From the primitive symbols, certain formulas are defined as well formed, some of which are listed as axioms; and rules are stated for inferring one formula as a conclusion from one or more other formulas taken as premises.

公式即基设符号所形成的一种良构表式,其中一部分被列为公理;推演规则被用来从一个或多个作为前提的公式推演出一个作为结论的公式。

属类：自然科学-数学-

A theorem within such a system is a formula capable of proof through a finite sequence of well-formed formulas, each of which either is an axiom or is validly inferred from earlier formulas.

在这样的系统中,一条定理即是可以通过合式公式的有限序列加以证明的一个公式,这些合式公式中的每一个公式不是公理,就是从前面公式可以推得的公式

属类：自然科学-数学-

"Statement that there are no natural numbers x, y, and z such that xn + yn = zn, in which n is a natural number greater than 2. About this, Pierre de Fermat wrote in 1637 in his copy of Diophantus's Arithmetica, "I have discovered a truly remarkable proof but this margin is too small to contain it." "

在n大于2的情况下,使xn＋yn=zn成立的自然数x、y、z不存在。对此问题,法国数学家费马于1637年在他那本巴赫(C.-G.Bachet)所翻译的丢番图《算术》中写道︰"我已发现了一个真正不凡的证明,但页边太小,写不下。"

属类：自然科学-数学-

Although the theorem was subsequently shown to be true for many specific values of n, leading to important mathematical advances in the process, the difficulty of the problem soon convinced mathematicians that Fermat never had a valid proof. In 1995 the British mathematician Andrew Wiles (b. 1953)and his former student Richard Taylor (b. 1962)published a complete proof, finally solving one of the most famous of all mathematical problems.

数学家们长期对这个命题感到困惑,因为他们不能证明它成立,也不能做反证,虽然已经证实许多n的特定值。英国数学家怀尔斯(A.Wiles,1953～)在从前学生泰勒(R.Taylor,1962～)的帮助下,完成费马大定理的证明,终于解决了这个最著名的数学难题。

属类：自然科学-数学-

"In an axiomatic system, the primitive symbols are undefined and all other symbols are defined in terms of them. In Euclidean geometry, for example, such concepts as "point," "line," and "lies on" are usually posited as primitive terms. "

在任何公理系统中,基设符号都是不下定义的,其它所有符号都藉基设符号来界定。例如,在欧几里德几何中,"点"、"线"、"介于"都是基设名词。

属类：自然科学-数学-

In topology, a long-standing conjecture asserting that no more than four colours are required to shade in any map such that each adjacent region is coloured differently. First posed in 1852 by Francis Guthrie, a British math student,

拓扑学问题,找出给地图着色所需用的不同颜色的最小数目,使得没有两个相邻的区域有相同的颜色。最早在1852年由一英国学生格思里(F.Guthrie)提出

属类：自然科学-数学-

In mathematical analysis, an integral transform useful in solving certain types of partial differential equations.

数学分析中的一种积分变换,可用来解决特定类型的偏微分方程式。

属类：自然科学-数学-

A function's Fourier transform is derived by integrating the product of the function and a kernel function (an exponential function raised to a negative complex power)over the interval from-∞to +∞. Such transforms, discovered by Joseph Fourier, are particularly useful in studying problems concerning electrical potential.

欲取得一个函数的傅立叶变换,可以在-∞与＋∞的间隔中把该函数与核函数(提升至负复数幂的指数函数)的结果整合起来。这样的变换(由约瑟夫?傅立叶发现)在研究电势的相关问题时特别有用。

属类：自然科学-数学-

fraction ,In arithmetic, a number expressed as a quotient, in which a numerator is divided by a denominator.

分数,在算术中指两个数量相除的商,被除数称为分子,除数称为分母

属类：自然科学-数学-

In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator.

简分数的分子和分母都是整数;如果分子或分母(或两者)本身也是分数,则称为繁分数

属类：自然科学-数学-