To anyone who loathed school algebra,
the notion of mathematical beauty may sound unlikely,
yet among mathematicians there is no higher praise than to have a new result
hailed as not only merely correct but also beautiful
Opinions naturally differ about just how beautiful a particular
result truly is. Some years ago, a poll was taken among mathematicians to
find out which discovery was thought to be the most beautiful of them all.
The winner was a formula found by the Swiss mathematician Leonhard Euler
in 1748, which states that when one is added to the transcendental
number "e" (roughly 2.71828)raised to the power of pi (roughly
3.14159) multiplied by the square-root of minus
one, the result is precisely zero.
Combining the five most important numbers in all mathematics,
the formula is clearly a marvel of brevity. Yet it is the sheer
implausibility of any relationship existing between such disparate
numbers that gives Euler's formula its intellectual shock value. I
can still recall exactly where I was a quarter of a century ago when Mr Clark,
our A-level maths teacher, first wrote Euler's formula on the blackboard.
Among theoretical physicists, the search for
beauty among the equations counts for even more
than mere plaudits from their colleagues. For them it has become almost
an article of faith that, as Keats put it, "beauty is truth,
It centres on attempts to find the equations governing the cosmos.
For most of human history, the universe was
thought to be infinite, everlasting and static - not least because the
alternatives were too mind-boggling to
A decade later, Einstein discovered that he had made the biggest
blunder of his life. Astronomers had found that the universe is expanding
after all - just as Einstein's original equations had shown. Incensed at
having ignored his own aesthetic instincts, Einstein dropped the ugly extra
term, and vowed never to deal with it again.
For the next 70 years cosmologists followed
suit, with such luminaries as Prof Stephen
Hawking coming up with elegant arguments for why Nature would never allow
the ugly extra term to sully Einstein's masterpiece.