One of the first court cases regarding the nature of source code as free speech involved University of California mathematics professor Dan Bernstein, who had published on the Internet the source code for an encryption program that he created.

* Daniel J. Bernstein ( born 1971 ), American mathematics professor, creator of qmail and djbdns, and plaintiff in Bernstein v. United States

Bernstein earned his bachelor's degree in mathematics from New York University ( 1991 ) and has a PhD in mathematics from the University of California, Berkeley ( 1995 ), where he studied under Hendrik Lenstra.

Bernstein has published a number of papers in mathematics and computation.

The technique has been applied in the study of mathematics and logic since before Aristotle ( 384 – 322 B. C.

In mathematics, the axiom of regularity ( also known as the axiom of foundation ) is one of the axioms of Zermelo – Fraenkel set theory and was introduced by.

The axiom of regularity is arguably the least useful ingredient of Zermelo – Fraenkel set theory, since virtually all results in the branches of mathematics based on set theory hold even in the absence of regularity ( see chapter 3 of ).

In mathematics, the arithmetic – geometric mean ( AGM ) of two positive real numbers and is defined as follows:

In mathematics, the Borsuk – Ulam theorem, named after Stanisław Ulam and Karol Borsuk, states that every continuous function from an n-sphere into Euclidean n-space maps some pair of antipodal points to the same point.

His father, Étienne Pascal ( 1588 – 1651 ), who also had an interest in science and mathematics, was a local judge and member of the " Noblesse de Robe ".

William Frederick Schelter ( 1947 – July 30, 2001 ) was a professor of mathematics at The University of Texas at Austin and a Lisp developer and programmer.

Similarly, the influences of philosophers such as Sir Francis Bacon ( 1561 – 1626 ) and René Descartes ( 1596 – 1650 ), who demanded more rigor in mathematics and in removing bias from scientific observations, led to a scientific revolution.

The contributions of Kurt Gödel in 1940 and Paul Cohen in 1963 showed that the hypothesis can neither be disproved nor be proved using the axioms of Zermelo – Fraenkel set theory, the standard foundation of modern mathematics, provided ZF set theory is consistent.

He passed the examination in the elements of mathematics and the theory of navigation at the Royal Naval Academy on 2 – 4 September 1816, and became a 1st Lieutenant on 1 September 1818.

In 1949, while doing unrelated archival work, the historian of mathematics Carolyn Eisele ( 1902 – 2000 ) chanced on an autograph letter by Peirce.

* Theoretical chemistry – study of chemistry via fundamental theoretical reasoning ( usually within mathematics or physics ).

In mathematics, the Cauchy – Riemann differential equations in complex analysis, named after Augustin Cauchy and Bernhard Riemann, consist of a system of two partial differential equations which must be satisfied if we know that a complex function is complex differentiable.

" The new grounding of mathematics: First report ," 1115 – 33.

" The logical foundations of mathematics ," 1134 – 47.

" The foundations of mathematics ," with comment by Weyl and Appendix by Bernays, 464 – 89.

In contrast to real numbers that have the property of varying " smoothly ", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic – do not vary smoothly in this way, but have distinct, separated values.

The Englert – Greenberger duality relation provides a detailed treatment of the mathematics of double-slit interference in the context of quantum mechanics.

* 500 – Science ( including mathematics )

In mathematics, an infinite series will sometimes converge –

In mathematics, the Euler – Maclaurin formula provides a powerful connection between integrals ( see calculus ) and sums.

In mathematics, more specifically in abstract algebra and ring theory, a Euclidean domain ( also called a Euclidean ring ) is a ring that can be endowed with a certain structure – namely a Euclidean function, to be described in detail below – which allows a suitable generalization of the Euclidean division of the integers.

In mathematics, the Sato – Tate conjecture is a statistical statement about the family of elliptic curves E < sub > p </ sub > over the finite field with p elements, with p a prime number, obtained from an elliptic curve E over the rational number field, by the process of reduction modulo a prime for almost all p. If N < sub > p </ sub > denotes the number of points on E < sub > p </ sub > and defined over the field with p elements, the conjecture gives an answer to the distribution of the second-order term for N < sub > p </ sub >.

In mathematics, an algebraic number is a number that is a root of a non-zero polynomial in one variable with rational coefficients ( or equivalently — by clearing denominators — with integer coefficients ).

Initially a study of systems of polynomial equations in several variables, the subject of algebraic geometry starts where equation solving leaves off, and it becomes even more important to understand the intrinsic properties of the totality of solutions of a system of equations, than to find a specific solution ; this leads into some of the deepest areas in all of mathematics, both conceptually and in terms of technique.

In mathematics, a Diophantine equation is an indeterminate polynomial equation that allows the variables to be integers only.

In mathematics, Horner's method ( also known as Horner scheme in the UK or Horner's rule in the U. S .) is either of two things: ( i ) an algorithm for calculating polynomials, which consists in transforming the monomial form into a computationally efficient form ; or ( ii ) a method for approximating the roots of a polynomial.

In mathematics, a polynomial is an expression of finite length constructed from variables ( also called indeterminates ) and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents.

In advanced mathematics, polynomials are used to construct polynomial rings, a central concept in abstract algebra and algebraic geometry.

In mathematics, a quadratic equation is a univariate polynomial equation of the second degree.

In mathematics, a transcendental number is a ( possibly complex ) number that is not algebraic — that is, it is not a root of a non-constant polynomial equation with rational coefficients.

* Equally spaced polynomial in mathematics

In mathematics, a Hurwitz polynomial, named after Adolf Hurwitz, is a polynomial whose coefficients are positive real numbers and whose zeros are located in the left half-plane of the complex plane, that is, the real part of every zero is negative.

* Reciprocal polynomial, in mathematics

" One such example of his impact on pure mathematics is his framework for understanding the Jones polynomial using Chern – Simons theory.

In mathematics, a Laurent polynomial ( named

In mathematics, factorization ( also factorisation in British English ) or factoring is the decomposition of an object ( for example, a number, a polynomial, or a matrix ) into a product of other objects, or factors, which when multiplied together give the original.

In mathematics, a Diophantine equation is an equation of the form P ( x < sub > 1 </ sub >, ..., x < sub > j </ sub >, y < sub > 1 </ sub >, ..., y < sub > k </ sub >)= 0 ( usually abbreviated P (,)= 0 ) where P (,) is a polynomial with integer coefficients.

In mathematics, a quadric, or quadric surface, is any D-dimensional hypersurface in ( D + 1 )- dimensional space defined as the locus of zeros of a quadratic polynomial.

In mathematics, if L is a field extension of K, then an element a of L is called an algebraic element over K, or just algebraic over K, if there exists some non-zero polynomial g ( x ) with coefficients in K such that g ( a )= 0.

A quadratic function, in mathematics, is a polynomial function of the form

In mathematics, a polynomial is said to be irreducible if it cannot be factored into the product of two or more non-trivial polynomials whose coefficients are of a specified type.

In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence that arise in probability, such as the Edgeworth series ; in combinatorics, as an example of an Appell sequence, obeying the umbral calculus ; in numerical analysis as Gaussian quadrature ; in finite element methods as Shape Functions for beams ; and in physics, where they give rise to the eigenstates of the quantum harmonic oscillator.

In mathematics, a polynomial sequence is a sequence of polynomials indexed by the nonnegative integers 0, 1, 2, 3, ..., in which each index is equal to the degree of the corresponding polynomial.

In mathematics, a polynomial sequence, i. e., a sequence of polynomials indexed by

In mathematics before the 1970s, the term umbral calculus referred to the surprising similarity between seemingly unrelated polynomial equations and certain shadowy techniques used to ' prove ' them.