New Scientist - USA (2019-07-13)

10 | New Scientist | 13 July 2019

News

Mathematics

TAKING sperm directly from the

testicles rather than using semen

may help some couples conceive

through IVF.

The approach has been used for

some time in men who are infertile

because they have a blockage in the

tubes that take sperm to the penis,

for example. It is now being offered

more widely, partly because of a

suspicion that some infertility may

be down to damage occurring to

sperm after they have formed,

through exposure to free radicals.

“Free radicals are very

detrimental to sperm DNA,” says

Sandro Esteves of Androfert, a male

infertility centre in Campinas, Brazil.

But sceptics are concerned that

by taking sperm from the testicles,

doctors may inadvertently select

less fit sperm, which could lead

to health problems for the baby.

Esteves and his colleagues

looked at data from 86 couples

with unexplained infertility and

sperm DNA damage who visited

the Androfert centre. Thirty-six had

IVF using sperm from their testicles.

The rest had IVF using sperm

from semen.

Regardless of the method used,

the team found that the eggs had

a similar chance of being fertilised

and developing into embryos with

the right number of chromosomes.

Esteves presented the results at

the European Society of Human

Reproduction and Embryology

conference in Vienna.

Kevin McEleny at the Newcastle

Fertility Centre, UK, would still like

to see evidence of improved live

birth rates before the technique is

used more widely. ❚

THE legendary mathematician

Srinivasa Ramanujan was

known for coming up with

unconventional mathematical

ideas. He has now inspired a

computer program that does

the same.

Called the Ramanujan Machine,

the software poses conjectures

for generating equations

whose output is fundamental

mathematical constants such as π

and e. A conjecture is an unproven

mathematical statement.

Born in 1887 in what is now

Tamil Nadu in India, Ramanujan

was a self-taught mathematician.

He often claimed that his

results came to him in a

dream, and disliked the formal

proofs favoured by most

mathematicians. Ramanujan

moved to the UK in 1914 to study

at the University of Cambridge

with the mathematician G. H.

Hardy, and their long friendship

led to a series of important results

in the field of number theory.

“Ramanujan had a way of

producing things which looked

true [but] he couldn’t necessarily

convince other people why they

were true,” says Saul Schleimer

at the University of Warwick, UK.

Many of Ramanujan’s conjectures

were later formally proven.

The theorems Ramanujan

produced often involved

continued fractions, which

express a number as the sum

of infinitely nested fractions.

To mimic this approach, Gal

Raayoni at the Israel Institute of

Technology and his colleagues

created the Ramanujan Machine.

It has already come up with tens

of conjectures that use continued

fractions to approximate π and e

(arxiv.org/abs/1907.00205).

One method the program uses

to search for new conjectures is a

“meet in the middle” approach.

This involves generating many

mathematical expressions,

computing their value for a

limited number of iterations

and eliminating the expressions

that give inaccurate results.

For example, when trying to

approximate e, whose value is a

decimal that begins 2.718..., any

potential conjectures that yield

numbers with a value that is too

high or too low are eliminated.

Conjectures that appear to work

are then calculated for more

iterations to identify ones likely

to be true. This approach gave the

new conjecture shown on the left.

Schleimer likens the method

to an extensive process of trial

and error. “What they’re doing

is a nice piece of experimental

mathematics,” he says. “But it’s not

like this is a new way of thinking.”

Some of the formulas the

Ramanujan Machine has come

up with are new, while others have

previously been discovered by

human mathematicians.

The team wants people to

submit suggested proofs to the

new conjectures, as it is impossible

to prove they are correct with

simple arithmetic since they

involve infinite sums.

“It produces conjectures

without exactly knowing why

they’re true and it likes continued

fractions, which Ramanujan was

very, very fond of, ” says Schleimer.

But it can’t really match him, he

says. “Ramanujan’s continued

fractions were more subtle and

in some sense more mature.”

The researchers behind the

Ramanujan Machine have also

shared its software, so anyone can

download the programme to run

on their own computer while it

isn’t in use. Any conjectures a

participant discovers will be

named after them, says the team. ❚

Infertility

Donna Lu

SC

IEN

CE

PH

OT

O^ L

IBR

AR

Y

Extracting sperm

from testicles may

help infertility

Clare Wilson

Computer attempts to replicate the

dream-like maths of Ramanujan

US

UM

U^ N

ISH

INA

GA

/SP

L

Sperm in the

testicles haven’t

been exposed

to as many free

radicals, which

damage DNA

e=^3 +

(^4) +
(^5) +
(^6) +
(^7) +...
— 1
— 2
— 3
— 4
Srinivasa Ramanujan, above,
came up with many equations
similar to the one below, but
this formula for the constant e
was created by a machine
“ Ramanujan had a way of
producing things which
looked true but he couldn’t
always convince others”