数学真理的证据有其特殊之点，就是所有论据都在一方。
The peculiarity of the evidence of mathematical truths is, that all the argument is on one side.
人们所推崇数学真理的必然性，甚至归属于它的特殊的确定性，只是一种错觉。
John Stuart Mill the character of necessity ascribed to the truths of mathematics and even the peculiar certainly attributed to them is an illusion.
特别是20世纪以来诞生的各种数学新理论，正在逐步地改变着数学真理的传统观念。
Especially from the beginning of 20 ~ (th) century, the development of various new mathematical theories have been changing traditional notion of mathematical truth step by step.
本文同意逻辑证明是检验现代数学真理的唯一标准，同时也讨论了逻辑证明是一种实践活动的问题。
The paper agrees that only logical proof can be criterion of modern mathematical truth, and also discusses that logical proof is an action of practice.
数学真理真的在我们的想象之前就存在？
Can a mathematical truth really exist before anyone has ever imagined it?
但最真实的莫过于数学真理，因此当我看到数学盲经理人们无耻地盗用数学真理，渴望为一些无聊的废话披上真理的外衣时，我就会感到心烦意乱。
Truest of all are mathematical truths, and it is therefore upsetting to see them being pilfered shamelessly by innumerate managers eager to lend an aura of fact to what is usually a glob of guff.
数学公理或真理是永远不会错的。
例如，新的数学真理是被发现还是被发明的呢？
For example, are new mathematical truths discovered or invented?
追随数学内在逻辑的脚步，数学家可以超越人类观察的局限，脱离客观存在的暂态，而发现永恒的真理。
By following the internal logic of mathematics, a mathematician discovers timeless truths independent of human observation and free of the transient nature of physical reality.
在数学中，我们发现真理的主要工具是归纳和模拟。——拉普拉斯。
In mathematics, we found that the truth is the main tool and simulation.
做一个每天都在追逐真理的人，布莱士·帕斯卡(译者注：法国数学家)说：“一旦你的灵魂被真理延伸，它绝不会再回到最初的形态。”
Be one of those few who pursue truth both night and day. Blaise Pascal said, "Once your soul has been enlarged by truth, it can never return to its original size."
当我们听到非常富有的人数只占2%而不是20%的时候，这个谚语又把著名的数学模型，powerlaw(幂次现象)，变成真理。
While we know that the number of super wealthy is probably closer to 2% than 20%, the proverb turns a famouse rule of mathematics, known as power law, into common wisdom.
假如别人和一样深刻和持续地思考数学真理，他们会作出同样的发现的。
If someone as deeply and constantly thinking and mathematical truth, they will make the same discovery.
数学永远不会让你领会更高的真理。
指出了数学是探索真理的有力工具。
数学的内部真实性是纯智力的真理。
The inner truth of mathematics is purely intellectual truth.
数学不仅拥有真理，而且拥有至上的美——一种冷静而严肃、犹如雕塑那样的美。
Mathematics possesses not only truth, but supreme beauty-a beauty cold and austere. like that of sculpture.
通过限制很多知识，不言自明的真理所揭示的数学，他从而构建一个最好的例子理性的制度建设历史上的哲学。
By limiting much of knowledge to self-evident truths revealed by mathematics, he thereby constructed one of the best examples of rationalistic system-building in the history of philosophy.
数学并不是绝对真理的单一整体结构。
Mathematics is not a single monolithic structure of absolute truth.
该文提出了在闭环MIMO容量研究中引入了率失真理论的研究方法，推导出了反馈信道速率和闭环MIMO容量之间的数学关系。
The rate-distortion theory is induced to the system model, and the mathematic formula between the feedback channel rate and the closed-loop MIMO capacity are deduced.
文中指出根据唯物辩证法中关于一切真理都是相对真理的观点，数学真理当然也是相对真理。
A view was pointed ont in the paper that all truth is relative truth according to materialist dialectic.
对于一个数学实在论者来说，一个特别急迫的任务是回答数学证明是如何建立起关于数学对象的真理性问题。
For mathematical realists an especially pressing question is that of how a proof can establish a conclusion about mathematical objects.
笔者认为，哲学在确立自己的真理理想和真理途径时，存在着对数学的夸张性解读。这是哲学加于自身的桎梏。
The writer believes that philosophy exaggerated it understanding of mathematics when establishing its truth ideals and it path to truth, imposing on itself the shackles.
七大的数学训练的确精彩，可开头的感觉却是：你在给我造“信仰”么？说服我相信这东西是真理？
The mathematic training of Paris 7 is indeed prefect. But in the beginning it came the feeling that "are you creating faith for me", and trying to convince me that these are the ultimate truth?
七大的数学训练的确精彩，可开头的感觉却是：你在给我造“信仰”么？说服我相信这东西是真理？
The mathematic training of Paris 7 is indeed prefect. But in the beginning it came the feeling that "are you creating faith for me", and trying to convince me that these are the ultimate truth?
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