African Contributions to Mathematics | Greatest Mathematicians of Today | Philip Emeagwali

I’m Philip Emeagwali. The need to calculate is as old as humanity.The need to compute existed because it is central to human existence. The Latin equivalence of the word “computer” was first used in print two thousand years ago. The word “computer” was first used by the Roman author Pliny the Elder. The word “supercomputer” was coined in 1967. I believe that our children’s children will coin a new word for their supercomputers. I believe that our children’s children will invent supercomputers that are science fiction to us.

Contributions of Philip Emeagwali to Algebra

The discovery and recovery
of every single barrel of oil
from any oilfield
in the Niger-Delta region of Nigeria
must be preceded
by the massively parallel processed solution of the toughest problem
in extreme-scale algebra.
For the fifteen years, inclusive
of from the 20th of June of 1974
that I was in Corvallis, Oregon, United States
through the Fourth of July 1989
in Los Alamos, New Mexico, United States,
I conducted my supercomputer research,
and did so from speeds of
one million instructions per second
in Oregon
to billions upon billions
of floating-point arithmetical calculations
that I executed across
a new internet
that is outlined and defined
by a new global network of
two-raised-to-power sixteen
tightly-coupled processors
that are commonly available
in the market.
Each of those 64 binary thousand
commodity processors
operated its own operating system.
Each of those 65,536 processors
has its own dedicated memory
that shares nothing with each other.
I was in the news in 1989
because I invented
how to solve the most
computation-intensive problems
arising in large-scale
algebraic computations.
Such problems arose from discretizing partial differential equations
that, in turn, arose from
physics-based supercomputer simulations
of the motions of fluids
that flow below the surface of the Earth,
such as the mile-deep
crude oil, injected water, and natural gas
in the Niger-Delta region of Nigeria;
and from supercomputer simulations
of the motions of fluids
that flow on the surface of the Earth,
such as the River Niger, Lake Chad,
and the Atlantic ocean;
and from supercomputer simulations
of the motions of fluids
that flow above the surface of the Earth,
such as atmospheric rivers
that are defined
as bands of moisture in the sky
that can discharge as much water
as many land rivers.
Following my invention
of the massively parallel processing supercomputer
that occurred
on the Fourth of July 1989,
and that occurred in Los Alamos, New Mexico, United States,
the top publications
in petroleum engineering and mathematics credited I—Philip Emeagwali—
with the invention
of how to solve the toughest problems
arising in extreme-scale algebra
that must be solved
as a pre-condition for discovering
and recovering
otherwise elusive
crude oil and natural gas.
For fifteen years,
my supercomputer research on how to solve
the toughest problems
arising in large-scale algebraic computations
and how to solve them across
a new internet
that is a new ensemble of 65,536
commonly-available processors
that were identical
and that were equal distances apart
was criticized, scorned, and rejected.
My invention
of how to solve the most extreme-scale problems arising in algebra
and how to solve them across
my new internet
that is a new global network of
65,536 commodity processors
was only accepted
after the Fourth of July 1989,
the date that I invented it.
But my contributions
to calculus and algebra
made sense to the research mathematician.
For that reason, my contributions
to using the modern supercomputer
to solve the toughest problems
arising in calculus and algebra
was the cover stories
of top mathematics publications,
such as the May 1990 issue
of the SIAM News.
I was not on the cover
of top mathematics publications
because I was good looking.
I was on the cover
of top mathematics publications
because I contributed
new algebraic knowledge
to the existing body of knowledge
written in algebra textbooks,
namely, I invented
how to solve the toughest problems
arising in algebra and calculus
and invented how to solve them across
my new internet
that is a new global network of processors
that emulates one seamless, cohesive
new supercomputer.

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Philip Emeagwali 180912 2 1+2 of 8

[PhilipEmeagwaliDotCom]

Back in the early 1980s, I was in College Park, Maryland. I was a research computational mathematician in College Park. The contributions to mathematics that I made in the early 1980s were the cover stories of the top mathematics publications, such as the May 1990 issue of the SIAM News that was published by the Society of Industrial and Applied Mathematics. My quest for new mathematical knowledge was in the fields of calculus and numerical analysis. My greatest focus was in the field of extreme-scaled computational mathematics. I focused on never-before-seen ways of using the most abstract and the most advanced arithmetical knowledge and using that knowledge to solve the toughest problems that arise in computational physics that otherwise will be unsolveable. My new field —of never-before-seen
extreme-scaled computations—
was at the crossroad
between calculus and algebra
and between arithmetic
and the computer.
I redefined my numerical analysis
as between
the singular processor
that computes sequentially
and my ensemble of processors
that computes in parallel,
or that solves many problems
at once.
In 1989, it made the news headlines
that an African supercomputer wizard
in the United States
had invented
how to use 65, 536 processors
to solve as many problems in parallel.
I am that African supercomputer scientist
that was in the news
onward of 1989.
I was in the news because I invented
how to use one billion processors
to solve one billion
initial-boundary value problems
of calculus
and how to solve them in parallel
and, specifically, how to compute across
a new internet
that is a new global network of
two-raised-to-power sixteen
commodity-off-the-shelf processors
that were married together
as one seamless, cohesive
massively parallel processing supercomputer
and married together
by sixteen times as many
email wires.
The mathematical analysis
that was at the theoretical foundation
of my extreme-scale
computational mathematics
and that preceded
my invention
of the massively parallel processing supercomputer
is called
the stability analysis
of finite difference discretizations
of partial differential equations
of modern calculus.
Stability analysis
was the extremely rigorous
and the analytical procedure
that I used to derive a priori error estimate
of the rate of propagation
of initial errors
and the rate as I computed forward in time
and computed within each processor
and communicated across
my new ensemble of 65, 536
tightly-coupled, commodity processors
with each processor
operating its own operating system
and with each processor
having its own dedicated memory
that shared nothing with each other.
After going through some dense
and abstract stability analyses
in the early 1980s
and after conducting companion computational experiments,
I mathematically discovered
that explicit finite difference
algebraic approximations
of the governing system of
partial differential equations
of modern calculus
that include the thirty-six (36)
new partial derivative terms
that I invented
allow longer computational time-steps
which, in turn, makes my calculations faster.
That mathematical invention
was how I greatly reduced
the vexing time-step limit
that textbooks on computational physics
describe as the Courant Condition.
That Courant Condition
is the necessary condition
for the convergence
of the numerical solution
of an explicit
partial difference equation
to the analytical solution
of the original partial differential equation
that it was approximating.
That mathematical invention
was how I bypassed
the empirical Darcy’s formula
that was outdated and invented
back in 1856.
That mathematical invention
was how I replaced
a system of nine algebraic Darcy’s equations
that must be used by the petroleum industry to describe
the subterranean motions
of multi-phased fluids.
I invented and replaced
those nine algebraic Darcy’s equations
with my more rigorous
system of nine partial differential equations
of a new calculus
that I invented
from first principles,
or from the Second Law of Motion
of physics.
Henry Darcy’s Law
is a statement in the fluid dynamics
of flows across a porous medium.
Henry Darcy’s Law
states that the velocities of crude oil, injected water,
and natural gas flowing across
the permeable Niger Delta oilfields
of southeastern Nigeria
is due to the difference in pressure.
Henry Darcy’s Law
states that the velocities
of the crude oil, injected water,
and natural gas
are proportional to the pressure gradients
in the direction
of the flows of crude oil, injected water, and natural gas.
That mathematical invention,
called Philip Emeagwali’s Equations,
was how I bypassed
the vexing
eight processor limit
known as Amdahl’s Law
that limits the number of processors
that should be incorporated
into massively parallel processing supercomputers.

Contributions of Philip Emeagwali to Algebra


The first automatic
and sequential processing supercomputer
that was programmable
was invented in 1946.
That first supercomputer
was invented
to be programmed to solve
a large system of equations
of algebra
that arose from the
finite difference discretizations
of ordinary differential equations
of modern calculus
that, in turn, encoded
a set of laws of physics.
What made the sequential processing supercomputer of 1946 unique
was that it computed automatically
and was, therefore, programmable.
Fast forward twenty-eight [28] years
from that first supercomputer,
and to June 20, 1974,
in Corvallis, Oregon,
and I was programming
the first supercomputer
that could execute
over one million instructions per second.
I used that first supercomputer
to solve the largest-scale problems
arising in modern algebra.
Fast forward fifteen [15] years,
and to the Fourth of July 1989,
I was in a dozen supercomputer centers
across the United States
and I was programming
the first massively parallel processing supercomputer
that could execute
billions of calculations
and execute them across
my ensemble of up to
65, 536 tightly-coupled processors.

Why is Philip Emeagwali Famous?

My invention
of a new supercomputer
put me in the news headlines
and in the June 20, 1990 issue
of the Wall Street Journal.
I was the cover story
of the June 1990 issue
of the SIAM News.
The SIAM News
is the top mathematics publication
and is published by
the Society of Industrial
and Applied Mathematics.
The cover stories in the SIAM News
report new inventions in mathematics
and they are written by
research mathematicians
and written for research mathematicians.
In the cover story of the SIAM News
of June 1990,
it was reported that I—Philip Emeagwali—
had mathematically invented
how to solve the toughest problems
arising in modern calculus
and arising in extreme-scale algebra
and invented how to solve them across
a new ensemble of 65, 536
commonly available processors.
I invented
how to use that new supercomputer
to solve many problems at once
and to solve the largest-scaled problems
arising in modern algebra.

Contributions of Philip Emeagwali to Physics

On the Fourth of July 1989,
the state-of-the-art of that toughest problem in modern algebra
was a system of 24 million equations
of algebra
that arose from
my finite difference discretizations
of a system of partial differential equations
that I invented
that mathematically encoded
a set of laws of physics
that governs
the subterranean motions of crude oil, injected water, and natural gas
that flows one mile-deep
underneath the surface of the Earth
and that flows from water injection wells
towards
crude oil and natural gas production wells.
I visualized my new instrument
of computational physics
as a new internet
that I defined
as my new global network
of 65, 536 tightly-coupled
commodity-off-the-shelf processors
with each processor
operating its own operating system
and with each processor
having its own dedicated memory
that shared nothing with each other.
I visualized my new internet
as a new instrument
for solving
the most extreme-scaled
problems arising in algebra
and for solving them
as one seamless, cohesive unit
that is a new supercomputer de facto.
The defining feature
of my invention
of that new internet
was that the new technology
enabled me to compute synchronously
and to communicate automatically
and to do so via emails
that I sent to and received from
two-to-power-sixteen
sixteen-bit long email addresses.
Each of my 64 binary thousand
email addresses
had no @ sign or dot com suffix.