Being someone who really loves mathematics I enjoy reading about the lives of mathematicians, about how they think, and about how they solve problems. And, as an OSTI consultant I recognize the value of having access to the ideas of others when performing research.

As I read stories of the brilliant
mathematicians, especially ones like Gauss, Fermat, and Pythagoras who lived
hundreds of years ago, I wonder how much more they might have accomplished if
each had access to all of the important works of all of his or her predecessors
and contemporaries, not only in his or her specialized fields but in all of the
natural sciences. The cross-fertilization of ideas, the unexpected connections
between seemingly disjoint fields of science, that is critical to advancing
science. Through a number of powerful products and services OSTI provides a
tremendous foundation for this cross-fertilization.

I recently read "The Music of the Primes," by Marcus du
Sautoy. The book tells a very fascinating story about the search for patterns
among prime numbers. It turns out that this search is not just driven by
intellectual curiosity. Important results that affect our lives are derived
from our understanding of prime numbers. Alan Turing's success in cracking the German
Enigma machine and the security of our electronic financial transactions come
directly from our understanding of the primes. Error detecting and error correcting
technology, so critical to modern electronic communication systems, owes its
existence to the primes as well. Casting a wide net is critical to making those
unexpected connections and to advancing science. WorldWideScience.org, the
global gateway to science conceived at OSTI, accesses scientific and technical
information from countries that include 73% of the world's population.

Du Sautoy's book chronicles the heroic efforts of
mathematicians and physicists to crack the 150 year-old Riemann Hypothesis, a
very esoteric conjecture that is closely related to patterns among primes. A
major theme of these creative thinkers is that they depend heavily upon the
efforts of others. Each mathematician must stand on the shoulders of those who explored
the problem earlier and he or she must join forces with his or her cohorts.
This is the way it is for all of science. There are so many new ideas being
presented, and new discoveries being made, and many of these new ideas and
discoveries build upon the insights of others. And, these "others" are not
always scientists in one's own narrow field.

A good illustration of the importance of cross-fertilization
is the mammoth effort to prove Fermat's Last Theorem,
which was technically a conjecture until Andrew Wiles proved it in 1994. Fermat's
Last Theorem is related to prime numbers in some subtle ways and it resisted
proof for 300 years. Although Wiles worked secretly for seven years so as to
not be distracted, and undoubtedly to not share the glory, Wiles did build on
the research results of others, including work that had been performed related
to the Riemann Hypothesis. Plus, the development of ring theory and the
bridging of algebra and analysis owes much to the search for the proof of
Fermat's Last Theorem.

We know that during the years that Wiles worked in isolation
he scoured the mathematical research in search of conjectures, theorems, and
approaches to solving related problems that might help him to crack this most
favorite problem. In light of what it took Wiles to solve the famous theorem,
we can all appreciate the value of making a wide array of science available to
researchers. Diversity of sources is just as important as is diversity of
research papers because different publishers, in the US and abroad, may publish
content with different perspectives based on their editorial policies.
WorldWideScience.org exemplifies the power of forming an alliance of nations
with the sole purpose of making their best science available to the public.
Never before has the American public been able to search over 300 million pages
of scientific literature from dozens of nations in a single search form. It may
be that someday, as a result of documents found via WorldWideScience.org, that
the Riemann Hypothesis will itself give way to the power of cross-fertilization
of ideas.

Sol Lederman

OSTI Consultant