1 Where Did Mathemat ics Come From?
©PHILIP EMEAGWALI
My Quest for an
Internet
In this, the 13th installment of our weekly series at emeagwali.com, we review how Philip
Emeagwali created new mathematics.
Equations From Internet
Transcribed and edited from a lecture delivered by Philip Emeagwali. The unedited video is posted at
emeagwali.com.
The old technique was that I used my human brain to solve 100 math problems in .... the Swedish
called the computer "matematikmaskin" or "mathematics machine. ... The word "computer" has
been around for six centuries and meant different ...
I was once asked:
“Where did mathematics come
from?”
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My general observation is this:
Behind biology is chemistry;
behind chemistry is physics;
behind physics is mathematics;
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2 Where Did Mathemat ics Come From?
and behind mathematics is God
who created biology. And
behind a mathematical equation
is a mathematician who who
invented it and a matematikmaskin that
inspired him.
©PHILIP EMEAGWALI
For me, the equations of mathematical
physics I invented came from physics. I
created a new set of mathematical equations
from a rule that governs the motion of all
objects in our universe. The rule is called the
Second Law of Motion. The equations I
invented from that law are called partial
differential equations. My inventions were
previously unseen in books on the subject of
oil recovery. Specifically, I invented 72
inertial terms which mathematicians call
partial derivatives to account for what
physicists call temporal and convective
inertial forces. Those terms improve the
accuracy of petroleum reservoir simulators
and, consequently, will increase the amount
of oil recovered from oilfields.
Indianborn
Bramagupta’s book Brahmasphutasiddhanta (The
Opening of the Universe) is one of the sources of
modern mathematics.
.
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3 Where Did Mathemat ics Come From?
©PHILIP EMEAGWALI
Advanced Level Physics by Michael Nelkon and Philip
Parker was first published in 1958. I self-taught myself
at Sacred Heart Primary School with this 1970 edition.
The mathematics I created came from the Second Law
of Motion described in high school physics textbooks
such as the above.
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4 Where Did Mathemat ics Come From?
©PHILIP EMEAGWALI
As a research mathematical physicist, my primary goals were to discover useful mathematical
equations that hadn't been seen before on a blackboard, and, I invented theorized techniques,
called algorithms, for solving them on a hyperboard, comprised of 65,536 connected
motherboards.
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5 Where Did Mathemat ics Come From?
©PHILIP EMEAGWALI
I pose with student dancers after speaking at an Africa Day event at Richard Stockton College of New Jersey,
Pomona, New Jersey, February 23, 2004.
My theorized algorithms are explanations based on mathematical reasoning of how the partial
differential equations I invented can be solved on sub-computers connected as an internet. The
final step of solving my equations on an internet with sub-computers at its nodes is mandatory
because, according to the scientific method, a theory is an idea that is not positively true.
I wanted to make scientific discoveries and knew I must go beyond theorizing. So I made a clear
distinction between my theories, which were nine equations and nine algorithms I wrote on my
blackboards, and my facts, which were 24 million equations—a world record in 1989—I solved
with my nine algorithms on my 65,536 connected motherboards.
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6 Where Did Mathemat ics Come From?
©PHILIP EMEAGWALI
Thus my ensemble of 65,536 computers that are connected as an internet cannot be considered to
be invented as an internet until it is experimentally demonstrated that it computes as a
supercomputer and communicates as an superinternet while solving useful problems.
This photo was taken in the year I morphed from being a mathematical physicist who creates new mathematics to a
supercomputer scientist that performed the world’s fastest computations. [Philip Emeagwali, 1983]
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7 Where Did Mathemat ics Come From?
©PHILIP EMEAGWALI
I learned to distinguish between experiment and theory, between fact and fiction, and between
theory and discovery, and to invent algorithms grounded on equations, and formulate equations
grounded on the laws of physics, and, most importantly, to hear and trust my inner voice.
I also needed to develop technologies for solving my new equations on a giant, distributed
motherboard which I did by programming an ensemble of 65,536 sub-computers that computed
cohesively as an unconventional supercomputer and communicated seamlessly in an unorthodox
internet. I used these techniques and technologies to solve the nine partial differential equations
that I invented.
This is the publicity photo for a lecture I gave on July 8, 1991 at ICIAM ‘91, which is the World Cup of
Mathematics. I told the field’s foremost experts that my new mathematics came from inside a petroleum reservoir.
[Philip Emeagwali, 1990]
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8 Where Did Mathemat ics Come From?
©PHILIP EMEAGWALI
So where did my mathematical inventions come from? The mathematical equations I invented
came from the physics of petroleum reservoirs. The 72 mathematical terms I invented came from
the inertial forces that I discovered were missing in petroleum reservoir simulators. So my
mathematics came from oilfields.
I invented 36 partial derivatives and used them to reinvent nine partial differential equations that
can be used by the petroleum industry to recover oil. My equations were the most advanced and
the most useful form of calculus. I invented them by borrowing the algebraic formula, force
equals mass times acceleration (F=ma), from Isaac Newton, who lived three centuries ago in
England.
So where did modern mathematics come from? It came from Africa.
AS I was going to Saint Ives
Three hundred and thirty years ago, Isaac Newton invented F=ma by borrowing algebraic
knowledge from Mohammad Bin Musa Al-Khwarizmi, the father of algebra, who lived nine
centuries earlier in Bagdad. Newton also co-invented calculus by borrowing geometrical
knowledge from Euclid, the father of geometry, who lived twenty centuries earlier in the Valley
of the River Nile. Euclid’s book, The Elements, in turn, was influenced by Ahmes Papyrus, which was
compiled by Ahmes, who lived fourteen centuries before Euclid in the Valley of the Nile.
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9 Where Did Mathemat ics Come From?
©PHILIP EMEAGWALI
A mathematical papyrus written by Ahmes from 1650 to 1550 BC.
Certainly, the quadratic equation did not spontaneously create itself and was not known to our
hunter-gatherer ancestors. So “Where did mathematics come from?” It came from both the Nile
Valley civilization of Africa and the Tigris-Euphrates civilization of Mesopotamia, a region
corresponding to modern Iraq and parts of Syria, Turkey, and Iran.
Since the oldest mathematical papyri were excavated in Africa, I assume that mathematics has its
roots in Africa. Since Euclid, the father of geometry, never travelled outside the Nile Valley, I
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10 W h e r e D i d M a t h e m a t i c s C o m e F r o m ?
©PHILIP EMEAGWALI
assume that geometry has its roots in the Nile Valley of Africa. Since Euclid lived in a
predominately black city, I assume that he is black. The portrait of Euclid, as white, in textbooks
is a figment of the painter’s imagination.
This portrait of Euclid as an old white male is fictitious. Euclid lived 2,300 years ago and there is no true portrait of
any person that lived 300 years ago. Primary sources show that Euclid is an African, not Greek.
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11 W h e r e D i d M a t h e m a t i c s C o m e F r o m ?
©PHILIP EMEAGWALI
For me, an African in America, my discovery of nine partial differential equations is the
culmination of a body of stories told and retold and passed on through generations of
mathematicians’ minds—the oldest story originating 3,700 years ago in the 4,100-mile-long
Valley of the Nile in Africa.
Two pages from Euclid’s The Elements containing mathematics created along the Nile Valley of Africa.
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12 W h e r e D i d M a t h e m a t i c s C o m e F r o m ?
©PHILIP EMEAGWALI
Two pages from Euclid’s The Elements showing the Pythagorean Theorem as Proposition 47 of Book I.
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13 W h e r e D i d M a t h e m a t i c s C o m e F r o m ?
©PHILIP EMEAGWALI
I was nicknamed and known as “Calculus” after my favorite book “An Introduction to the Infinitesimal Calculus”
(by George William Caunt) and positively mentioned in the Science Column of the Daily Times (Nigeria’s
equivalent of the New York Times) at age 17. Here I am also at age 17 in circa July 1972 in Enugu, Nigeria.
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14 W h e r e D i d M a t h e m a t i c s C o m e F r o m ?
©PHILIP EMEAGWALI
In this photo, I wrote on the board the actual equations used by the oil company Exxon (now
Exxon Mobil) to simulate the flow of oil, water, and gas inside its petroleum reservoirs. I
discovered a fundamental error in the equations used by oil companies, namely, four forces exist
inside every petroleum reservoir; yet Exxon Mobil equation had summed only three forces. I
created new mathematics by correctly summing all four forces, namely: pressure, viscosity,
gravity, and inertia. After learning about my discovery, Mobil Research and Development
Corporation invited me (in a letter dated March 19, 1990) to help the company in “reservoir
simulation.” Certainly, for oil producing nations, it is an important mathematical discovery that
helps produce more oil. [Philip Emeagwali, June 1996]
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15 W h e r e D i d M a t h e m a t i c s C o m e F r o m ?
©PHILIP EMEAGWALI
I am an astronomer and a meteorologist who created new calculus for weather forecasting. This is an excerpt from
an old memo I forwarded to a physicist explaining how to create new mathematics called partial differential
equations from the wind velocities in the Earth’s atmosphere. (Handwriting of Philip Emeagwali)
Philip Emeagwali
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16 W h e r e D i d M a t h e m a t i c s C o m e F r o m ?
©PHILIP EMEAGWALI
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