John Baez, University of California - Riverside
The
number
24
plays
a
central
role
in
mathematics
thanks
to
a
series
of
"coincidences"
that
is
just
beginning
to
be
understood.
One
of
the
first
hints
of
this
fact
was
Euler's
bizarre
"proof"
that
1 + 2 + 3 + 4 + ... = -1/12
which
he
obtained
before
Abel
declared
that
"divergent
series
are
the
invention
of
the
devil".
Euler's
formula
can
now
be
understood
rigorously
in
terms
of
the
Riemann
zeta
function,
and
in
physics
it
explains
why
bosonic
strings
work
best
in
26=
24+2
dimensions.
The
fact
that
1^2 + 2^2 + 3^2 + ... + 24^2
is
a
perfect
square
then
sets
up
a
curious
link
between
string
theory,
the
Leech
lattice
(the
densest
known
way
of
packing
spheres
in
24
dimensions)
and
a
group
called
the
Monster.
A
better-known
but
closely
related
fact
is
the
period-12
phenomenon
in
the
theory
of
modular
forms.
We
shall
do
our
best
to
demystify
some
of
these
deep
mysteries
DC 1302
Refreshments will served in DC 1301 at 3:00pm