## Unintentional Haiku in the Princeton Companion to Mathematics

reaches out gracefully to
pick up an object.

The difference between
the two definitions of
a secret is huge.

These ideas will
occupy us for the rest
of the article.

This opens you up
to new influences and
opportunities.

In our case, there are
two natural properties

Suppose that households
are able to observe one
another’s outputs.

Everything is now
a martingale and there can
be no arbitrage.

The magician can
at once identify which
digit has been changed.

This definition
flexibility.

Let us briefly sketch
the argument, since it is
an instructive one.

Moreover, it was
a thought that took many years
to be clarified.

The blocks are the sets
of seed varieties used
on the seven farms.

If you didn’t know where it came from, this could be about anything, but it also sums up the appeal of mathematics:

But then again, who
can deny the power of
a glimpse at the truth?

And a more transparent statement about the nature of mathematics:

and the mathematical
world is “connected.”

But I really love it when you can’t tell it’s about mathematics until the last line:

to be that we should weaken
our hypotheses.

It is important
of mathematics.

We will focus on
the most important special
case: vector bundles.

Sometimes relations
are defined with reference to
two sets A and B.

This remains as an
outstanding open problem
of mathematics.

Church’s thesis is
therefore often known as the
Church–Turing thesis.

How, though, can we be
sure that this process really
does converge to x?

It turns out that both
choices are possible: one
automorphism

We shall now describe
the most important of these
extra assumptions.

Several themes balance
in Hilbert’s career as a
mathematician.

Indeed, the study
of such designs predates their
use in statistics.

This turns out to be
a general fact, valid
for all manifolds.

However, it is
a well-understood kind of
singularity.

In particular,
we can define the notion
of winding numbers.

This is exactly
proof complexity.

How much better would
you do if you could compound
this interest monthly?

Why are spherical
harmonics natural, and
why are they useful?

What consequence should
this have for the dimension
of the Cantor set?

Can we reduce this
computational problem
to a smaller one?

small numbers a, in order,
until one is found?

For what values of
the edge-probability
p is this likely?

Is every even
number greater than 4 the
sum of two odd primes?

Can one make sense of
the notion of a random
continuous path?

In mathematical
research now, there’s a very
clear path of that kind.

This one sounds like some kind of ‘how many roads must a man walk down’ question:

How many walks of
length 2n are there that start
and end at 0?

And while this isn’t actually a haiku, I can imagine it being sung in response to that song, with ‘the number of such walks’ to the tune of ‘the answer my friend’:

The number of such
walks is clearly the same as
W (k − 1).

Mathematicians don’t always answer questions in ways that other people find useful:

to ask each person “How big

In particular,
the average family size
becomes infinite

It follows that at
some intermediate r

Things only a mathematician would feel the need to state explicitly:

This is a sum of
exponentials — hence the phrase
“exponential sums.”

What makes them boring
is that they do not surprise
us in any way.

Proof is left as an exercise for the reader; it probably takes several pages, but:

If you do know it,
then the problem becomes a
simple exercise.

Once this relative
primality is noticed,
the proof is easy.

All we have to do
is use one more term in the
Taylor expansion.

Doing things this way
seems ungainly to us, but
it worked very well.

It is not hard to
see that the two approaches
are equivalent.

(Of course, one needs to
check that those two expressions
really are equal!)

But this subtlety
is not too important in
most applications.

Some interesting statements:

For every person
P there exists a drink D
such that P likes D.

That is exactly
what a sphere is: two disks (or
cups) glued together!

Thus, recursion is
a bit like iteration
but thought of “backwards.”

Nevertheless, it
turns out that there are games that
are not determined.

(It can be shown that
there is exactly one map
with this property.)

The remainders get
smaller each time but cannot
go below zero.

There are other ways
to establish that numbers
are transcendental.

(The term “Cartesian
plane” for R2 is therefore
anachronistic.)

As usual, we
identify R2 with
the complex plane C.

Note that a block of
size 1 simply consists of
an eigenvector.

The upshot is that
we should always use a prime
number as our base.

Among the other
important number fields are
the cyclotomic fields.

Thus we obtain a
number that is less than the
quantity we seek.

So we might define
the “points” of a ring R to
be its prime ideals.

(For both halves, the pinched
equator is playing the
part of the point s.)

Thus, we have deduced
that length-minimizing curves
are geodesics.

For example, the
geodesics on the sphere
are the great circles.

The generators
correspond to loops around each
of the two circles.

The image of this
map will be a closed loop C
(which may cross itself).

We consider what
happens to C if we add
a small ball to it.

It is not hard to
show that the orbits form a
partition of X.

There are many ways
of combining groups that I
have not mentioned here.

I have thrown classes
of groups at you thick and fast
in this last section.

To apply Newton’s
method, one iterates this
rational function.

A quick overview
of physics will be useful
for the discussion.

can get away with
not understanding quantum
mechanics at all.

The quantum version
of Hamilton’s principle
is due to Feynman.

These encapsulate
the idea of a proof

(A graph is simple
if it has neither loops nor
multiple edges.)

It is really an
algorithm that inputs
n and outputs an.

(An involution
is a permutation that
equals its inverse.)

If the tree has 2
vertices, then its code is
the empty sequence.

But the number of
possible orders of A,
B, and C is 6.

Number theory is
one of the oldest branches
of mathematics.

The percolation
and Ising models appear
to be quite different.

First, Albert shouts out
a large integer n and
an integer u.

This one is interesting if you imagine it’s about lines of poetry:

Another affine
concept is that of two lines
being parallel.

A mathematical protest slogan:

equality if
and only if x and y
are proportional.

A title of the mathematician’s equivalent of a song about unrequited love:

5.1.5
Why Is It so Difficult
to Prove Lower Bounds?

A series of short films:

10 Differences in
Economic Life among
Similar People

And something said in a soothing tone after a litany during a maths/mass:

Now let us return
to polynomials with
n variables.

The probability of finding a good haiku in the end matter is low, but I think this one’s pretty neat, even if it only has the right syllable counts if you say the ‘and’ in 906 but not 753:

law of large numbers,
753,
906

1. #1 by dulzimordash on May 18, 2013 - 10:14 pm

Reblogged this on Spontaneous Creativity.

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2. #2 by Teena Carroll on July 11, 2020 - 4:37 pm

I love your found math haiku. We would like to include our favorites in the math haiku project. http://www.mathhaikuproject.com and invite you to write us some more!

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