“In the history of culture, the discovery of zero will always
stand out as one of the greatest single achievements of the
human race.” Tobias Danzig
• THERE WOULD BE NO CALCULUS.
• NO FINANCIAL MATHEMATICS.
• NO ALGEBRA
• NO ABILITY TO DO CALCULATIONS QUICKLY.
• NO COMPUTERS.
ZERO IS A SPECIAL NUMBER
• IF WE ADD ZERO TO ANY NUMBER THE RESULT IS THE
ORIGINAL NUMBER. A + 0 = A
•(THE SAME IS TRUE FOR SUBTRACTION). A – 0 = A
• IF YOU MULTIPLY ANY NUMBER BY ZERO THE PRODUCT
IS ZERO. A x 0 = 0
•IF YOU RAISE ANY NON-ZERO NUMBER TO THE POWER
OF ZERO, THE RESULTING NUMBER IS 1: Aº = 1
• IF YOU DIVIDE ZERO BY ANY NON-ZERO NUMBER, THE
QUOTIENT IS ZERO. 0 ÷ A = 0
• ANY NUMBER DIVIDED BY ZERO IS UNDEFINED. A ÷ 0 is
Error: Division by Zero
The error here is the division by (a-b) which is ZERO which is an
operation that is inadmissible in mathematics.
A Brief History of ZERO
•The Maya civilization (2000 B.C. – 900 A.D.) in what is now
Mexico used the concept of zero as a PLACEHOLDER: that is, 705
is a way bigger number than 75. (Like using a comma in written
language.) The Babylonians used it similarly in the 7th century
• The 7th century Indian mathematician Brahmagupta treated zero
as a “number” and not just as a place-holder. He elaborated the
rules mentioned on page 2 of this presentation.
• The Hindu-Arabic numbering system that included zero in the
way that was used in the West by Leonardo of Pisa – Fibonacci -
in his Book of Counting, published in 1202.
• Zero gained a central place in the number system soon
afterwards, with it literally separating the positive numbers from
the negative ones as in the number line.
• In the decimal system, zero serves as a place holder which
enables us to use both huge numbers and microscopic figures.
• Hence the sheer beauty and usefulness of zero which could lend
its use to science in its wonderfully succinct scientific notation.
ZERO IS NOT NOTHING
• LATIN: “cifra” = zero; FRENCH: “chiffre”
• In English we use the word “nought” to mean
zero, a derivation from the word “nothing.”
• However, Nought is really a mathematical
misnomer (that is, a wrong name), for it would
be wrong to think of zero as nothing.
• 0 is certainly SOMETHING: it is a powerful
symbol, 0, that gives our modern notation
Zero as Central Point or Start Point
• In the Real Number System, 0 is the only number
that is neither negative nor positive.
• It holds the unique position, almost the Still Point
to use Eastern Philosophy, between the positive
numbers and the negative ones.
• This position makes 0 the natural starting point or
origin on many scales such as on the axes of
Cartesian Geometry or Co-ordinate Geometry, or on
the many scales used in scientific measurement from
Temperature to Air Pressure to Acidity/Basicity etc
A Little Bit of Religion (Theology)
• The mainline Christian religions believe that God created the world
out of NOTHING. But there are other viewpoints among different
religions that God could have created the world from pre-existing
matter (chaos) etc. This contradicts mainline science on the origins
of the Universe.
• Creation out of nothing, or creation ex nihilo, is the belief
that God created the world out of nothing, ex nihilo being Latin for
"from nothing." This view does not contradict THE BIG BANG
THEORY of the origin of the Universe. So this view can be
reconciled with the teachings of science.
• Scientists say that there was no time or space, therefore literally
nothing, there before the great explosion of THE BIG BANG.
• For believers “creation out of nothing” is a religious tenet that
shows both the power and mystery of God.
A Little Bit of Philosophy (Wondering)1
• Asking the Big Questions of Life.
• “Why is there Something rather than Nothing?” – a question
asked by the philosopher Martin Heidegger (1889-1976).
• What is some-thing? What is no-thing?
• Some mathematicians have said that zero is not “nothing” as it
is a very important symbol and indeed a number very necessary
to all modern calculations. However, philosophers would say
that this is true to some extent only, as zero as a symbol
represents “nothing” and that it is important to ask the question
as to what that nothing is.
• Did I come from Nothing into life and then do I return into
• Is there a spiritual world there beyond the visible world? Or just
• Or again, good philosophers of mathematics ask what are
A Little Bit of Philosophy (Wondering) 2
• Does a hole exist in itself? Is it some-thing or no-thing?
• Do letters that are engraved in or cut into solid stone exist in
themselves? Something made out of Nothing!
• Does the year ZERO, 0, exist? The Year 1 B.C. is actually
followed by the year 1 A.D.
• Does the floor Zero exist? We call the ground floor no. 1.
• What is absolute ZERO? Ask a Chemistry student.
• Tacticians speak about zeroing in on a target.
• A zero-sum game is one where the loss of one player is
balanced by the gain of another or others .e.g., poker where
what the winner wins equals what the losers lost.
• Is the Stock Market a Zero-Sum game?
Some Final Thoughts
• How tiny are you in comparison to the size of the universe? How big
is the universe in comparison to you? Is your size actually
• Limits are important in algebra and in differentiation: We speak of
the limits of certain expressions in x as x approaches ZERO or
INFINITY etc. The mathematical principle is that x or y or whatever
letter you choose may approach either 0 or Infinity, but never get
there. In mathematical terms division by ZERO and INFINITY is
• Limits are always about approaching ZERO or INFINITY but never
• Maybe the Mystery of God is like the Mystery of Zero or the Mystery
of Infinity – we can never really understand it in this life – we cannot
simply get there through human reasoning.
• Let the Wonder of ZERO, 0, begin!!