Popular Mechanics - USA (2019-12)

George Reitwiesner,

Clyde Hauff, Homé

McAllister and W.

Barkley Fritz use

the newly invented

ENIAC computer to

compute π to 2,035

decimal places.

Emma Haruka Iwao

uses Google’s cloud

computing service

to calculate π to a

staggering 31 trillion

decimal places.

The Babylonians

invent the earli-

est calculator, the

abacus.

A computer cracks

the Four Color

Theorem, making

it the first computer-

assisted proof to be

solved.

The first handheld

digital calculator,

Te x a s I n s t r u m e n t s ’

CalTech, is invented.

It costs $85.

William Oughtred

invents the slide

rule, a mechanical

analog computer

designed to multiply

and divide numbers.

The software

MATLAB debuts.

Charles Babbage

designs “Difference

Engine #2,” a mechan-

ical contraption to

solve equations auton-

omously. He never

sees the machine

in action.

The first volunteer

computing project,

the Great Internet

Mersenne Prime

Search, kicks off.

Alan Turing pub-

lishes his seminal

paper “On Comput-

able Numbers.”

Mathematician

Thomas Hales for-

mally proves the

Kepler Conjecture

using proof assis-

tant software.

300 BCE

1967 1976

1622

1984

1849

1996

1936

2014

1949

2019

IT IS ALWAYS

EXCITING AND

SATISFYING

IN MATHEMATICS

TO SEE A LONG-

STANDING

PROBLEM FINALLY

BEING RESOLVED.

“

Computer x

Mathematics

Timeline

12

needed is 3^3 +3^3 +(–1)^3. Other num-
bers, like 51, grow increasingly
complicated: (–796)^3 +659^3 +602^3.
For others—4, 5, 13, 14, 22, 23, 31,
32—it is mathematically impos-
sible. Then there are the numbers
that verged on unsolvable but
seemed hypothetically possible,
like 33 and 42.
In March 2019, Booker
cracked 33. The computer he
used searched through 10 qua-
drillion numbers and turned
up three within a matter of
weeks: 8,866,128,975,287,528^3 ,
(–8,778,405,442,862,239)^3 ,
and (–2,736,111,468,807,040)^3.
Encouraged, he reached out to
Andrew Sutherland of M.I.T. to
see if he might help solve for 42.
The number has a mythical rep-
utation in pop culture—most
notably in Douglas Adams’s
Hitchhiker’s Guide to the Gal-
axy, but also within the works of
Lewis Carroll, author of Alice in

Wonderland (a nd a mat hema -

tician). Sutherland agreed.

The chance to find a set of

mystery numbers equaling

42 was irresistible, but they

needed more juice.

Then Mark McAndrew,

founder of Charity Engine,

a supercomputing system

that harnesses unused com-

puting power from more

than 500,000 home PCs,

caught a Numberphile video

about Booker’s quest for 42.

He wanted in, too. “I was lit-

erally jumping around,” he

says. Over the course of a day,

the vast network of PCs logged

more than a million comput-

ing hours on Charity Engine’s

volunteer computer network.

Finally, they got their answer:

(–80,538,738,812,075,974)^3

+ 8 0,4 3 5,75 8 ,14 5, 817, 51 5^3 +

12,602,123,297,335,631^3.

“The team’s discovery is a

major piece of progress

on this problem,” says

mathematician Chao Li of

Columbia University. “It

is always exciting and sat-

isfying in mathematics to

see a longstanding prob-

lem finally being resolved.”

(Booker and Sutherland

also recently found a new

way to make a sum of three

cubes equal 3.) Sutherland

knows that when problems

are solved with the help of

supercomputers, that’s all the

public tends to see. “But the way

these things work, there’s always

an interplay between algorithm

and computational power,” he

says. Supercomputers are like

tractors, threshers, or any other

machine. All the power in the

world is great, but without know-

ing how to use it, you’re stuck—be

it in a field or amidst 10 quadril-

lion numbers.

46 December 2019