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1. Introduction
Just at the close of the 20th century a dramatic announcement was made: the
completion of a blueprint for the human genome. This milestone for mankind was
the culmination of a nearly 150 year old odyssey begun with the research and
dramatic discoveries of the monk Gregor Johann Mendel (1822-1884). Without question,
developing this blueprint for the human genome was one of the landmarks of the
history of biology.
The 20th century was a period of dramatic progress in all the sciences. However,
perhaps no work was more dramatic in its implications than the birth of molecular
biology. Molecular biology offered a vision of human beings understanding the
complexities of life from the bottom up. Yet one of the characteristics of 20th
century science was that no part of science was an island unto itself; all the
sciences benefited from insights and accomplishments drawn from the others.
During this exciting period mathematics proved to be a handmaiden of the progress
that was being made across the board. However, the way that mathematical science
has played an accelerating role in speeding up the developments in understanding
the genome is part of an ongoing partnership between mathematics and biology
in general. While once molecular biology was a new subject, it is now a mature
subject which has bifurcated into many parts, including molecular genetics.
Molecular genetics has fused with a long tradition of mathematical support for
genetics in general.
The ways that mathematics has contributed to insight into the genome of humans
and other species is a fascinating subject. Here I can only touch a few aspects
of this interaction. I will begin with a brief history of mathematical involvement
with genetics, then I will look at how the mathematical insight into the concept
of distance has proved to be a boon for insight into complex biological (as
well as other) problems. Sprinkled throughout I will point out some of the problems
still open that are sources of further investigation. Before continuing you
may wish to consult the primer of molecular
biology and genetics which helps put in perspective the discussions that follow.
Joseph Malkevitch
York College (CUNY)
Email: malkevitch@york.cuny.edu
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