数学为什么叫“数学”
2018-04-24 21:09
“数学”一词是来自希腊语，它意味着某种“已学会或被理解的东西”或“已获得的知识”，甚至意味着“可获的东西”；“可学会的东西”，即“通过学习可获得的知识”，数学名称的这些意思似乎和梵文中的同根词意思相同。甚至伟大的辞典编辑人利特雷（E·Littre也是当时杰出的古典学者），在他编辑的法语字典（1877年）中也收入了“数学”一词。牛津英语字典没有参照梵文。公元10世纪的拜占庭希腊字典“Suidas”中，引出了“物理学”、“几何学”和“算术”的词条，但没有直接列出“数学”一词。
“数学”一词从表示一般的知识到专门表示数学专业，经历一个较长的过程，仅在亚里士多德时代，而不是在柏拉图时代，这一过程才完成。数学名称的专有化不仅在于其意义深远，而在于当时古希腊只有“诗歌”一词的专有化才能与数学名称的专有化相媲美。“诗歌”原来的意思是“已经制造或完成的某些东西”，“诗歌”一词的专有化在柏拉图时代就完成了。而不知是什么原因辞典编辑或涉及名词专有化的知识问题从来没有提到诗歌，也没有提到诗歌与数学名称专有化之间奇特的相似性。但数学名称的专有化确实受到人们的注意。
亚里士多德
首先，亚里士多德提出，“数学”一词的专门化使用是源于毕达哥拉斯的想法，但没有任何资料表明对于起源于爱奥尼亚的自然哲学有类似的思考。其次在爱奥尼亚人中，只有泰勒斯（公元前640？--546年）在“纯”数学方面的成就是可信的，因为除了第欧根尼·拉尔修简短提到外，这一可信性还有一个较迟的而直接的数学来源，即来源于普罗克洛斯对欧几里得的评注：但这一可信性不是来源于亚里士多德，尽管他知道泰勒斯是一个“自然哲学家”；也不是来源于早期的希罗多德，尽管他知道塞利斯是一个政治、军事战术方面的“爱好者”，甚至还能预报日蚀。以上这些可能有助于解释为什么在柏拉图的体系中，几乎没有爱奥尼亚的成份。赫拉克利特（公元前500--？年）有一段名言：“万物都在运动中，物无常往”，“人们不可能两次落进同一条河里”。这段名言使柏拉图迷惑了，但赫拉克赖脱却没受到柏拉图给予巴门尼德那样的尊敬。巴门尼德的实体论，从方法论的角度讲，比起赫拉克赖脱的变化论，更是毕达哥拉斯数学的强有力的竞争对手。
对于毕达哥拉斯学派来说，数学是一种“生活的方式”。事实上，从公元２世纪的拉丁作家格利乌斯和公元３世纪的希腊哲学家波菲利以及公元４世纪的希腊哲学家扬布利科斯的某些证词中看出，似乎毕达哥拉斯学派对于成年人有一个“一般的学位课程”，其中有正式登记者和临时登记者。临时成员称为“旁听者”，正式成员称为“数学家”。
毕达哥拉斯
这里“数学家”仅仅表示一类成员，而并不是他们精通数学。毕达哥拉斯学派的精神经久不衰。对于那些被阿基米德神奇的发明所深深吸引的人来说，阿基米德是唯一的独特的数学家，从理论的地位讲，牛顿是一个数学家，尽管他也是半个物理学家，一般公众和新闻记者宁愿把爱因斯坦看作数学家，尽管他完全是物理学家。当罗吉尔·培根（1214--1292年）通过提倡接近科学的“实体论”，向他所在世纪提出挑战时，他正将科学放进了一个数学的大框架，尽管他在数学上的造诣是有限的，当笛卡儿（1596--1650年）还很年轻时就决心有所创新，于是他确定了“数学万能论”的名称和概念。然后莱布尼茨引用了非常类似的概念，并将其变成了以后产生的“符号”逻辑的基础，而20世纪的“符号”逻辑变成了热门的数理逻辑。
在18世纪，数学史的先驱作家蒙托克莱说，他已听说了关于古希腊人首先称数学为“一般知识”，这一事实有两种解释：一种解释是，数学本身优于其它知识领域；而另一种解释是，作为一般知识性的学科，数学在修辞学，辩证法，语法和伦理学等等之前就结构完整了。蒙托克莱接受了第二种解释。他不同意第一种解释，因为在普罗克洛斯关于欧几里得的评注中，或在任何古代资料中，都没有发现适合这种解释的确证。然而19世纪的语源学家却倾向于第一种解释，而20世纪的古典学者却又偏向第二种解释。但我们发现这两种解释并不矛盾，即很早就有了数学且数学的优越性是无与伦比的。
∑编辑 | Gemini
とても興味深く読みました：
\documentclass[12pt]{article}
\usepackage{latexsym,amsmath,amssymb,amsfonts,amstext,amsthm}
\numberwithin{equation}{section}
\begin{document}
\title{\bf Announcement 409: Various Publication Projects on the Division by Zero\\
(2018.1.29.)}
\author{{\it Institute of Reproducing Kernels}\\
Kawauchi-cho, 5-1648-16,\\
Kiryu 376-0041, Japan\\
}
\date{\today}
\maketitle
The Institute of Reproducing Kernels is dealing with the theory of division by zero calculus and declares that the division by zero was discovered as $0/0=1/0=z/0=0$ in a natural sense on 2014.2.2. The result shows a new basic idea on the universe and space since Aristoteles (BC384 - BC322) and Euclid (BC 3 Century - ), and the division by zero is since Brahmagupta (598 - 668 ?).
In particular, Brahmagupta defined as $0/0=0$ in Brhmasphuasiddhnta (628), however, our world history stated that his definition $0/0=0$ is wrong over 1300 years, but, we showed that his definition is suitable.
For the details, see the references and the site: http://okmr.yamatoblog.net/
We wrote two global book manuscripts \cite{s18} with 154 pages and \cite{so18} with many figures for some general people. Their main points are:
\begin{itemize}
\item The division by zero and division by zero calculus are new elementary and fundamental mathematics in the undergraduate level.
\item They introduce a new space since Aristoteles (BC384 - BC322) and Euclid (BC 3 Century - ) with many exciting new phenomena and properties with general interest, not specialized and difficult topics. However, their properties are mysterious and very attractive.
\item The contents are very elementary, however very exciting with general interest.
\item The contents give great impacts to our basic ideas on the universe and human beings.
\end{itemize}
Meanwhile, the representations of the contents are very important and delicate with delicate feelings to the division by zero with a long and mysterious history. Therefore, we hope the representations of the division by zero as follows:
\begin{itemize}
\item
Various book publications by many native languages and with the author's idea and feelings.
\item
Some publications are like arts and some comic style books with pictures.
\item
Some T shirts design, some pictures, monument design may be considered.
\end{itemize}
The authors above may be expected to contribute to our culture, education, common communications and enjoyments.
\medskip
For the people having the interest on the above projects, we will send our book sources with many figure files.
\medskip
How will be our project introducing our new world since Euclid?
\medskip
Of course, as mathematicians we have to publish new books on
\medskip
Calculus, Differential Equations and Complex Analysis, at least and soon, in order to {\bf correct them} in some complete and beautiful ways.
\medskip
Our topics will be interested in over 1000 millions people over the world on the world history.
\bibliographystyle{plain}
\begin{thebibliography}{10}
\bibitem{kmsy}
M. Kuroda, H. Michiwaki, S. Saitoh, and M. Yamane,
New meanings of the division by zero and interpretations on $100/0=0$ and on $0/0=0$,
Int. J. Appl. Math. {\bf 27} (2014), no 2, pp. 191-198, DOI: 10.12732/ijam.v27i2.9.
\bibitem{ms16}
T. Matsuura and S. Saitoh,
Matrices and division by zero $z/0=0$,
Advances in Linear Algebra \& Matrix Theory, {\bf 6}(2016), 51-58
Published Online June 2016 in SciRes. http://www.scirp.org/journal/alamt
\\ http://dx.doi.org/10.4236/alamt.2016.62007.
\bibitem{ms18}
T. Matsuura and S. Saitoh,
Division by zero calculus and singular integrals. (Submitted for publication)
\bibitem{mms18}
T. Matsuura, H. Michiwaki and S. Saitoh,
$\log 0= \log \infty =0$ and applications. Differential and Difference Equations with Applications. Springer Proceedings in Mathematics \& Statistics.
\bibitem{msy}
H. Michiwaki, S. Saitoh and M.Yamada,
Reality of the division by zero $z/0=0$. IJAPM International J. of Applied Physics and Math. {\bf 6}(2015), 1--8. http://www.ijapm.org/show-63-504-1.html
\bibitem{mos}
H. Michiwaki, H. Okumura and S. Saitoh,
Division by Zero $z/0 = 0$ in Euclidean Spaces,
International Journal of Mathematics and Computation, {\bf 2}8(2017); Issue 1, 2017), 1-16.
\bibitem{osm}
H. Okumura, S. Saitoh and T. Matsuura, Relations of $0$ and $\infty$,
Journal of Technology and Social Science (JTSS), {\bf 1}(2017), 70-77.
\bibitem{os}
H. Okumura and S. Saitoh, The Descartes circles theorem and division by zero calculus. https://arxiv.org/abs/1711.04961 (2017.11.14).
\bibitem{o}
H. Okumura, Wasan geometry with the division by 0. https://arxiv.org/abs/1711.06947 International Journal of Geometry.
\bibitem{os18}
H. Okumura and S. Saitoh,
Applications of the division by zero calculus to Wasan geometry.
(Submitted for publication).
\bibitem{ps18}
S. Pinelas and S. Saitoh,
Division by zero calculus and differential equations. Differential and Difference Equations with Applications. Springer Proceedings in Mathematics \& Statistics.
\bibitem{romig}
H. G. Romig, Discussions: Early History of Division by Zero,
American Mathematical Monthly, Vol. {\bf 3}1, No. 8. (Oct., 1924), pp. 387-389.
\bibitem{s14}
S. Saitoh, Generalized inversions of Hadamard and tensor products for matrices, Advances in Linear Algebra \& Matrix Theory. {\bf 4} (2014), no. 2, 87--95. http://www.scirp.org/journal/ALAMT/
\bibitem{s16}
S. Saitoh, A reproducing kernel theory with some general applications,
Qian,T./Rodino,L.(eds.): Mathematical Analysis, Probability and Applications - Plenary Lectures: Isaac 2015, Macau, China, Springer Proceedings in Mathematics and Statistics, {\bf 177}(2016), 151-182. (Springer) .
\bibitem{s17}
S. Saitoh, Mysterious Properties of the Point at Infinity, arXiv:1712.09467 [math.GM](2017.12.17).
\bibitem{s18}
S. Saitoh, Division by zero calculus (154 pages: draft): http//okmr.yamatoblog.net/
\bibitem{so18}
S. Saitoh and H. Okumura, Division by Zero Calculus in Figures -- Our New Space --
\bibitem{ttk}
S.-E. Takahasi, M. Tsukada and Y. Kobayashi, Classification of continuous fractional binary operations on the real and complex fields, Tokyo Journal of Mathematics, {\bf 38}(2015), no. 2, 369-380.
\end{thebibliography}
\end{document}
List of division by zero:
\bibitem{os18}
H. Okumura and S. Saitoh,
Remarks for The Twin Circles of Archimedes in a Skewed Arbelos by H. Okumura and M. Watanabe, Forum Geometricorum.
Saburou Saitoh, Mysterious Properties of the Point at Infinity、
arXiv:1712.09467 [math.GM]
arXiv:1712.09467 [math.GM]
Hiroshi Okumura and Saburou Saitoh
The Descartes circles theorem and division by zero calculus. ２０１７．１１．１４
L. P. Castro and S. Saitoh, Fractional functions and their representations, Complex Anal. Oper. Theory {\bf7} (2013), no. 4, 1049-1063.
M. Kuroda, H. Michiwaki, S. Saitoh, and M. Yamane,
New meanings of the division by zero and interpretations on $100/0=0$ and on $0/0=0$, Int. J. Appl. Math. {\bf 27} (2014), no 2, pp. 191-198, DOI: 10.12732/ijam.v27i2.9.
T. Matsuura and S. Saitoh,
Matrices and division by zero z/0=0,
Advances in Linear Algebra \& Matrix Theory, 2016, 6, 51-58
Published Online June 2016 in SciRes. http://www.scirp.org/journal/alamt
\\ http://dx.doi.org/10.4236/alamt.2016.62007.
T. Matsuura and S. Saitoh,
Division by zero calculus and singular integrals. (Submitted for publication).
T. Matsuura, H. Michiwaki and S. Saitoh,
$\log 0= \log \infty =0$ and applications. (Differential and Difference Equations with Applications. Springer Proceedings in Mathematics \& Statistics.)
H. Michiwaki, S. Saitoh and M.Yamada,
Reality of the division by zero $z/0=0$. IJAPM International J. of Applied Physics and Math. 6(2015), 1--8. http://www.ijapm.org/show-63-504-1.html
H. Michiwaki, H. Okumura and S. Saitoh,
Division by Zero $z/0 = 0$ in Euclidean Spaces,
International Journal of Mathematics and Computation, 28(2017); Issue 1, 2017), 1-16.
H. Okumura, S. Saitoh and T. Matsuura, Relations of $0$ and $\infty$,
Journal of Technology and Social Science (JTSS), 1(2017), 70-77.
S. Pinelas and S. Saitoh,
Division by zero calculus and differential equations. (Differential and Difference Equations with Applications. Springer Proceedings in Mathematics \& Statistics).
S. Saitoh, Generalized inversions of Hadamard and tensor products for matrices, Advances in Linear Algebra \& Matrix Theory. {\bf 4} (2014), no. 2, 87--95. http://www.scirp.org/journal/ALAMT/
S. Saitoh, A reproducing kernel theory with some general applications,
Qian,T./Rodino,L.(eds.): Mathematical Analysis, Probability and Applications - Plenary Lectures: Isaac 2015, Macau, China, Springer Proceedings in Mathematics and Statistics, {\bf 177}(2016), 151-182. (Springer) .
再生核研究所声明371（2017.6.27）ゼロ除算の講演― 国際会議 https://sites.google.com/site/sandrapinelas/icddea-2017 報告
1/0=0、0/0=0、z/0=0
http://ameblo.jp/syoshinoris/entry-12276045402.html
1/0=0、0/0=0、z/0=0
http://ameblo.jp/syoshinoris/entry-12263708422.html
1/0=0、0/0=0、z/0=0
ソクラテス・プラトン・アリストテレス その他
Title page of Leonhard Euler, Vollständige Anleitung zur Algebra, Vol. 1 (edition of 1771, first published in 1770), and p. 34 from Article 83, where Euler explains why a number divided by zero gives infinity.
私は数学を信じない。 アルバート・アインシュタイン / I don't believe in mathematics. Albert Einstein→ゼロ除算ができなかったからではないでしょうか。
ドキュメンタリー 2017: 神の数式 第２回 宇宙はなぜ生まれたのか
〔NHKスペシャル〕神の数式 完全版 第3回 宇宙はなぜ始まったのか
〔NHKスペシャル〕神の数式 完全版 第1回 この世は何からできているのか
NHKスペシャル 神の数式 完全版 第4回 異次元宇宙は存在するか
再生核研究所声明 411(2018.02.02): ゼロ除算発見4周年を迎えて
ゼロ除算の論文
Mysterious Properties of the Point at Infinity
Mysterious Properties of the Point at Infinity
Algebraic division by zero implemented as quasigeometric multiplication by infinity in real and complex multispatial hyperspaces
Author: Jakub Czajko, 92(2) (2018) 171-197
WSN 92(2) (2018) 171-197
Author: Jakub Czajko, 92(2) (2018) 171-197
WSN 92(2) (2018) 171-197
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