他毕业于科罗拉多大学荣誉北方数学的哲学额外工作。
He graduated with honors from the University of Northern Colorado in mathematics with additional work in philosophy.
其次，学校的每一门教育科目都是系统的，如语文、数学、科学和哲学。
Secondly, every subject of education in school is systematic, such as Chinese, mathematics, science and philosophy.
视觉化对象并归纳数学规律的能力这样的问题连一些最优秀的诗人和哲学家都无法解答，又如何能让一个人找到那些问题的答案呢？这一点并不明朗。
It's not obvious how the capacity to visualize objects and to figure out numerical patterns suits one to answer questions that have eluded some of the best poets and philosophers.
世界也不是最后的定论，你们记住，哲学问题不像数学问题，因此没有答案。
The world is not the last word. You remember, it's not like a mathematical problem so there's no solution.
乔查尼先生穿着像个流浪汉，然而却是个深解人类多种领域学问的大师，包括科学，数学，哲学，特别是犹太法典《塔木德》他都擅长。
Chouchani dressed like a vagabond but was a master of vast areas of human knowledge, including science, mathematics, philosophy and especially the Talmud.
这些哲学和数学问题成了我们的困惑。
These problems of philosophy and mathematics are personal riddles also; was it always just like this, and did we fail to notice?
高德的不完备定理更像是一组非常有趣的关于逻辑和哲学的数学定理，而不是严格意义上的科学。但是整体上，这些逻辑和哲学与科学密切相关。
It is not strictly science, but rather a very interesting set of mathematical theorems about logic and the philosophy that is definitely relevant to science as a whole.
人类的自由意志似乎是最难以处理的哲学课题，远非数学证明所能表达。
Human free will might seem like the squishiest of philosophical subjects, way beyond the realm of mathematical demonstration.
这一领域的先驱中最早的是希腊数学家和哲学家克劳迪•托勒密(约公元90年～168年)，历史上多称他托勒密。
At the forefront of the pioneers in the field was the Greek mathematician and philosopher Claudius Ptolemaeus (c. AD 90 ?168), more popularly known to history as Ptolemy.
他建议，比如将孩子们集合到一个团队中就某一问题展开辩论，可以让他们更轻松地掌握数学或哲学中的抽象问题。
He suggests, for example, that children may have an easier time learning abstract topics in mathematics or physics if they are put into a group and allowed to reason through a problem together.
另一个哲学家，笛卡尔在思考上帝万能的时候觉得，如果万能的上帝无法改变数学，那么便不能称为万能。
And another philosopher, Descartes, in thinking about God's omnipotence, thought that it wouldn't be good enough if God as omnipotent couldn't change the facts of mathematics.
牛顿的研究成果在1687年首次出版的《自然哲学的数学原理》一书中发表。 在这本书里牛顿对以前科学家所关心的大部分力学难题做出了解答。
The outcome was the famous "Principia Mathematica", first published in 1687, in which Newton presented solutions to most of the problems of motion that had concerned earlier scientists.
当时狄拉克的同行们正在为他们的公式的哲学内涵争论不休，而他认为语言是靠不住的，在理论物理上数学有着绝对的优势。
But while his colleagues struggled with the philosophical implications of their equations, Dirac thought words were treacherous and saw merit only in mathematics.
笛卡尔除了是哲学家之外也是一位杰出的数学家，对于还记得这点的人来说以上这种偏见应该并不让人惊讶。
This bias shouldn't surprise those who remember that Descartes was a brilliant mathematician in addition to being a philosopher.
然后蒙卡拉马里人教给新一代夸润人数学，哲学，科学和其他文明社会的基础知识。
The Mon Calamari then taught this new generation of Quarren mathematics, philosophy, science and the other foundations of civilization.
1713年牛顿在进一步阐发其经典代表作“自然哲学的数学原理”的证据与推理过程的注释里写道。
In the General Scholium (from the 1713 edition) of his masterpiece Mathematical Principles of Natural Philosophy (1686), Newton writes.
阿基米德毕生从事哲学和数学研究。对于他那个时代的希腊人来说，体力劳动是丢人的，他们厌恶和看不起实验工作。
Archimedes spent his life in philosophical and mathematical studies. To the Greeks of his day, manual labor was degrading, and they looked down upon experimentation with distaste.
休姆是一个学生的数学和哲学谁设立了诗人俱乐部讨论他的理论的诗歌。
Hulme was a student of mathematics and philosophy who had established the Poets' Club to discuss his theories of poetry.
他是希腊第一位哲学家、科学家和数学家，写过一本关于航海的书，据说是阿那克西曼德的老师。
He was the first Greek philosopher, scientist, and mathematician, is credited with writing a book on navigation, and is rumored to have been Anaximander's teacher.
希腊哲学家安那萨哥拉斯时期，哲学家，数学家，佩里克·利斯的老师。
The Time Period of the Greek philosopher Anaxagoras, philosopher, mathematician and teacher of Pericles.
1687年，牛顿在很多前人知识的基础之上，发表了一部专著叫作《自然哲学的数学原理》，改变了整个人类的进程。
In 1687, on the basis of a lot of previous knowledge, Newton published a book called the mathematical principles of natural philosophy.
庞加莱是法国著名的数学家、天文学家、理论物理学家和科学哲学家，是横跨19、20世纪的科学大师。
A renowned French mathematician, astronomer, theoretical physicist and scientific philosopher, Poincare saw his remarkable scientific life spanning the 19th and 20th centuries.
本文简介数学教育哲学的内容、重要性及其应用。
This paper introduces the contents of maths educational philosophy , its importance and application.
他们宣告他们不是“学数学的料”，然后他们转去了哲学专业。
They proclaim that they are "not math people." they switch to a philosophy major.
他们宣告他们不是“学数学的料”，然后他们转去了哲学专业。
They proclaim that they are "not math people." they switch to a philosophy major.
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