The Contributions of Philip Emeagwali
Philip Emeagwali Author Philip Emeagwali
https://www.youtube.com/watch?v=vC8pY4z-M20           An African Mathematician and His Contributions to Mathematics             Philip Emeagwali Lecture 180914 Visit http://emeagwali.com for complete transcripts of 100+ lectures. Video: https://YouTube.com/emeagwali Podcast: https://SoundCloud.com/emeagwali     The need to calculate is as old as humanity. The need to compute existed because…
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Philip Emeagwali Lectures
An African Mathematician and His Contributions to Mathematics

Philip Emeagwali Lecture 180914

Visit http://emeagwali.com for complete transcripts of 100+ lectures.

Video: https://YouTube.com/emeagwali

Podcast: https://SoundCloud.com/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.

To the non-mathematician,

my mathematical invention is abstract

and impenetrable.

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.

The SIAM News

is the flagship publication

of the mathematics community.

The SIAM News

is published by the Society for

Industrial and Applied Mathematics.

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.

Who Invented the Quadratic Equation?

My first introduction to algebra

was in mid-1964

in the fifth grade

in Agbor, in the Midwestern Region

of Nigeria.

My first algebra textbook

was written by an English schoolmaster

named Clement Vavasor “CV” Durell.

Who invented the quadratic equation

of algebra?

The quadratic equation

is one of the most important contributions

to mathematics

that was made by Africans

and made in Africa.

The quadratic equation

was first solved

in the Berlin Papyrus.

The Berlin Papyrus

was excavated in Africa

but renamed after Berlin, Germany.

In the history of mathematics,

it was the tradition

credit the mathematical knowledge

that was developed in Africa

to Europe.

Following that tradition

of historians of mathematics,

the Berlin Papyrus

was credited to the city of Berlin, Germany

and not named after

the city in Africa

that the Papyrus was excavated from.

The [quote unquote] “Berlin Papyrus”

was written in Africa

and written by Africans

and written between

three thousand seven hundred and twenty [3,720] years ago

and four thousand one hundred and eighty [4,180] years ago.

In that African Papyrus

that was written four thousand years ago,

the quadratic equation

was stated as

x squared plus y squared

equals 100

and y equals three-quarters

divided by the product of four and x.

Contributions of Philip Emeagwali to Algebra

The quadratic equation of algebra

that is in the homework assignment

of a 12-year-old

contains at least one unknown variable

that is squared.

That unknown variable

is often called x.

The 24 million system of

partial difference equations

of algebra

that I solved

on the Fourth of July 1989

and solved across a new internet

that is a new global network of

65,536 tightly-coupled,

commonly available processors

that made the news headlines

contained 24 million unknown variables.

That was a world record in algebra.

In my Fourth of July 1989

invention,

I computed across a new internet.

I visualized my new internet

as my new global network of

65,536 tightly-coupled processors

with each processor

operating its own operating system

and with each processor

having its own dedicated memory

that shared nothing with each other.

Each processor within my new internet

had one hundred and thirty-one thousand

and seventy-two [131,072] bytes of memory

that I used

for the integer and logical operations

that arose

from my algebraic computations.

I also used

two thousand and forty-eight [2,048] floating point co-processors.

I used those co-processors

to execute

my floating point arithmetical computations.

Each co-processor

had four megabytes of memory.

The frontier of extreme-scale algebra

is far beyond the quadratic equation

that contains two unknown variables

that was first solved

four thousand years ago

in Africa.

Extreme-scale algebra

arise during the general circulation modeling

that must be used to foresee

otherwise unforeseeable

global warmings.

Extreme-scale algebra

is used to discover and recover

otherwise elusive

crude oil and natural gas.

Extreme-scale algebra

is used to solve the toughest problems

arising in computational physics.

The most important quest

in algebra

was to theoretically

and experimentally invent

how to solve extreme-scale

tri-diagonal system of equations

of algebra

and how to solve those equations across

millions upon millions

of tightly-coupled processors

with each processor

operating its own operating system

and with each processor

having its own dedicated memory

that shared nothing with each other.

One reason I was the cover stories

of mathematics publications

was because

I mathematically discovered

that it’s impossible

to reduce a tri-diagonal system of equations

of algebra

and reduce it

to a mathematically equivalent

diagonal system of equations

of algebra.

I, de facto, circumvented that impossibility

by taking two steps backward

and to the granite core

of the physical problem

that is mathematically modeled,

namely, the extreme-scale

petroleum reservoir simulation,

that was governed by

a tri-diagonal system of equations

of algebra

that arose from discretizing

a system of partial differential equations

of modern calculus

and arose from approximating

that system

by a companion system

of partial difference equations

of a new algebra.

It was at that granite core

of the most excruciatingly-detailed

petroleum reservoir simulation

that I reformulated

the partial differential equations

that is a new calculus

that was not in any calculus textbook

that was printed in the 1970s or earlier.

The reason my contributions to mathematics

was the cover story

of the top mathematics publication, namely,

the May 1990 issue

of the SIAM News

of the Society of Industrial

and Applied Mathematics

was that I created a new calculus

and I did so

by inventing thirty-six [36] additional

partial derivative terms

of calculus.

In the old calculus

that is used to recover

otherwise unrecoverable

crude oil and natural gas,

only forty-five [45]

partial derivative terms

represented the Second Law of Motion

of physics

that was encoded

into the three-phased—crude oil,

injected water, and natural gas—

extreme-scaled

petroleum reservoir simulator.

My contributions

to the body of mathematical knowledge

called calculus and algebra are these:

I added the thirty-six [36]

partial derivative terms

of modern calculus

that I invented

to the forty-five [45]

partial derivative terms

that prior research mathematicians

invented.

And I did so to bring the total

partial derivative terms

to eighty-one (81).

In the advanced calculus textbooks

and in the old paradigm

of extreme-scale algebraic computations

arising from

petroleum reservoir simulations,

the governing system of coupled, non-linear,

time-dependent, and state-of-the-art

partial differential equations

of modern mathematics

was parabolic, instead of hyperbolic.

In my new paradigm

of extreme-scale algebraic computations,

that enabled me to

massively parallel process

and to process across a new internet

that I visualized

as a new global network of

65,536 tightly-coupled,

commonly available processors

that shared nothing with each other

and in that new paradigm

my system of coupled, non-linear,

time-dependent, and state-of-the-art

partial differential equations

of modern calculus is hyperbolic,

not parabolic as written in

calculus textbooks.

My contributions to calculus

was a paradigm shift because

such governing

partial differential equations

are described in all the textbooks

as parabolic, instead of hyperbolic.

They are described in calculus textbooks

on the multi-phase and multi-physics

porous media flow

of crude oil, injected water, and natural gas,

such as the crude oil and natural gas

flowing from the water injection wells

to the crude oil and natural gas wells

across the oilfields

of the Niger Delta region

of southeastern Nigeria.

Predicting Algebraic Error Propagation

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.

Sometimes, the Impossible is Possible

Back in 1989,

no author of any mathematics textbook

understood the concept of

solving many problems at once,

or in parallel.

Back in 1989,

Seymour Cray

was the spokesman

for the supercomputer community.

If Seymour Cray’s granddaughter

came to him for help

with her homework assignment

on how to solve

many mathematical problems at once,

Seymour Cray

would not have been able

to help her

to solve her problem in parallel.

The reason was that Seymour Cray

ardently believed that

the supercomputer technology

that I invented

that enables parallel processing across

my ensemble of 65,536

tightly-coupled processors

was impossible and science fiction.

A Day in the Life of a Black Mathematician

Quest of Philip Emeagwali for New Mathematical Physics

I was an apprentice supercomputer scientist

for forty-five [45] years.

After investing forty-five [45] years

in the craft of supercomputing,

I had the command of materials

that I needed to deliver

my supercomputer lectures

in prose and poetry,

rather than on blackboards and power points.

After nearly half a century

of supercomputing,

I knew one or two things

about supercomputers

that nobody else knew.

That new knowledge

that I alone had

was how to solve the toughest problems

arising in physics

and how to solve them at once.

My mathematical maturity

grew from the algebraic representation

of the Second Law of Motion

of physics

that was written as

F=ma,

or Force equals

mass times acceleration.

That iconic formula, F=ma,

is the most important formula

in mathematics, science, and engineering.

I learned that formula, F=ma,

back in June 1970

and I learned it in the eighth grade

of Christ the King College,

Onitsha, East Central State, Nigeria.

Contributions of Philip Emeagwali to Mathematical Physics

Fast forward a dozen years,

I had taken as my second home

half a dozen mathematics

and physics departments

that were across the United States.

My second home

was mathematics and physics departments

from Corvallis (Oregon)

to Washington (District of Columbia)

to College Park (Maryland).

For my first sixteen years

in the United States,

I made those mathematics

and physics departments

my second home.

After sixteen years

in mathematics and physics departments,

I had grown intellectually

to become a research

computational mathematician

and to become a research

computational physicist.

That intellectual maturity

as a research mathematician

and as a research physicist

was what enabled me

to discover thirty-six [36] critical errors

in the advanced textbooks

in the mathematical physics

that governs

the flow of crude oil, injected water,

and natural gas

that flows a mile-deep

inside production oilfields.

I corrected those thirty-six [36]

critical mathematical errors

by inventing

thirty-six [36] partial derivative terms

that ensured that F=ma

and that ensured that

the equality holds

within a system of nine new

partial differential equations

that I invented

and that encoded

the Second Law of Motion

of physics

and that encoded that law

for three-dimensional, three-phase flows

within porous media,

such as flow of crude oil, injected water,

and natural gas across

the Oloibiri Oil Field

of Bayelsa State of southeastern Nigeria

that was the first oilfield

that was discovered

in West Africa back in 1956.

Those thirty-six [36]

partial derivative terms encoded

the thirty-six [36]

temporal and spatial components

of the inertial forces

in the three phases

of crude oil, injected water, and natural gas

that were flowing along

the temporal

and the three spatial directions

of my new nine

partial differential equations

of modern calculus.

I continued across

my ensemble of 64 binary thousand

tightly-coupled,

commodity-off-the-shelf processors

that shared nothing with each other

and I continued and I invented

my new nine partial differential equations.

I discretized the latter

from its formulation

as a differential problem

of modern calculus

to the extreme-scaled problem

of modern algebra.

I did so to enable me

to more accurately encode

the invisible subterranean motion

of water

that is pumped into water injection wells

and pumped because

water is cheaper than oil and natural gas

and is, therefore, used to push

oil and natural gas

towards production wells.

Things I Did in the Nation’s Capital

For me, the answer

to the Grand Challenge Problem

of mathematics and supercomputing

demanded my sixteen-year-long journey, onward of June 20, 1974

from Corvallis, Oregon, United States

through Los Alamos, New Mexico,

United States

to receiving the top prize in supercomputing

from Silicon Valley, California.

A research pure mathematician

is re-searching a new proof

of a deep and abstract theorem.

I sojourned

to an unknown world of technology.

In that sojourn, I used

sixteen supercomputer-hopefuls

as my guideposts along the new pathways

to the never-before-seen

global network of processors

that is a new internet

that is a new supercomputer

and that is a new computer.

A research applied mathematician

is seeking

a new and better mathematical description,

such as a system of coupled, non-linear,

time-dependent, and state-of-the-art

partial differential equations

that governs

an initial-boundary value problem

of modern calculus.

A research computational mathematician

is seeking

a faster computational model,

that explains or predicts

a phenomenon

that is otherwise impossible

to explain or predict.

In the late 1970s and early ‘80s,

I was a research

computational mathematician

that lived in room eight hundred

and seventy-seven [877]

of Meridian Hill Hall

at twenty-six hundred and one [2601]

16th Street

that was at the corner of

16th Street and Euclid Street

of Adams-Morgan neighborhood

of northwest Washington, D.C.

On a Friday evening, I might have dinner

with my future-wife, Dale.

Our favorite place

was an Ethiopian restaurant

that was a short walk

down 18th street

from Columbia Road

in the Adams-Morgan neighborhood.

My other favorite places are the small cafes

along “T” and “U” streets,

and the Meridian Hill Park Drum Circle.

In the late 1970s and early ‘80s,

I was most likely to be seen

in the nation’s capital, Washington, D.C,

jogging across the Smithsonian’s

National Zoo of Washington, D.C.

at 6 a.m. in the mornings.

I also walked or jogged across

the Adams-Morgan neighborhood,

or across the Dupont Circle neighborhood,

or across the Foggy Bottom neighborhood,

or across Rock Creek Park.

The 12-mile-long Rock Creek Park

extends from the Potomac River

to the border of Maryland.

Foggy Bottom

is named after the fog

that clings to the neighborhood

in the morning.

Foggy Bottom

is a late 18th-century neighborhood

and is one of the oldest neighborhoods

in Washington, D.C.

The Dupont Circle

has a famous traffic circle

and a water fountain at its center.

For me, the Dupont Circle drum circle

and its array of late afternoon drummers and dancers

was like a church.

Fast forward to the late 1990s,

and from the drum circles

of Washington, D.C.

to West African drummers

in Baltimore, Maryland.

My wife Dale and I took lessons

on African dance and rhythm

and from a charismatic griot

and choreographer

named Kibibi Ajanku.

Kibibi Ajanku

was the founding mother

of the Sankofa Dance Theatre

of Baltimore, Maryland.

My Night Life in the Nation’s Capital

From October 1978 to May 1981,

I lived a short walk

from the Kilimanjaro Restaurant

and Nightclub

that was started in 1982.

Kilimanjaro Restaurant

and Nightclub was throbbing with

live African music and reggae.

Kilimanjaro Restaurant

and Nightclub

was in the Adams-Morgan neighborhood

of Washington, D.C.

In the early 1980s,

I lived at 1915

East-West Highway,

apartment three zero three [303],

Silver Spring, Maryland.

And I walked the short distance

to the railway subway station

called Metro Station.

That underground railway station

was at the boundary

between Silver Spring, Maryland

and Washington, District of Columbia.

On weekdays, I took the

Washington, D.C. rapid transit system

to Foggy Bottom Station

that is west of the White House

and in downtown Washington.

Foggy Bottom

was a very short walk

to the computer center

where I programmed fast computers

and used them to solve

the most computation-intensive

initial-boundary value problems

of modern calculus

that was the mathematical foundation

of computational fluid dynamics.

My Supercomputing in Washington, DC

In the early 1980s,

my massively parallel processing supercomputer research interests

were multidisciplinary.

I investigated

computation-intensive problems

arising in mathematical biology,

such as the evolution equations.

I investigated

fluid-structure interactions

within the cardiovascular system.

And I investigated

hydrodynamical computations

that included

the simulation of the propagation

of tsunami waves

arising from earthquakes.

I was an unorthodox

research supercomputer scientist.

The mathematician’s blackboard

that is scribbled with matrices,

tensors, summation indices,

and partial derivatives

is not the playground

of a traditional computer scientist.

A traditional computer scientist

that challenged me

on the mathematician’s blackboard

was like Daniel

challenging the lion in the lion’s den.

A Day in My Life

By the late afternoons of the early 1980s,

I become mentally exhausted

from programming computers

to solve extreme-scaled

partial difference equations

of modern algebra

that arose from and approximated

partial differential equations

of mathematical physics.

In the late weekday afternoon

of the early 1980s,

I often walked to the nearby

Embassy of Nigeria

to read the Daily Times newspaper

and socialize with Embassy staff

and Nigerian visitors.

At about 4:30 p.m.,

I will be playing tennis

at the nearby four lighted tennis courts

that were at the intersection

of “O” Street northwest

and “23rd” street northwest.

If it’s too cold for outdoor tennis,

I will swim for two hours

at the Olympic-sized indoor swimming pool

that was located at

600 22nd Street northwest,

Washington, D.C.

Or I might play indoor tennis

or play squash

in the indoor courts

at the same address.

About one Friday evening a month,

I will spend a few hours

in the nearby swanky Zanzibar Night Club.

Zanzibar

maintained its image

as the classy African

and international night club

of Washington, D.C.

Zanzibar

enforced a strict dress code.

To be admitted into Zanzibar,

gentlemen must wear a dignified

national dress,

such as the Nigerian agbada,

or wear a suit

along with a collared shirt,

a tie, and dress shoes.

In the mid-1980s,

Zanzibar Night Club

was then in the

Foggy Bottom neighborhood

of Washington, D.C.

Dairy of a Black Meteorologist

Back in 1981,

I was doing more rigorous

mathematical analyses

than I was programming supercomputers.

I did my mathematical analyses

inside the Gramax Heliport Building

in Silver Spring, Maryland.

The Gramax Heliport Building

was an approved landing pad

for helicopters.

In the early 1980s,

the Gramax Heliport Building

at 8060 13th Street, Silver Spring, Maryland

was the headquarters

of the U.S. National Weather Service.

I was at the National Weather Service

because of my interest

in using the fastest supercomputers

to solve

the primitive equations of meteorology.

The primitive equations

were a system of coupled, non-linear,

time-dependent, and state-of-the-art

partial differential equations

of modern calculus.

The primitive equations

are used to model the flow of air

and moisture across

the surface of the Earth.

I was at the U.S. National Weather Service

because the Gramax Building

was a walking distance

from the Silver Spring Metro station,

in Silver Spring, Maryland.

The Gramax Building

was also a brisk walk

from my residence

at 1915 East-West Highway,

Apartment 303, Silver Spring, Maryland.

A few months earlier

and in early 1981,

I was still living at Room 877,

of Meridian Hill Hall

that was at the corner of

16th and Euclid Streets,

of the Adams-Morgan neighborhood,

of northwest, Washington,

District of Columbia.

My Struggles to Invent New Algebra

Inside the Gramax Building,

I wrote and rewrote and re-calculated

a hundred versions

of my Taylor’s expansion

of various finite difference discretizations

of the system of nine

coupled, non-linear, time-dependent,

and state-of-the-art

partial differential equations

of modern calculus,

called Philip Emeagwali’s Equations

that governed

my initial-boundary value problem

that was at the mathematical foundation

of my computational fluid dynamics

codes.

I invented those nine

partial differential equations

and they are my contributions

to mathematics.

As a research numerical analyst,

my research goal was to invent

nine corresponding

finite difference algorithms

or discretization schemes,

and finite difference

algebraic approximations

of my nine partial differential equations,

called Philip Emeagwali’s Equations.

I discretized

my new partial differential equations

and I did so

in a manner that will enable me

to first

define and email

their algebraic approximations

as well as their companion codes

and email them

as 65,536

petroleum reservoir simulations

or email them as 65,536

extreme-scale

computational physics problems

that made the news headlines

when I invented

how to solve them

in parallel

and solve them across

my new global network of

65,536 tightly-coupled,

commodity-off-the-shelf processors.

Each of my 65,536 processors

operated its own operating system.

And each processor

had its own dedicated memory

that shared nothing with each other.

Those identical processors

were married together

by 1,048,576 identical email wires

and married together

as one seamless, cohesive unit

that is a new supercomputer

that encircled the globe

in the way the internet does

in sixteen-dimensional hyperspace.

My invention was not a new computer per se

but was a new internet de facto.

My Struggles to Invent New Mathematics

My laborious Taylor’s expansions

of 1981

were how I approximated

the value of each of my solution

by taking the sum of its derivatives

at a given point.

Taylor’s expansions yielded

my a priori error estimates

that I used to pre-select

the most, hopefully, accurate

finite difference algebraic approximations

of the nine partial differential equations,

called Philip Emeagwali’s Equations,

that I invented.

I contributed to mathematical knowledge

and my contribution to algebra and calculus

was the cover story

of top mathematics publications,

such as the June 1990 issue

of the SIAM News.

One fact that I never mentioned before

was that I often pursued

false mathematical trails.

Back in 1981,

I was unreasonably obsessed

with the Hopscotch algorithms

as a numerical solution of

partial differential equations.

I was obsessed with Hopscotch methods

because I was unreasonably optimistic

and believed that

Hopscotch methods are hybrid

explicit-implicit methods

that could be very accurate

and that Hopscotch methods

could enable me to email

my initial-boundary value problems

and email them across

a new internet

that I visualized

as a new global network of

65,536 commodity-off-the-shelf processors.

After a year of seemingly endless mathematical analyses

of Hopscotch algorithms

and computational experiments

of Hopscotch

computational fluid dynamics codes

I discovered that

I was following a false trail

and that hopscotch algorithms

were over hyped.

After wasting extraordinary amount of time,

I resettled

on explicit finite difference approximations.

In the end,

I invented explicit finite difference

algebraic approximations

of the nine partial differential equations,

called Philip Emeagwali’s Equations,

that I contributed to modern calculus.

That was how I scribbled new calculus

that had never been scribbled

on any blackboard before.

That was how I coded new algebra

that had never been coded

by any computational algebraist before.

That was how I saw a new supercomputer

that had never been seen

by any supercomputer scientist before.

Father of Large-Scale Algebra

It’s often said that

parallel processing across

millions upon millions

of tightly-coupled commodity-off-the-shelf processors

that shared nothing with each other

is the biggest advance in computing

since the programmable computer

was invented

back in 1946.

In my country of birth, Nigeria,

a million billion trillion

floating-point arithmetical computations

are massively parallel processed

each day

and massively parallel processed

to discover and recover

the otherwise elusive