48
R. Barrett and P. P. Delsanto
Not all of Ramanujan’s conjectures 4 turned out to be true, but many
of them did, and they were ground-breaking in their originality. Hardy
and Ramanujan worked together to develop formal proofs for them, an
exercise that interested Hardy much more than Ramanujan, who preferred
to approach his Goddess for further exciting titbits of information. This
unusual collaboration was cut short by the untimely death of Ramanujan
from consumption in 1920 at the age of 32. The story of this strange partnership has been narrated by Robert Kanigel [6]. Some of Ramanujan’s
highly unorthodox results have inspired much research by later generations
of mathematicians, with applications in fields as diverse as String Theory and
Crystallography. The reason for recounting this story here is to show how,
even in the normally rigorous discipline of mathematics, different points
of view can be adopted. Certainly no modern mathematician would feel
comfortable with the ad hoc conjectural methodology of Ramanujan, and
would not be satisfied until a formal proof of their conjectures had been
established. However, how many are willing to go to the lengths of Whitehead and Russell in their search for rigour? This last question becomes even
more relevant when we discover, in Chap. 4, that such a quest is doomed
from the outset to failure.
3.5 Truth and Beauty
‘Beauty is Truth, Truth Beauty,’ - that is All Ye Know on Earth, and All Ye Need
to Know.
The above lines from John Keats’ “Ode to a Grecian Urn” have incited
much debate in the world of English literature. Whether the poem can be
classed as good or bad is not for us to discuss here. Suffice it to say that on
that topic there is a multitude of different opinions.
A Sosibios Greek vase from the Louvre was one of the sources of Keats’
inspiration. It is of a classic form that was regarded by the Greeks as possessing
great beauty. Figure 3.2 below shows a terracotta amphora from the period
ca. 525 – 500 BCE that demonstrates this classical shape. The cylindrical
symmetry of the vase is elegantly broken by the two handles, which have
their own bilateral symmetry about a vertical plane.
It may seem incongruous, in a book on physics, to talk about beauty, and
yet, as we shall see in the following, beauty and symmetries have played their
part in guiding scientific thought, and we shall see that analogies can be
4 Conjectures in mathematics are statements which are believed to be true, but have not (yet) been
proved.
R. Barrett and P. P. Delsanto
Not all of Ramanujan’s conjectures 4 turned out to be true, but many
of them did, and they were ground-breaking in their originality. Hardy
and Ramanujan worked together to develop formal proofs for them, an
exercise that interested Hardy much more than Ramanujan, who preferred
to approach his Goddess for further exciting titbits of information. This
unusual collaboration was cut short by the untimely death of Ramanujan
from consumption in 1920 at the age of 32. The story of this strange partnership has been narrated by Robert Kanigel [6]. Some of Ramanujan’s
highly unorthodox results have inspired much research by later generations
of mathematicians, with applications in fields as diverse as String Theory and
Crystallography. The reason for recounting this story here is to show how,
even in the normally rigorous discipline of mathematics, different points
of view can be adopted. Certainly no modern mathematician would feel
comfortable with the ad hoc conjectural methodology of Ramanujan, and
would not be satisfied until a formal proof of their conjectures had been
established. However, how many are willing to go to the lengths of Whitehead and Russell in their search for rigour? This last question becomes even
more relevant when we discover, in Chap. 4, that such a quest is doomed
from the outset to failure.
3.5 Truth and Beauty
‘Beauty is Truth, Truth Beauty,’ - that is All Ye Know on Earth, and All Ye Need
to Know.
The above lines from John Keats’ “Ode to a Grecian Urn” have incited
much debate in the world of English literature. Whether the poem can be
classed as good or bad is not for us to discuss here. Suffice it to say that on
that topic there is a multitude of different opinions.
A Sosibios Greek vase from the Louvre was one of the sources of Keats’
inspiration. It is of a classic form that was regarded by the Greeks as possessing
great beauty. Figure 3.2 below shows a terracotta amphora from the period
ca. 525 – 500 BCE that demonstrates this classical shape. The cylindrical
symmetry of the vase is elegantly broken by the two handles, which have
their own bilateral symmetry about a vertical plane.
It may seem incongruous, in a book on physics, to talk about beauty, and
yet, as we shall see in the following, beauty and symmetries have played their
part in guiding scientific thought, and we shall see that analogies can be
4 Conjectures in mathematics are statements which are believed to be true, but have not (yet) been
proved.