14 | New Scientist | 14 September 2019
BAR-HEADED geese migrate across
the Himalayas, reaching altitudes of
up to 7270 metres where the thin
air contains just 30 to 50 per cent of
the oxygen that air at sea level has.
To understand this feat,
Jessica Meir at NASA’s Johnson
Space Center in Texas and her
colleagues raised bar-headed geese
from eggs so that the birds would
imprint on them, seeing them as
their parents. Then, they trained the
birds to fly in a wind tunnel wearing
a breathing mask that simulated the
limited oxygen at high altitudes.
They discovered that the geese
lowered their metabolism during
these taxing flights and their heart
rates didn’t increase. The team also
found that the blood in the birds’
veins cooled as they flew in the
wind tunnel (eLife, doi.org/c96s).
Cold blood can carry more
oxygen than warm blood, which
may help the geese fuel the muscles
that help them fly. ❚Animal physiologyIT MIGHT not tell us the meaning
of life, the universe and everything,
but mathematicians have cracked
a tricky problem involving the
number 42.
The origins of this puzzle
go back a long way. In 1825, a
mathematician known as S. Ryley
proved that any fraction could be
represented as the sum of three
cubes of fractions. Then, in the
1950s, a mathematician named
Louis Mordell asked whether the
same could be done for integers,
or whole numbers.
In other words, are there
whole numbers k, x, y and z such
that k = x^3 + y^3 + z^3 for each possible
value of k? It is an example of a
maths riddle that is easy to statebut fiendishly difficult to solve.
Andrew Booker at the
University of Bristol, UK,
and Andrew Sutherland at
the Massachusetts Institute of
Technology have now solved
the problem for 42, the onlynumber under 100 for which a
solution hadn’t been found.
Some numbers have simple
solutions. The number 3, for
example, can be expressed as
13 + 1^3 + 1^3 and 4^3 + 4^3 + (-5)^3. But
solving the problem for othernumbers requires vast strings of
digits and computing power.
The solution for 42, which
Booker and Sutherland found
using an algorithm, is:
42 = (-80538738812075974)^3 +
804357581458175153 +
126021232973356313.
They worked with software
firm Charity Engine to run the
program across more than
400,000 volunteers’ idle
computers, using processing
power that would otherwise be
wasted. It is equivalent to a single
computer processor running
continuously for more than
50 years, says Sutherland.
Earlier this year, Booker found
a sum of cubes for the number 33,which was previously the lowest
unsolved example.
We know for certain that
some whole numbers, such as
4, 5 and 13, can’t be expressed as
the sum of three cubes. However,
the problem is still unsolved for
10 numbers under 1000, the
smallest of which is 114.
The team will next search for
another solution to the number 3.
“It’s possible we’ll find it in the
next few months; it’s possible
it won’t be for another 100 years,”
says Booker.
Those interested in aiding the
search can volunteer computing
power through Charity Engine,
says Sutherland. ❚MathsElusive mystery of the number 42 solved
Chelsea WhyteGoose blood runs cold
Some birds have unusual ways to cope with high-altitude flying
OHN DOWNER/GETTYNews
“ It is an example of a
maths riddle that is easy
to state but fiendishly
difficult to solve”Donna Lu