1916年，香农出生于密歇根州的佩托斯基，他很早就显现出在数学和制造小玩意方面的天赋，学生时代时就在计算机技术的基础上取得了突破。
Born in 1916 in Petoskey, Michigan, Shannon showed an early talent for maths and for building gadgets, and made breakthroughs in the foundations of computer technology when still a student.
微积分是数学史上的一次重大突破，因为她使连续变量可以被处理。
Calculus was a mathematical breakthrough, because it dealt with continuously varying quantities.
未来的科技突破将在多学科的领域中产生，包括生物、物理、计算机科学和数学等。
Many future breakthroughs are likely to emerge from multidisciplinary work at the nexus of biology, physics, computer science, and mathematics.
顾名思义，基本引理是整个朗兰兹纲领的立足点，但几十年来数学家都无力证明它，ngo的突破将促进朗兰兹纲领其他方面的新进展。
As its name suggests, the Fundamental Lemma is a technical point, but one that had stymied mathematicians for decades. Ngo's breakthrough makes other advances in the Langlands Program look possible.
这些突破不仅是对经济学价值的弘扬光大，也是对理论、数学和圈外人等其余三者的广而考之。
These breakthroughs are adverts not just for the value of economics, but also for three other things: theory, maths and outsiders.
寻找合适的数学工具从可测电气量中提取直接反映故障距离信息是重要的突破点。
It is a breakthrough to extract key information, which directly reflect fault distance from fathomable electrical measurements with appropriate mathematics tool.
结构设计、内外弹道、数学模拟都取得了重大突破，已达动态发射试验阶段。
The critical breakthroughs have been taking place in the structural designs, internal and external ballistics, and mathematical models, and it is now in dynamic firing test phase.
基于对窄化和泛化现象的反思，进行数学探究学习的理论构建和实践探索，是本课题研究的突破口和推进轴。
The theoretical and practical study on the inquiry learning of mathematics which is based on these phenomena should be considered as the breakthrough of the paper.
经证实这就是我那是一直着手处理的数学难题的一个实质上的突破。
It turned out to be a real breakthrough for solving the mathematical problem I was working on.
要充分认识数学教学中揭示思维过程的意义，把握三个立足点，找准三个突破口，注重合理性、简洁性、系统性、主体性，善于在数学教学实践中揭示思维过程。
We must be aware of the importance of the thinking process in maths teaching by holding three key points on the basis of rationality, conciseness, systematism and student-orientation.
20世纪50年代早期，美国经济学家肯尼斯。阿罗和2004年过世的法国数学家罗拉尔。德布鲁在此得到突破。
The breakthrough was made in the early 1950s by Kenneth Arrow, an American economist, and Gérard Debreu, a French mathematician who died in 2004.
20世纪50年代早期，美国经济学家肯尼斯。阿罗和2004年过世的法国数学家罗拉尔。德布鲁在此得到突破。
The breakthrough was made in the early 1950s by Kenneth Arrow, an American economist, and Gérard Debreu, a French mathematician who died in 2004.
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