# A Mathematical Perspective

Of all the branches of modern science, mathematics has been the common
denominator to progress and it is an appropriate starting point for
our scientific discussion. However, it will be argued that there is
a key distinction between a mathematical proof and a physical proof,
because mathematics may only be correct within the assumptions of an
original model. So, as science has moved ever further beyond the realm
of *human experience*, the nature
of *empirical verification* has become
increasingly problematic and increasingly dependent on mathematical
proof. Therefore, we need to initially reflect on this aspect of mathematics
and, in part, consider the philosophical implications of how and why
mathematics has come to underpin modern scientific models.

The Greek philosopher, Plato, was one of the first to articulate
the relationship between mathematics and the underlying order of the
universe, when he wrote of his *
Doctrine of Forms*`. Euclid
had proved that there are only five solid shapes that can be made from
simple polygons, but it was Plato who went on to speculate that there
were, in fact, two different universes:

- A physical universe of everyday objects.
- A mathematical universe of perfect forms.

Plato argued that there were mathematical laws governing all of nature
and, as such, mathematics was not an invention of humanity, but rather
the discovery of its independent existence. In fact, the corollary of
Plato's argument suggests that the deeper we try to examine physical
reality, the more we will become aware of a larger reality comprised
of mathematical truth. Of course, at this point, you might be thinking
that this idea is simply reflective of the general philosophy of the
*ancient Greeks*. However, it seems
to be an idea supported by modern mathematicians and physicists,
such as Roger Penrose, Professor of Mathematics at Oxford University and
Max Tegmark, a physicist at MIT. In fact, Max Tegmark is the author
of a theory called the *'Mathematical Universe Hypothesis (MUH)'*
in which he claims that mathematical entities actually exist, which
is an extension of Platonism that merely suggests that mathematical
objects exist in another reality. Without recourse to too much detail,
Tegmark suggestion is based on a modern scientific interpretation of
*physical reality*:

"If we assume that reality exists independently of humans, then for a description to be complete, it must also be well-defined according to non-human entities - aliens or supercomputers, say - that lack any understanding of human concepts. Put differently, such a description must be expressible in a form that is devoid of any human baggage like 'particle', 'observation' or other English words."

As such, he concludes that a universe of pure mathematics, free of human baggage, would be a likely contender for the basis of our reality:

"A description of objects in this external reality and the relations between them would have to be completely abstract, forcing any words or symbols to be mere labels with no preconceived meanings whatsoever."

Of course, there are other schools of thought, which hold to a more
pragmatic notion that mathematical concepts, like musical scores, are
simply an extension of human thought. However, no matter how you align
to these philosophical arguments, it is clear that any understanding
of scientific development requires some complementary understanding
of developments within mathematics, which is now the focus of the rest
of the section.