children's education and provided them private tutoring at home-Leopold's younger brother Hugo Kronecker would also follow a scientific path later becoming a notable physiologist.

Although he held no official university position, as a member of the Academy Kronecker had the right to hold classes at the University of Berlin and he decided to do so starting with 1862.

If we restrict the local coordinates to be Cartesian coordinates with the same scale centered at the point of interest, the metric tensor is the Kronecker delta.

which are linearly independent at each point q in U. Conversely, given such a coframe, there is a unique moving frame X < sub > 1 </ sub >, X < sub > 2 </ sub >, ..., X < sub > n </ sub > which is dual to it, i. e., satisfies the duality relation α < sup > i </ sup >( X < sub > j </ sub >) = δ < sup > i </ sup >< sub > j </ sub >, where δ < sup > i </ sup >< sub > j </ sub > is the Kronecker delta function on U.

:: Kronecker teaches at the University of Heidelberg, and scolds Nina for being late for class.

Kronecker first postulated that the values of elliptic functions at torsion points should be enough to generate all abelian extensions for imaginary quadratic fields, an idea that went back to Eisenstein in some cases, and even to Gauss.

He spent one year there attending lectures by Klein, before spending the academic year 1877 – 1878 at the University of Berlin where he attended classes by Kummer, Weierstrass and Kronecker, after which he returned to Munich.

Newton encouraged Moore to study in Germany, and thus he spent an academic year at the University of Berlin, attending lectures by Kronecker and Weierstrass.

He died at Schöneberg near Berlin in 1863 and was buried in the St Matthäus Kirchhof Cemetery in Schöneberg close to the ( eventual ) gravesites of Gustav Kirchhoff and Leopold Kronecker.

After receiving a substantial inheritance upon his father's death in 1863, Cantor shifted his studies to the University of Berlin, attending lectures by Leopold Kronecker, Karl Weierstrass and Ernst Kummer.

The Academy in Berlin honored him with a formal memorial speech held by Kummer in 1860, and later ordered the publication of his collected works edited by Kronecker and Lazarus Fuchs.

Famous researchers, such as the chemist August Wilhelm Hofmann, the physicist Hermann von Helmholtz, the mathematicians Ernst Eduard Kummer, Leopold Kronecker, Karl Weierstrass, the physicians Johannes Peter Müller, Albrecht von Graefe, Rudolf Virchow and Robert Koch, contributed to Berlin University's scientific fame.

Grave of Kronecker ( St Matthäus, Berlin )

Dirichlet, whose wife Rebecca came from the wealthy Mendelssohn family, had introduced Kronecker to the Berlin elite.

Kronecker died on December 29, 1891 in Berlin, several months after the death of his wife.

In 1867, after graduating, he went to the University of Göttingen where he began his university studies but he only studied there for one semester before returning to Berlin, where he attended lectures by Kronecker, Kummer and Karl Weierstrass.

In the last days of December 1891 Kronecker died and, therefore, his chair in Berlin became vacant.

After publishing his thesis Bukreev went abroad and took lectures of Karl Weierstrass, Lazarus Fuchs, and Leopold Kronecker in Berlin.

As a post-doc he completed his mathematical studies in Berlin attending lessons by Leopold Kronecker and Karl Weierstraß.