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.

TAGS: supercomputer, world’s fastest supercomputer, parallel processing, high performance computing, parallel computing, Grand Challenge Problems, vector processors, vector supercomputers, computational mathematics, computational physics, partial differential equations, algebra, calculus, black physicists, African American physicists, African American Inventors, black inventors, black history month, black scientist, famous black inventors

Philip Emeagwali 180912 2 3 of 8

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