First Zero Ever Written? Scientists Argue Over Ancient Indian Math Symbols
Researchers are challenging a claim that an ancient Indian mathematical document contains the oldest recorded use of a zero.
The Bodleian Libraries at Oxford University announced last month that experts recently dated the Bakhshali manuscript to as early as 200 BCE and, because it is full of symbols that signify the number zero, said it represents the earliest known use of that number. The next recorded use occurred about 500 years after the alleged date of the manuscript. But a group of historians specializing in Indian mathematics are challenging this discovery. According to a statement from the University of Alberta, the calculations would have been written much later than asserted.
The difference in interpretation stems from the material from which the manuscript is made: dozens of birch bark leaves collected in different eras. While the scientists at Oxford made their announcement about finding the earliest zero after radiocarbon-dating the oldest parts of the document to between 1,600 and 1,800 years ago, other leaves came from more recent centuries.
A leaf from the Bakhshali Manuscript, showing off Indian mathematical genius. A zero symbol has been highlighted in the second image.
Bodleian Libraries
The math historians are arguing that because the calculations are cohesive writings, the zeroes must have been jotted down after the last leaf was set into place, making them centuries older than the Oxford researchers are suggesting.
“The treatise shows no signs of being a jumble of fragments from different periods,” the university said. “Both the handwriting and the topic being discussed are continuous across the boundary of the first two dated leaves. It looks very much as if the scribe, who may have lived at the end of the eighth century, wrote out his treatise on a group of leaves that had been manufactured at very different times.”
If the critics of the Bakhshali manuscript’s analysis are right, the earliest confirmed recorded use of the number zero would still be a ninth-century inscription on a temple wall in Gwalior, India.
Although ancient civilizations had previously come up with the concept of nothingness, it took a while for that to translate to mathematics. When people started using zero as a number in calculations, it was a turning point in the discipline.
The Bakhshali manuscript was found in the late 1800s in what is now Pakistan. According to researchers, it contains numerous dots that are supposed to represent zeroes, placeholders in a series of calculations. “It was used to indicate orders of magnitude in a number system — for example, denoting 10s, 100s and 1000s,” the libraries explained last month.
Eventually that dot transformed into the ring symbol we use as a zero today.
“This isn’t some sort of theoretical text, it seems to be a practical document that is being used by merchants to do calculations,” mathematics professor Marcus du Sautoy said about the Bakhshali manuscript in a video. He referred to the first use of zero as a time when “mathematicians in India planted the seed of the idea that would later become so fundamental to the modern world. … The findings show how vibrant mathematics have been in the Indian subcontinent for centuries.”
Although the math historians are dissenting on the age of the zeroes in the Bakhshali manuscript, they say the number contains more significance in the document than Oxford gave it credit for.
“The Bakhshali treatise does indeed know the ‘true’ zero, and contains calculations like long multiplication that would have necessitated using zero as an arithmetical number” rather than just a placeholder, the University of Alberta said. “Furthermore, the treatise even contains a statement saying, ‘having added one to zero,’ thus proving that the early Sanskrit author was thinking about zero in a numerical way.”http://www.ibtimes.com/first-zero-ever-written-scientists-argue-over-ancient-indian-math-symbols-2606714
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 380: What is the zero?\\
(2017.8.21)}
\author{{\it Institute of Reproducing Kernels}\\
Kawauchi-cho, 5-1648-16,\\
Kiryu 376-0041, Japan\\
}
\date{\today}
\maketitle
\section{What is the zero?}
The zero $0$ as the complex number or real number is given clearly by the axions by the complex number field and real number field.
For this fundamental idea, we should consider the {\bf Yamada field} containing the division by zero. The Yamada field and the division by zero calculus will arrange our mathematics, beautifully and completely; this will be our natural and complete mathematics.
\medskip
\section{ Double natures of the zero $z=0$}
The zero point $z=0$ represents the double natures; one is the origin at the starting point and another one is a representation of the point at infinity. One typical and simple example is given by $e^0 = 1,0$, two values. {\bf God loves two}.
\section{Standard value}
\medskip
The zero is a center and stand point (or bases, a standard value) of the coordinates - here we will consider our situation on the complex or real 2 dimensional spaces. By stereographic
projection mapping or the Yamada field, the point at infinity $1/0$ is represented by zero. The origin of the coordinates and the point at infinity correspond each other.
As the standard value, for the point $\omega_n = \exp \left(\frac{\pi}{n}i\right)$ on the unit circle $|z|=1$ on the complex $z$-plane is, for $n = 0$:
\begin{equation}
\omega_0 = \exp \left(\frac{\pi}{0}i\right)=1, \quad \frac{\pi}{0} =0.
\end{equation}
For the mean value
$$
M_n = \frac{x_1 + x_2 +... + x_n}{n},
$$
we have
$$
M_0 = 0 = \frac{0}{0}.
$$
\medskip
\section{ Fruitful world}
\medskip
For example, for very and very general partial differential equations, if the coefficients or terms are zero, then we have some simple differential equations and the extreme case is all the terms are zero; that is, we have trivial equations $0=0$; then its solution is zero. When we consider the converse, we see that the zero world is a fruitful one and it means some vanishing world. Recall Yamane phenomena (\cite{kmsy}), the vanishing result is very simple zero, however, it is the result from some fruitful world. Sometimes, zero means void or nothing world, however, it will show {\bf some changes} as in the Yamane phenomena.
\section{From $0$ to $0$; $0$ means all and all are $0$}
\medskip
As we see from our life figure (\cite{osm}), a story starts from the zero and ends with the zero. This will mean that $0$ means all and all are $0$. The zero is a {\bf mother} or an {\bf origin} of all.
\medskip
\section{ Impossibility}
\medskip
As the solution of the simplest equation
\begin{equation}
ax =b
\end{equation}
we have $x=0$ for $a=0, b\ne 0$ as the standard value, or the Moore-Penrose generalized inverse. This will mean in a sense, the solution does not exist; to solve the equation (6.1) is impossible.
We saw for different parallel lines or different parallel planes, their common points are the origin. Certainly they have the common points of the point at infinity and the point at infinity is represented by zero. However, we can understand also that they have no solutions, no common points, because the point at infinity is an ideal point.
Of course. we can consider the equation (6.1) even the case $a=b=0$ and then we have the solution $x=0$ as we stated.
We will consider the simple differential equation
\begin{equation}
m\frac{d^2x}{dt^2} =0, m\frac{d^2y}{dt^2} =-mg
\end{equation}
with the initial conditions, at $t =0$
\begin{equation}
\frac{dx}{dt} = v_0 \cos \alpha , \frac{d^2x}{dt^2} = \frac{d^2y}{dt^2}=0.
\end{equation}
Then, the highest high $h$, arriving time $t$, the distance $d$ from the starting point at the origin to the point $y(2t) =0$ are given by
\begin{equation}
h = \frac{v_0 \sin^2 \alpha}{2g}, d= \frac{v_0\sin \alpha}{g}
\end{equation}
and
\begin{equation}
t= \frac{v_0 \sin \alpha}{g}.
\end{equation}
For the case $g=0$, we have $h=d =t=0$. We considered the case that they are the infinity; however, our mathematics means zero, which shows impossibility.
These phenomena were looked many cases on the universe; it seems that {\bf God does not like the infinity}.
\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{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{ms}
T. Matsuura and S. Saitoh,
Matrices and division by zero $z/0=0$, Advances in Linear Algebra
\& Matrix Theory, 6 (2016), 51-58. http://dx.doi.org/10.4236/alamt.2016.62007 http://www.scirp.org/journal/alamt
\bibitem{mos}
H. Michiwaki, H. Okumura, and S. Saitoh,
Division by Zero $z/0 = 0$ in Euclidean Spaces.
International Journal of Mathematics and Computation Vol. 28(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), 1(2017), 70-77.
\bibitem{romig}
H. G. Romig, Discussions: Early History of Division by Zero,
American Mathematical Monthly, Vol. 31, No. 8. (Oct., 1924), pp. 387-389.
\bibitem{s}
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{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.
\bibitem{ann179}
Announcement 179 (2014.8.30): Division by zero is clear as z/0=0 and it is fundamental in mathematics.
\bibitem{ann185}
Announcement 185 (2014.10.22): The importance of the division by zero $z/0=0$.
\bibitem{ann237}
Announcement 237 (2015.6.18): A reality of the division by zero $z/0=0$ by geometrical optics.
\bibitem{ann246}
Announcement 246 (2015.9.17): An interpretation of the division by zero $1/0=0$ by the gradients of lines.
\bibitem{ann247}
Announcement 247 (2015.9.22): The gradient of y-axis is zero and $\tan (\pi/2) =0$ by the division by zero $1/0=0$.
\bibitem{ann250}
Announcement 250 (2015.10.20): What are numbers? - the Yamada field containing the division by zero $z/0=0$.
\bibitem{ann252}
Announcement 252 (2015.11.1): Circles and
curvature - an interpretation by Mr.
Hiroshi Michiwaki of the division by
zero $r/0 = 0$.
\bibitem{ann281}
Announcement 281 (2016.2.1): The importance of the division by zero $z/0=0$.
\bibitem{ann282}
Announcement 282 (2016.2.2): The Division by Zero $z/0=0$ on the Second Birthday.
\bibitem{ann293}
Announcement 293 (2016.3.27): Parallel lines on the Euclidean plane from the viewpoint of division by zero 1/0=0.
\bibitem{ann300}
Announcement 300 (2016.05.22): New challenges on the division by zero z/0=0.
\bibitem{ann326}
Announcement 326 (2016.10.17): The division by zero z/0=0 - its impact to human beings through education and research.
\bibitem{ann352}
Announcement 352(2017.2.2): On the third birthday of the division by zero z/0=0.
\bibitem{ann354}
Announcement 354(2017.2.8): What are $n = 2,1,0$ regular polygons inscribed in a disc? -- relations of $0$ and infinity.
\bibitem{362}
Announcement 362(2017.5.5): Discovery of the division by zero as
$0/0=1/0=z/0=0$.
\end{thebibliography}
\end{document}
The division by zero is uniquely and reasonably determined as 1/0=0/0=z/0=0 in the natural extensions of fractions. We have to change our basic ideas for our space and world
Division by Zero z/0 = 0 in Euclidean Spaces
Hiroshi Michiwaki, Hiroshi Okumura and Saburou Saitoh
International Journal of Mathematics and Computation Vol. 28(2017); Issue 1, 2017), 1
-16.
http://www.scirp.org/journal/alamt http://dx.doi.org/10.4236/alamt.2016.62007
http://www.ijapm.org/show-63-504-1.html
http://www.diogenes.bg/ijam/contents/2014-27-2/9/9.pdf
http://okmr.yamatoblog.net/division%20by%20zero/announcement%20326-%20the%20divi
http://okmr.yamatoblog.net/
Relations of 0 and infinity
Hiroshi Okumura, Saburou Saitoh and Tsutomu Matsuura：
http://www.e-jikei.org/…/Camera%20ready%20manuscript_JTSS_A…
https://sites.google.com/site/sandrapinelas/icddea-2017
2017.8.21.06:37
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
1/0=0、0/0=0、z/0=0
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