Experience Mathematics

A book I wrote long ago. Recently, I re-edited it based on comments made by Professor Dick Askey. Looking for a publisher, but meanwhile here it is for my friends and their kids...

Click here to view the PDF File

The q-disease

Special Functions,
by Andrews, Askey and Roy.
Here's a belated review,
and a thank you.


Beauty in mathematics,
said Polya,
is seeing the truth
without effort.

in The Book
is as elegant,
as could be.

as simple,
as effortless,
as should be.

as beautiful,
as it is.


Design II

Design II
Ambigram by punyamishra

A great design:
Everything fits in nicely
into one complete whole.

Not a hair out of place,
and not one thing
than what is

The form
and the function,
made for each other.

GB #32


Ambigram by punyamishra

All Cretans are liars
said Epiminedes,
a Cretan,
a classic Paradox.

If Epiminedes tells the truth
then he must be lying.
And if he is lying,
he is telling the truth.


Ambigram by punyamishra

Watson and Crick
what fun it is
to be
a scientist.

What fun it is
to discover
something new.

What fun it is
to compete
with the best
and win.

Watson and Crick
the secret of life
GB #30


Ambigram by punyamishra

The Internet
inking pacts
across the world.

and connecting
all humanity.

all the dots
into one
continuous whole.

GB #29

Internet II

Internet II
Ambigram by punyamishra

Small knots
woven together
become a net.
Flexible, stable,
and very strong.

Small computers
become the Net.

the power
of communication,
of creativity,
of community.

Small individuals,
linked together
become the

GB #28

Douglas R Hofstadter

Ambigram by punyamishra

Douglas R Hofstadter
sides reversed is
Retdatsfoh R Salgoud
sides reversed is
Douglas R Hofstadter
is one Strange Loop.

Hofstadter wrote
Godel, Escher and Bach:
An eternal golden braid.

A personal review follows.


Originally uploaded by punyamishra

A dog,
wags his tail,
seeks attention.
And licks your face,
without asking for
your permission.

Comes up close
and becomes

And becomes
your best friend.

GB #26


Originally uploaded by punyamishra

looks the same
whichever way
you look at it.

Look down from the top
or up from bottom --
and find GOD.

Look in the mirror
and see GOD.

Just like the 0,
symbol for

But still,
to count from
one to infinity.

GB #25

I Love My India

Tejasi made this using My Paint Free, on my iPhone.




Math Poettary - Infinite

Check out the post here.

A brief explanation

The post mentions the sphere as a "one-point compactification" of the (complex) plane (by adding a point at infinity). The property of the sphere being compact somehow makes it a little closer to being "finite" and therefore easier to handle. But to understand more precisely what all this means you need to take a good course in Complex Analysis or Topology.

When studying complex analysis, I thought that the theorems are simpler, more beautiful, and closer to the finite case than analogous theorems in Real Analysis. I don't know whether that is due to the relationship with the sphere, but I suspect it is so.

Here is an example: You know that a polynomial p(x) with real coefficients (and a finite degree) can be written as a product of factors of the form (x-a) where a is a zero of the polynomial. (The root a is of-course a complex number). Turns out, under certain conditions, we can write a function (which can be viewed as an infinite series) as an (infinite) product of its zeros. For example, consider this formula:

Euler's Product:

Euler Product

(The formula above taken from Wikipedia's entry on the Wallis Product.)

The formula looks nicer if you replace x by (pi)x. Then the expression on the left has zeros at +1, +2, +3, ... and -1, -2, -3, .... And on the right you get factors of the form (1-x/n)(1+x/n) which is zero for x = +n and -n.
In fact, the way we write the product is something to do with making the product "converge" (or make sense).

This formula is definitely something I will write about one day. I think I need to pick up a complex analysis book again...its been too long...and have almost forgotten the beautiful stuff I used to see everyday.