January/February 2019^ DISCOVER^59
FROM TOP: PASIEKA/SCIENCE SOURCE (3); GEMMA TARLACH/DISCOVER; UNIVERSITY OF SEVILLE
Q
What does a breakthrough in
mathematics look like?A
In my experience, breakthroughs
typically happen in two phases.
First, there’s an important and
interesting problem that’s been out
there for a while that you’re aware
of. You know the background to
that problem, read papers, know
about other people’s research, know
what difficulties everybody has come
up against and where people have
become stuck. Then, if you’re really,
really lucky, you develop a new tool,
a new trick, a new approach to attack
the problem in question. Often the
trick itself is relatively simple.Q
Algebraic geometry sounds
like a mashup of two
math subjects. How do they
come together?A
That’s the study of geometric
objects defined by solutions to
polynomial equations. We consider
objects defined by many equations
in many variables, of arbitrarily high
degree, and we try to classify them,
which means we try to understand
their general features and catalog
them in some reasonable way.Q
I almost hate to ask, but how
will it be useful?A
Algebraic geometry is one of
the more abstract fields of
mathematics, so direct applications
are hard to find. It does have some
applications to things like string
theory, differential geometry and
other related subjects. String theory,
even though it’s physics, has no
connection yet to experimental
science. So it’s still basically math.Q
Mathematicians are often
depicted working alone,
but aren’t we seeing a rise in
collaborations?A
I do believe that’s true, and
definitely seems to have
happened in the last 20 years. Small
collaborations — typically two to
three people, four people — are
definitely becoming more and
more commonplace. I think it’s
a good thing. It makes research
more pleasant, and progress seems
to be quicker.Q
So no more toiling away
in solitude?A
Well, the toiling on your own,
even when you work in a group,
there’s definitely a lot of that. You
exchange an email, and then you go
back to your office to think about it
for a day or two, before you exchange
emails, maybe even a week or two.
A lot of [math] is done in the privacy
of your office, with pencil and paper,
struggling on your own. But even just
this occasional feedback is useful and
productive and avoids stagnating for
months on one issue.Q
What big questions are you
tackling now?A
One problem that we still don’t
know the answer [to] in string
theory is this idea that there’s an
extra six dimensions to the universe
which have a special shape known as
a Calabi-Yau manifold. These extra
six dimensions are so smooth that
you’re not supposed to be able to
perceive them, even with the most
sophisticated experiment. They’re
higher-dimension analogs of a
doughnut. But they could potentially
have infinite shapes.Christopher HaconCalabi-Yau
manifoldsBees Know Nothing
An international team
of researchers
trained
honeybees
to learn the
numerical
concepts
of “greater
than”
or “less
than” and
concluded
that the insects
seemed to grasp the
concept of zero. “Bees demonstrated an
understanding that parallels animals such
as the African grey parrot, nonhuman
primates, and even preschool children,”
they observed in a June Science paper.Our Cells, Our Scutoids
In July, a team of
biologists unveiled
the scutoid
— a newly
identified
shape that
emerges
when the cells
of biological
tissue are
packed closely
together.FURTHER AFIELD
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