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The Importance of Cross-fertilization of Ideas

by Sol Lederman on Tue, 19 May, 2009

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., 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. 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, that the Riemann Hypothesis will itself give way to the power of cross-fertilization of ideas.

Sol Lederman

OSTI Consultant

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About the Author

Sol Lederman's picture
Sol Lederman

Contractor to OSTI serving in various technical and communication roles.