A good topological theorem to mention any time is
the theorem which, in essence, states that however
you try to comb the hair on a hairy ball, you can
never do it smoothly - the so-called 'hairy-ball'
theorem. You can make snide comments about the
grooming of the hosts' dog or cat in the meantime as
you pick hairs off your trouser leg.
-- R. Ainsley in Bluff your way in Maths, 1988
Pure mathematician - Anyone who prefers set theory to sex.
-- R. Ainsley in Bluff your way in Maths, 1988
Group theory - An exceedingly beautiful branch of pure mathematics
used for showing in how many ways blocks of wood can be painted.
-- R. Ainsley in Bluff your way in Maths, 1988
There are great advantages to being a mathematician:
a) you do not have to be able to spell
b) you do not have to be able to add up
The illiteracy of mathematicians is taken for granted.
There still persists a myth that mathematics somehow
involves numbers. Many fondly believe that university
students spend their time long dividing by 173 and
learning their 39 times table; in fact, the reverse is
true. Mathematicians are renowned for their inability to
add up or take away, in much the same way as geographers
are always getting lost, and economists are always
borrowing money off you.
-- R. Ainsley in Bluff your way in Maths, 1988
There are two glasses of wine, one white and one red. A teaspoonful of
wine is taken from the red and mixed in with the white. Then a teaspoonful
of this mixture is taken and mixed in with the red. Which is bigger, the
amount of red in the white or the amount of white in the red?
The answer is that the're both the same, because there's the same volume
in each glass, so whatever quantity of red is in the white must be equal
to the quantity of white in the red. However in practice it is impossible
to do this because the white always runs out first at parties and the red
always gets spilt on someone's white trousers.
-- R. Ainsley in Bluff your way in Maths, 1988
Taking logs - Broadly speaking, any equation which looks difficult
will look much easier when logs are taken on both sides. Taking logs
on one side only is tempting for many equations, but may be noticed.
-- R. Ainsley in Bluff your way in Maths, 1988
Proof by induction - A very important and powerful mathematical tool,
because it works by assuming something is true and then goes on to
prove that therefore it is true. Not surprisingly, you can prove almost
everything by induction. So long as the proof includes the following
phrases:
a) Assume true for n; then also true for n+1 because.. (followed by
some plausible but messy working out in which n, n+1 appear prominently).
b) But is true for n=0 (a little more messy working out with lots of
zeros sprayed at random through the proof).
c) So is true for all n. Q.E.D.
-- R. Ainsley in Bluff your way in Maths, 1988
The barber in a certain town shaves all the people who don't
shave themselves. Who shaves the barber?
This is meant to be a clever little paradox with no solution
but you can annoy the asker intensely by saying it's easy and
that the barber is a women.
You can then ask the following (a version of Russell's
Paradox, - point this out too): in a library there are some
books for the catalogue section which is a list of all books
which don't list themselves. Shold he or she include this book
in its own list? If so, then it becomes a book which lists
itself, so it shouldn't be in the list of books which don't
and vice versa. This should keep the most determined assailant
at bay while you attack the wine.
-- R. Ainsley in Bluff your way in Maths, 1988
Mathematics consists essentially of :
a) proving the obvious
b) proving the not so obvious
c) proving the obviously untrue
For example, it took mathematicians until the 1800'ies to
prove that 1+1=2 and not before the late 1970 were they
confident of proving that any map requires no more
than four colors to make it look nice, a fact known by
cartographers for centuries.
There are many not-so-obvious things which can be proved true
too. Like the fact that for any group of 23 people, there is
an even chance two or more of them share birthdays. (With
groups of twins this becomes almost certain. Not quite certain
as you will of course point out: they might all have been born
either side of midnight).
Mathematicians are also fond of proving things which are obviously
false, like all straight lines being curved, and an engaged telephone
being just as likely to be free if you ring again immediately after,
as if you wait twenty minutes.
-- R. Ainsley in Bluff your way in Maths, 1988
At the end of a proof you write Q.E.D, which stands not for
Quod Erat Demonstrandum as the books would have you believe, but
for Quite Easily Done.
-- R. Ainsley in Bluff your way in Maths, 1988
Prime number - A number with no divisors. Boxes of chocolates always
contain a prime number so that, whatever the number of people present,
somebody has to have that one left over.
-- R. Ainsley in Bluff your way in Maths, 1988
sin, cos, tan, cot, sec, cosec - Formulae derived from the sides of
triangles but which crop up in completely unexpected places. Sins are
extremely common, but rarely do you encounter secs in mathematics.
-- R. Ainsley in Bluff your way in Maths, 1988
Transcendental number : A number which is not the root of any
polynomial equation, like pi and e, and which can only be
understood after several hours meditation in the lotus position.
-- R. Ainsley in Bluff your way in Maths, 1988