New Scientist - UK (2022-06-11)

11 June 2022 | New Scientist | 27

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The columnist

Chanda Prescod-

Weinstein on the

physics of flight p28

Aperture

A photo competition

that celebrates our

environment p30

Letters

Privilege is more

about exclusivity

than comfort p32

Culture

Should you use big

data to make better

decisions? p34

Culture columnist

Simon Ings on the

80s nostalgia of Top

Gun: Maverick p36

W

HEN 18-time
international Go
champion Lee Sedol
retired from the game in 2019,
mathematicians everywhere
will have shared a moment
of quiet introspection. Three
years earlier, Lee had been beaten
4-1 by an artificial intelligence,
DeepMind’s AlphaGo. Having
observed the machine’s rapid
pace of progress since then, Lee
concluded that AI is an “entity
that cannot be defeated” – at least
by human Go players – a verdict
that prompted his retirement.
AI’s triumph in a game as
complex as Go might signal
that mathematics, a subject that
it has had in its cross hairs from
its beginnings, is also ripe for
automation. As talk of automated
theorem-proving gathers pace, it is
prudent to ask if mathematicians,
too, should be concerned by the
rise of machine intelligence.
Mathematicians must reckon
with the fact that computers are
smarter than the calculators of
previous generations. But they
should enjoy a more optimistic
outlook than Lee. For one thing,
mathematics is far more vast
in scope than Go. It is precisely
because it demands more creative
intellect, that mathematics leaves
room for us humans to think
and solve problems alongside
our silicon counterparts.
Human-machine collaboration
in mathematics isn’t new. Its
watershed moment came in
1976, when Kenneth Appel and
Wolfgang Haken delivered their

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proof of the four colour theorem

with the help of a computer. The

theorem states that any map can

be filled in with four colours in

such a way that no neighbouring

regions share the same colour: a

simple-sounding claim, the proof

of which eluded mathematicians

for over a century. Appel and

Haken reduced infinitely many

cases down to about 2000 highly

complex configurations, which

a computer could crunch through

to solve the problem. The division

of cognitive labour was clear: the

ingenious stroke came from the

humans, with the menial task of

computation left to the machine.

This dynamic is still at play

today. The pattern-recognition

skills displayed by DeepMind’s

machine-learning programs

have helped researchers to usher

in breakthroughs in abstract areas

of mathematics, such as knot

theory and algebra. Computers

are no longer restricted to just

churning out routine calculations,

now they can mine enormous

data sets to detect incredibly

subtle patterns that evade even

professional mathematicians.

But this is no cause for humans

to raise the white flag. On the

contrary, mathematicians are

seizing upon these tools to refine

their intuitions. The more

creative mathematical acts of

asking meaningful questions,

interpreting computer-generated

patterns and constructing

well- reasoned arguments remain

the preserve of humans. AI may

be the spaceship that will ferry

us to new mathematical vistas,

but we must captain it.

Mathematicians have

always welcomed the latest

tools and technologies as thinking

aids to which we can outsource

the aspects of cognition that come

least naturally to us. The abacus

alleviated the manual burden

of tracking large quantities;

the human eye for precision

hits a perceptual limit at just five

objects. The slide rule, a device

inspired by John Napier’s

logarithm tables, relieved the

notorious burden of multi-step

calculation – reducing the task

of multiplication down to one

of addition, for example.

Lee’s adversarial framing of

AI doesn’t apply to mathematics,

which is a tale of ever-evolving

collaboration between humans

and machines. Today’s computers

are smarter than their ancestors;

our thinking partners rather

than mere aids. Tomorrow’s

will be smarter still. But these

technologies were created to serve

as cognitive allies to humans. It is

time we embraced them as such. ❚

Adding to the team

AI is becoming smarter all the time, but mathematicians needn’t fear

they will be replaced by machine intelligence, argues Junaid Mubeen

Junaid Mubeen is a

mathematician turned

educator, and author of

Mathematical Intelligence