英语学习 辨析prove or disprove证实或推翻，improve改善，变得更好

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英语学习 辨析prove or disprove证实或推翻，improve改善，变得更好

gcd(na,b)=n*gcd(a,b) prove or disprove

【纽曼】第12章 有用的“功、力和能量”的等式

为什么说数学是一种语言

一、英语学习 辨析prove or disprove证实或推翻，improve改善，变得更好

prove or disprove证实或推翻,improve改善，变得更好

disprove英 [ˌdɪsˈpruːv] 美 [ˌdɪsˈpruːv]

vt. 反驳，证明……是虚假的

短语

disprove sb's views 不赞同某人的意见

Impossible to dispute or disprove 无法否认的

evidence to disprove a fact 反证

柯林斯英汉双解大词典

disprove /dɪsˈpruːv/ TEM8 ( disproving, disproved, disproven, disproves )

1. V-T To disprove an idea, belief, or theory means to show that it is not true. 证明 (想法、信念或理论) 为误

例：The statistics to prove or disprove his hypothesis will take years to collect.

要花数年来收集证实或推翻他的假设的数据。

同近义词

vt. 反驳，证明…是虚假的refute , contradict

双语例句原声例句权威例句

He hadn't done any more than Young had been able to do, so he couldn't disprove the dominant theory.

他所做的和杨所能做的一样多，所以他无法反驳占主导地位的理论。

They accepted what he had said in default of any evidence to disprove it.

由于缺乏相反的证据，他们相信了他的话。

improve英 [ɪmˈpruːv] 美 [ɪmˈpruːv]

v. 康复，健康好转；超过，胜过；提高……的价值；改善，变得更好

[ 第三人称单数 improves 现在分词 improving 过去式 improved 过去分词 improved ]

短语

Significantly improve 明显提高 ; 显着提高 ; 明显的提高

Improve Phase 改善阶段 ; 改进阶段

improve eyesight 改善视力

柯林斯英汉双解大词典

improve /ɪmˈpruːv/ CET4 TEM4 ( improving, improved, improves )

1. V-T/V-I If something improves or if you improve it, it gets better. 改进

例：Within a month, both the texture and condition of your hair should improve.

不出一个月，你头发的质地和状况应该都会改善。

2. V-T/V-I If a skill you have improves or you improve a skill, you get better at it. 提高

例：Their French has improved enormously.

他们的法语水平提高了很多。

3. V-I If you improve after an illness or an injury, your health gets better or you get stronger. 康复

例：He had improved so much the doctor had cut his dosage.

他康复了很多，医生减少了他的用药量。

4. V-I If you improve on a previous achievement of your own or of someone else, you achieve a better standard or result. 提高

例：We need to improve on our performance against Nabisco.

我们需根据纳贝斯克公司标准来提高我们的业绩。

词组短语同近义词同根词词语辨析

improve efficiency 提高效率

improve on 改进；对…加以改良

improve in 在…方面有改进

to improve the environment 改善环境

improve upon vt. 改进

improve the comprehensive quality 提高综合素质

improve the investment climate 改善投资环境

双语例句原声例句权威例句

I need to improve my English.

我需要提高我的英语水平。

I need to improve my French.

我得提高我的法语水平。

Don't expect it to improve overnight.

不要指望这事一下子就改善了。

prove

英 [pruːv] 美 [pruːv]

v. 证实，证明；证明是，结果是；显示（自己的）才干（或勇气）（prove oneself）；<法律> 检验，认证（遗嘱）；（用数学或科学原理）证明，验算；试（枪），查验；（面团）发酵

[ 第三人称单数 proves 现在分词 proving 过去式 proved 过去分词 proved或proven ]

短语

Prove It 蔡依林 ; 证明这一点 ; 急性冠脉综合征 ; 唱片名

Prove Up 试验 ; 勘探 ; 探明 ; 具备

Prove yourself 自我证明 ; 旧房东 ; 证明你自己 ; 证明自己

prove to be 结果是，证明为

go to prove 足以证明；证实[常用在it之后]  

prove yourself 证明你自己

prove up v. 勘探；证明符合…的条件；试验

What are you trying to prove ?

你想证明什么？

This all goes to prove my theory.

这一切都有助于证明我的说法是对的。

This advice was to prove valuable.

这忠告证明是有益的。

参考《有道词典》，如有侵权请通知。

码字不易，敬请【点赞】！谢谢您的支持！

每天分享外语知识，请点击【关注】，不漏掉任何一期，助你提高外语水平。

My email：ilikework_cz@126.com

图片来自网络。

一、gcd(na,b)=n*gcd(a,b) prove or disprove

楼主条件漏了吧?
a=2,b=3,n=2
gcd(na,b)=1
n*gcd(a,b)=2

二、【纽曼】第12章 有用的“功、力和能量”的等式

Chapter 12 USEFUL "WORK, FORCE, AND POWER" EQUATIONS

A. The mathematical equations involving "Work, Force, and Power" are engineering equations which satisfy the past and present-day industries of the world. They are not appropriate to future industries. Such equations are not universal, scientific equations and they do not satisfy a rigorous scientific scrutiny. The equations which I will propose below are scientific equations and do satisfy scientific scrutiny. In addition, these equations will fulfill the future engineering need of industry and will conceptually mesh with an understanding of the gyroscopic-action-entity which is the basic building block of all matter and represents the mechanical essence of E = MC^2 .

A. 关于“功、力、功率”的精确数学等式只能满足过去和当前世界工业的工程要求。它们不适用于未来的工业。这种等式不是普遍科学的等式，它们不满足严谨的科学审查。我下面提出的等式是科学的等式，满足科学的严谨性。另外，这些等式可以达到未来工业的工程需要，在概念上与自旋子的理解匹配，自旋子是所有物质的基础砖块并是E = MC^2的力学本质。

I will now define a "Force" in accordance with Newton's Laws:

我将定义和牛顿力学一致的“力”：

"A 'Force' is any action capable of causing a reaction from an entity which is in or may enter the influence of that 'Force'!"

“‘力’是可以引起一个进入‘力’影响范围实体反作用的任何运动！”

To an observer, "Force" may be perceived as "Obvious" or "Unobvious." I mathematically distinguish between "Obvious" or "Unobvious" Force. One cannot have (Obvious or Unobvious) "Work, Force, or Power" occurring without energy participation and transference.

对于观察者，“力”也许是“可见”或“不可见”。我区分“可见”或“不可见”力。不能有“功、力或功率”产生而没有能量参与和传输。

The consistent, semantic application of the terms Obvious or Unobvious to "Work, Force, or Power" will accurately stimulate the mind of the thinking individual which will further the progress of science and the improvement of the Human Race.

对于“功、力或功率”可见或不可见一致的、语义的术语应用将正确的激发个人的思想，将促进科学进程和人类进步。

B. It is the essence of the scientific method that a scientific theory should stand or fall with respect to whether its predictions correspond with the Facts. With this in mind, I will now apply the conventional mathematical formulas for Work, Power, and Force to a factual observation:

B. 科学方法的本质是一个科学理论好坏决定于预测结果是否和事实一致。基于这种思想，我将用传统功、功率和力的的数学等式观察事实。

"A man has a 400-pound mass placed upon his shoulders. The gravitational force pushes down with 400 pounds upon the man. The man pushes up with 400 pounds of force on the mass. The man supports the 400 pound mass for 10 minutes and then pivots from under the mass to permit it to fall. (Had the man continued to support the mass he would have become fatigued to the point of collapse and physical damage.)"

“一个人将400磅重量放到肩膀上。重力向下施加400磅在人身上。人向上施加400磅的力在物体上。人支持400磅10分钟，之后放开物质让它掉下来。（使人持续支持物体他将疲乏到倒下产生物理伤害。）”

WORK = FORCE * DISTANCE (by conventional mathematics)

功=力*距离（传统计算）

According to this simple formula, the man in the above example did no work.

根据这个简单的等式，上面的人没有做功。

POWER = WORK/TIME (by conventional mathematics)

功率=功/时间（传统计算）

According to this simple formula, the man in the above example exerted no power.

根据这个简单的等式，上面的人没有对外输出功率。

FORCE = MASS *ACCELERATION (by conventional mathematics)

力=质量*加速度（传统计算）

According to this simple formula, the man in the above example exerted no force.

根据这个简单的等式，上面的人没有对外施加力。

[I should point out that from the perspective of Statics, there is FORCE exerted but there is no POWER or WORK.]

[我将指出，从静态观点，有外部力但没有功和功率。]

Because the force of the man and the force of gravity upon the mass are equal and opposite, then conventional mathematics would state that there is a net force of zero.

因为人的力和重力在物体上相等并相反，传统计算将说净力为0.

C. I will now examine the internal actions of the man in Figure 26-B to determine if the predictions obtained via conventional mathematics correspond with the Facts.

C.我现在将调查图26-B中的人内部的运动来决定传统预测与事实是否一致。

The Facts are as follows: During strenuous exercise or stress, the heart may pump eight times as much blood as in a period of relative relaxation, i.e., as many as 12 gallons a minute. All of the following conditions drastically increased while the man held the mass: the heartbeat, blood flow, breathing, oxygen flow, the electromagnetic stimulation of the brain and body cells, and the fermentation process to produce energy occurring within the muscle cells.

事实如下：在剧烈运动或加压时，心脏也许可能跳动可能是放松时的8倍，也就是说，一分钟10加仑。下面的情况在人抗住物体时都大大的增加了：心跳、血的流速、呼吸、氧流动、大脑电信号和身体细胞，这复杂的进程在细胞内产生能量。

Internally speaking, the man did produce Work and Power which resulted in the man producing a Force. Internally speaking, Potential Energy was converted to Kinetic Energy. It is important to note that the Potential Energy of the mass being supported by the man was a direct result of the internal, Kinetic Energy within the man. In essence, the presently -accepted, mathematical equations concerning Work, Power, and Force do not correspond with the facts.

内在讲，人确实产生了功和功率导致人产生了力。内在讲，势能转化为了动能。注意，人支撑物体的势能是人内存动能的相撞结果。本质上，当前可接受的关于功、功率和力的数学等式与事实不一致。

D. To properly view the Facts from a scientific basis, the man in the above experiment did produce Unobvious Work, Unobvious Power, and Unobvious Force. Until he dropped the 400-pound mass, both the man and gravity exerted a force. Consequently, the net force could not be zero -only the net movement was zero.

D.从科学角度看这个事实，上面的人产生了不可见功，不可见功率和不可见力。在他抛下400磅物体之前，人和重力都施加一个外力。因此，净力不为0-只是净运动为0。

E. By subjecting them to proper scientific scrutiny, the presently-accepted, mathematical formulas describing Work, Power, Force, Potential and Kinetic Energy are not scientifically accurate! I propose that more explicit and scientific mathematical formulas would be as follows:

E.通过科学审查，当前可接受的描述功、功率、力、势能、动能的数学公式是不科学不精确的！我提出的更明确和科学的数学公式如下：

可见功=力 距离（Wo=FD）
可见功率=可见功/时间（Po=Wu/T）
可见力=物质 加速度（Fo=MA）
[宏观可见物质*加速度]

不可见功=力 时间（Wu=FT）
不可见功率=不可见功/时间（Pu=Wu/T）
不可见力=[静态]力（Fu=[S]F）
[分子、原子和/或次原子的质量 加速度]

可见动能（OKE）=所有可见能量
不可见动能（UKE）+势能（PE）=所有不可见能量

The above mathematical formulas do correspond with the facts. They satisfy all previous requirements as well as the example of the man supporting a 400-pound mass. The man did produce Unobvious Work, Unobvious Power, Unobvious Force, and Unobvious Kinetic Energy. He did not produce Obvious Work, Obvious Power, Obvious Force, or Obvious Kinetic Energy.

上面的数学公式是和事实一致的。它们满足所有上面人抗400磅物体例子的要求。人产生了不可见功、不可见功率、不可见力和不可见动能。它没有产生可见功、可见功率、可见力功或可见动能。

The L. Pearce Williams biography on Michael Faraday states that during the early years of Faraday's intellectual development, Faraday was very impressed with a book written by Dr. Isaac Watts entitled, The Improvement of the Mind. As a disciple of John Locke, Dr. Watts continually emphasized the importance of the observed fact and the dangers of imprecise language. In his book, The Improvement of the Mind [published in London, 1809], Dr. Watt cautions the student to carefully distinguish between words and things lest he "feed upon husks instead of kernels." Dr. Watt's emphasis upon careful observation and precisely described facts equipped Michael Faraday with a seemingly infallible guide, i.e., the essence of the scientific method. I wish to provide you, the reader, with the precise, mathematical equations which I have presented above in order to permit a better scientific understanding of matter.

L. Pearce Williams在法拉第传记中说，在法拉第早年学习中，法拉第对瓦特写的The Improvement of the Mind一书印象非常深刻。作为约翰·洛克的信徒，瓦特先生连续强调观察到的事实和不精确语言的危险的重要性。在这本眉目里，The Improvement of the Mind[伦敦印刷，1809]，瓦特先生劝告学生小心识别单词等，唯恐他“注重外在而不是核心”。瓦特先生强调小心观察和精确描述事实给法拉第一贯正确的指导，也就是，科学方法的本质。我希望提供给你，读者，我上面提出的精确的数学公式，来对物质有更科学的理解。

F. It can now be scientifically observed from the facts that all static forces and all potential energies exist as a result of continuing, Unobvious Kinetic Energy . (Verify this fact by observing the Unobvious Kinetic Energy internally produced within the man as long as he supported the 400-pound mass on his shoulders.)

F.现在可以从科学上观察到，所有的静止力和势能都是由于持续的、不可见的动能而存在的。(通过观察人体内部产生的不可见动能来验证这一事实，只要他把400磅重的物体支撑在肩膀上。)

"It can now be scientifically observed from the facts that all static forces and all potential energies exist as a result of continuing, Unobvious Kinetic Energy."

现在可以从科学上观察到，所有的静止力和势能都是由于持续的、不可见的动能而存在的。

There are additional observations which verify the existence of Unobvious Kinetic Energy: materials both fatigue and break/collapse from supporting a force. Gas molecules "heat up" when compressed by a force. Such observations prove that materials react with Internal, Unobvious Kinetic Energy when a static force or Potential Energy is exerted against them.

还有其他观察结果证实了不可见动能的存在：材料疲劳和断裂/坍塌都来自于支撑力。气体分子被力压缩时会“加热”。这些观察结果证明，当一个静态力或势能作用于材料时，材料与内部的、不可见的动能发生反应。

G. To improve your understanding of my statements, consider Einstein's equation of E = MC2. The nature of the mass-energy relationship is such that the mass (and weight) changes associated with Potential Energy conversion into Unobvious Kinetic Energy (which occurs internally within matter) is immeasurably small. Consider also that the gyroscopic-action-entity represents the Mechanical Essence of Einstein's equation of E = MC2 and that the mathematical formulas I present properly account for the existence of the gyroscopic-action-entity.

G. 为了让你更理解我的陈述，考虑爱因斯坦的E = MC^2方程。质能关系的理论是这样的，质量（和重量）的变化关系到势能转化为不可见动能（发生在物质内部），微小到不可测量。同时考虑到，自旋子代表爱因斯坦E = MC^2方程的力学本质，我提出的数学公式恰当的说明了自旋子的存在。

EXAMPLE:
Newton's Third Law of Motion states: by the law of Action and Reaction, a Force must be resisted by an Equal and Opposite Force.
What does the mathematical term "equal" really mean? It means "identical in mathematical value or logical denotation; equivalent.”

例子：
牛顿运动第三定律说明：根据作用力和反作用力，力会产生大小相等方向相反的力。
数学术语“相等”意味着什么？意味着“数值或逻辑标准一致”。

According to Newton's Third Law: if I hold an iron material at a distance (see Figure 26-G) from a strong, permanent magnet (causing me to resist a constant attraction force of 200 lbs.) -what happens to me? I must use Unobvious, Internal Kinetic Energy to continually resist the attraction force of the permanent magnet. According to Newton's Third Law, the magnet must also be utilizing Unobvious, Internal Kinetic Energy to produce the constant attraction force, i.e., an "equal” action and reaction!

根据牛顿第三定律：如果我握住一个铁块与一个强永磁铁一段距离（看图26-G）（让我抗拒一200磅恒定吸引力）-对我来说发生了什么？我必须用不可见的内在动能来持续抗拒永磁铁的吸引力。根据牛顿第三定律，磁铁必须利用不可见内在的动能产生恒定的吸引力，就也是说一个“相等”的作用力和反作用力！

If the magnet were not to react with Unobvious, Internal Kinetic Energy, then Newton's Third Law would be defied. In resisting a continual, attraction force, I had to expend a constant, Unobvious, Internal Kinetic Energy. If the magnet produced a constant attraction force and did not utilize any Unobvious, Internal Kinetic Energy, then such observed results would be "opposite" and not "equal.” Hence, such a conclusion would be obviously incorrect.

如果磁铁没有与不可见的内在动能交互，将不服从牛顿第三定律。为了抗拒连续的吸引力，我必须使用一个恒定不可见内在动能。如果磁铁产生一个恒定吸引力，但没有用任何不可见内在动能，那么这种观察结果将是“相反”并“不等”的。因此，这种结论显然是不正确的。

The Facts clearly show that the atoms within myself, the magnet, the iron material, and the wall all produced "Unobvious Work, Force, and Power.” There was no "Obvious Work, Force, or Power" produced.

事实清楚的说明，自己、磁铁、铁块和墙的原子都产生了“不可见功、力和功率”。没有“可见功、力或功率”产生。

H. I have presented more precise mathematical equations which are conducive to an improved scientific comprehension of Matter in accordance with the Mechanical Essence of Einstein 's Equation of E=MC2. Such a mechanical essence is represented by the gyroscopic-action-entity which is the basic building entity of all matter.

H.我已经提供了更多精确的数学公式，有助于增进对物质的科学理解，与爱因斯坦E=MC^2方程力的本质一致。这种力学本质体现在构成所有物质基础实体的自旋子。

I. A PIONEERING SOURCE OF ENERGY:

I.开创性的能量源头：

Consider once again the equations Wu = FT,( Pu =Wu/T), and Fu = [S]F.

再考虑公式Wu = FT、( Pu =Wu/T)和 Fu = [S]F。

A permanent magnet "X” that attracts an object "Y" with a constant force of 200 lbs., twenty-four hours a day for 30 days will have performed the following:

一个永磁铁“X”对一个物体"Y"的恒定吸引力为200磅，连续30天每天24小时将有如下结果：

Wu =(200) * (60 sec.) * (60 min.) * (24 hrs.) *(30 days)
Wu=518,400,000 lbs.-sec.
Fu = 200 lbs. constant
Pu = 200 lbs. constant

The gyroscopic energy in the magnetic field produced Unobvious Work, Unobvious Power, and Unobvious Force. The magnetic field also maintained Potential Energy via the use of Unobvious Kinetic Energy to accomplish this task. The mass loss is not easily measurable since we are describing the effects that generate atomic energy. As you know, we are discussing E = MC2. The existence of the Gyroscopic­Action-Entity exactly fits the First Law of Thermodynamics since it appears this Entity cannot be created or destroyed.

磁场区域自旋子能量产生不可见功、不可见功率和不可见力。磁场区域同时通过用不可见动能保持势能来完成任务。质量的损失是不容易测量的，因为我们描述的效果产生于次原子级能量。正如你所知，我们讨论E = MC^2。自旋子的存在精确的符合热力学第一定律，因为它出现了不能被创建和毁灭的实体。

The present utilization of atomic reactors as a source of energy production is extremely inadequate for the demand.

当前作为能量源的次原子反应器的利用对需求是严重不足的。

The energy machine I have innovated has no harmful side effects*, will cost little, and will be small in size compared to a nuclear reactor. All that I have written has been based upon the concept of the gyroscopic entity on which I started working in 1965. Since that time I have sought to prove or disprove this concept. The more I have learned the more certain I became of its truth.

我创建的能源机没有有害结果、花费少、可以作为小型核反应堆。所有我写的是基于我1965年开始研究的自旋子的概念。那时我就想证实这种概念是否正确。我学的越多我越觉得它正确。

If you have Mastered what I teach, then you must recognize the reality of my Pioneering Invention. However, the access to an unlimited source of energy is not by any means the ultimate discovery!

如果你已经精通我所教授的，那么你必须认识到我的创新发明白真实性。然而，通向无限能源的大门决不是最终的发现！

The energy machine I have innovated simply uses Universal Energy (the gyroscopic-action-entity). Such utilization must occur if man is to end his stupidity, hunger, greed, and wars -and advance to other solar systems! Consider how long it took our Species to discover how to harness the motion of flowing water via a simple waterwheel.

我发明的能源机是简单的利用了宇宙能源（自旋子）。这种利用会结束人类的愚蠢、饥饿、贪心和战争-进化到另一个太阳系。想一下我们人类通过简单水轮利用水的运动用了多长时间。

It has been obvious to me that what I have seen so clearly was unimaginable for most people. What I have seen is, at the very least, equal to the effect of Einstein's equation of E = MC2. It gives me much contentment if you now understand what I have presented. This is the purpose of my Book.

很明显，我看到的对大多数人来说是不可想象的。我看到的是，最基本的，爱因斯坦E = MC^2方程式的效果。如果你已经明白我所说的我将非常满足。这是我这本书的目的所在。

*Note: There are no harmful side effects because the size of the gyroscopic-action-entity is so small that it easily passes through the atomic structure of living tissue. In nuclear fission, the sub-atomic particles (representing agglutinations of gyroscopic particles) are far larger and can do damage to the atomic structure of living tissue. By analogy, if one threw a dust particle at a large fishnet, the particle would easily pass through the net. However, if one attempted to pass a large boulder (composed of millions of dust particles) through the same fishnet, it would cause damage to the net. By another analogy. my energy machine - in its utilization of nuclear energy - differs from conventional nuclear energy sources in the following manner: I have discovered a previously unknown source of "underground, unique running water." I have therefore devised a "waterwheel" (my energy machine) to tap into this existing energy of unique running water (the continual motion of the gyroscopic particles). The conventional nuclear energy approach would be to secure a cup of normal water and attempt to "smash" the normal water with a hammer to extract the atomic energy from the water. My process is 100%.(conversion) efficient and harmless (due to the minute size of the gyroscopic particles). Conventional nuclear fission is less than 1% efficient and harmful (due to the larger size of the released particles).

*注：完全无害，因为自旋子实体的大小小到它可轻易穿过活组织的次原子结构。在核裂变中，次原子粒子（由陀螺子凝结成）更大，能伤害到活组织的次原子结构。通过分析，抛一个灰尘到一个鱼网，它可以轻易穿过网。然而，如果试图抛一个大石块（由无数灰尘结成）穿过鱼网，它将毁坏鱼网。依此类推，我的能源机-它利用核能-在以下几方面不同于传统的核能：我已经发现一种未知的“地下、唯一的活水”源头。我因此设计一个“水轮机”（我的能源机）利用这唯一活水（连续运动的自旋子）存在的能量。传统核能是固定一杯水并试图用榔头“打碎”正常的水获取水中的次原子级能量。我的过程是100%（转化）效率并无害（由于陀螺子的尺寸）。传统核能效率小于1%并有害（由于释放粒子尺寸过大）。

三、为什么说数学是一种语言

大家先来玩一个猜谜语吧，看看下面的符号，打一句话：
假如你一眼看出来上面这幅图谜底的话，恭喜你，初等数学还没忘并且很多英语单词也还都记得，最关键的是你应该还保持着一定的机智。第一个是i，虚数单位；第二个等于8，谐音ate；第三个是把一串数加起来的符号，读作sum，谐音some；第四个我们小学的时候就知道是pai了，谐音pie。所以连起来就是：I ate some pie and it was delicious! （意思是我吃了一个馅饼，它很好吃！）这是很多数学人都喜欢的一则谜语，但是更多人看到这个会觉得莫名其妙或者呵呵一笑。
是的，很多时候，就算是数学教授，听到不同领域的数学，大概也跟我们一样，要是叫他们做那些不熟悉领域的题目，或许也会觉得自己很久没有选过D了吧。
数学家每天谈话都说些啥？是这些么？

Sheldon: "The best number is 73. Why? 73 is the 21st prime number. Its mirror, 37, is the 12th and its mirror, 21, is the product of multiplying 7 and 3... and in binary 73 is a palindrome, 1001001, which backwards is 1001001."
谢耳朵：最好的数字是73，因为73是第21个素数，把73倒过来就是37，37是第12个素数，同时12和21也是对称的。不仅如此，73的二进制表示法是1001001，这个数是回文数，到起来念还是1001001。（来源于美剧生活大爆炸）

学数学在日常生活是一种怎样的感受

我本科到现在学的都是数学，每当新认识一个人聊到我的专业，大家听到数学这个名字的时候，通常会用两种方式来表达那种貌似尴尬或者略带新奇的反应，会说话的人一般都说：“哇，好厉害！我从小数学就不好，或者说我从中学开始数学就不好了，真羡慕你们数学好的！”每次美国人问我我说“I'm majoring in Mathematics” 他们都会说："Wow, you must be smart!"
当我还是个懵懂少年的时候我听到了这种赞美，通常是把持不住的，心里乐开了花，满满的都是自豪感，显然当时我万万没想到有一天自己也会把这句话当作模版跟别人寒暄。当然不是所有人说话都比较委婉或者那么正能量，也有大部分人会问我：“数学啊？数学不就是数字嘛，有啥好学的？又不赚钱，还不实用......” 我也遇到了很多亲友，甚至来自很多非洲的朋友都劝过我：“孩子，学点经济或者金融吧，多火啊，多好就业啊，可挣钱了呢，数学能找着啥工作啊？除了教书还可以干什么？......”

的确，我当时也不知道数学有什么用，哪怕我现在写着这篇文章，我也一定不会是说得最贴切的。不过听到越来越多的人问我为什么学数学，也看着越来越少的人真的坚持学数学，尤其是我们华人里面，学数学的比例很低，我总觉得是不是我们哪里误解数学了，导致数学被渐渐遗忘在角落，没有得到应有的重视。
其实我一开始是想写一篇驳论文的，不过觉得怎么反驳别人的观点也没用，后来觉得那就立论吧：就说数学好好好，大家都来学啊！不过又觉得那样肯定更没用。所以，我就既不批判已有的误解也不要尝试说学数学有多好：数学不止眼前的这些苟且和无奈，它其实并不神秘，学数学的也不是都在玩数字，下面我们就一起窥探一下数学到底是在干啥吧。

数学有哪些分支
下面这张图还不一定概括了数学分类的全部，不过就算这幅图，日常生活里面大部分都不会被涉及到。
总体来说，数学分为三大板块：纯数学，应用数学还有数理统计学。
分门别类说数学
1，纯数学
纯数学也叫基础数学，是一门专门研究数学本身，不以实际应用为目的的学问，研究从客观世界中抽象出来的数学规律的内在联系，也可以说是研究数学本身的规律。相对于应用数学而言，和其它一些不以应用为目的的理论科学有密切的关系。纯数学又分为三类，研究空间形式的几何类，研究离散系统的代数类，研究连续现象的分析类。当然这些小类还可以细分，平常人们口中吐槽得最多，九年义务教育打下的基础，很多都是直接为修**高级的纯数学课程做的准备。那些说数学是数字的朋友，大都把纯数学算做了整个数学。

2，应用数学
在这里我要吐槽一下百度百科，它给出的应用数学的定义，是一个阐述性和指导性并不那么强的定义，不太贴切事实，我个人倾向于这个版本。

Applied mathematics is a branch of mathematics that deals with mahematical methods that find use in science, engineering, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge.
应用数学是应用数学理论和方法到科技，工程，商业，计算机以及各类工业的数学分枝，应用数学是数学理论与各相关专业结合而形成的学科。
那么应用数学常见的都有哪些呢？
如果武断一点，基本上任意给一门理科，和数学一结合，就是应用数学的领域了。举例来说，生物是一门理科，应用数学就有一个很大且很火的分枝：生物数学。生物数学包含帮医院处理实验数据，建立各种细胞的数学模型，生物模拟等等。那些很火的计算数学，精算数学，都是应用数学的分枝。

3，数理统计学
Mathematical statistics is the application of mathematics to statistics, which was originally conceived as the science of the state — the collection and analysis of facts about a country: its economy, land, military, population, and so forth.

数理统计有的时候被人们算作整个统计学，有的时候算作统计学的分枝，本质上就是利用数学方法将数学理论运用到统计领域的一门学科。关于这个我们之前的很多文章，以及网上各种**都有，就不赘述了。

学数学都可以干什么

假如我说数学无处不在的话，你一定会说我在胡扯。但是，我接下来就要开始胡扯了。

先看看数学家们的工资水平吧：（截图自美国劳工统计局）

数学家平均年薪是103720刀，约合人民币68万五千，市场需求量正以21%的速度上涨，远远高于所有行业平均水平。

以下是摘自美国劳工统计局的一些统计结果：

Mathematicians typically do the following:（通常情况下，数学家们在做以下这些与专业相关的事情）
Develop new mathematical rules, theories, and concepts in areas such as algebra and geometry
建立和完备数学理论和概念，例如在代数和几何领域（很多是纯数学）

Use mathematical formulas and models to prove or disprove theories
利用数学公式和模型来验证或者推翻一些理论（这些大概就是我们常说的证明吧）

Apply mathematical theories and techniques to solve practical problems in business, engineering, the sciences, and other fields
利用数学知识解决商业，工程，科学和其他领域的问题（具体点，航空航天的火箭轨道和模型；矿井开采深度以及定位；医院扫描图像处理；股票期货数学模型研究规律；保险公司保险定价理赔 ......所有大到全人类高精尖科技，小到自行车轮毂比例，都有数学的应用，假如你有感兴趣的领域，并且精通数学，你都可以把它们作为你的职业）
Develop mathematical or statistical models to analyze data
数据处理，大数据近来很火，数学家也有很多在处理数据；
Interpret data and report conclusions drawn from their analyses
解释数据并汇报数据处理的结果，例如GDP分析，客户问卷调查分析；
Use data analysis to support and improve business decisions
随机模型等应用到基金货币等金融行业，帮助商业运作
Read professional journals, talk with other mathematicians, and attend professional conferences to maintain their knowledge of current trends
整理文献，交流和传递最新的数学科研成果

数学家的工作环境
30%的数学家在联邦政府工作，做科研可发展研究的占16%，教育系统占13%，金融和保险类占7%，制造业占5%。大部分数学家都是在办公室坐着凭之三赚钱，他们也会和很多交叉领域一起工作。
写在最后
本可以写得更多更详细，但是短短的一篇文章真的没办法把最完整的数学体现给大家。很多人只关心工作，于是我只是简单地例举了数学可以干什么，但是远远不止那些。
数学是理科的基础，可以结合到所有理工科和商科，无论你以后有什么职业规划，有了很好的数学背景，你可以选择利用这个工具，做自己感兴趣的事情。数学不仅仅是给世界上所谓的聪明人设置的，它只是一门语言，一门帮助我们了解感兴趣学科的语言，一个研究我们周围世界的切入点。不要被纯数学的深奥所吓倒，更不要在下一代选择数学的时候即刻否定他们，在他们还不会选择的时候，可以建议他们选择数学和物理这种基础学科，等有了自己喜欢的领域的时候，再在研究生和博士阶段应用他们学到的数学，在心仪的领域，走得更远。