Sometimes mathematical theory is even more critical to performance. In the words of B.R. Rich, a recently retired vice-president of the Lockheed-Martin Corporation and former chief of Lockheed's Advanced Development Projects division (the so-called `Skunk Works'), ``the Rosetta Stone breakthrough for stealth [fighter] technology'' was a new theory developed by ``an exceptional 36-year-old Skunk-Works mathematician'', not a new development in engineering. The F-117A stealth fighter was designed using a novel mathematical theory for determining radar cross-sections of general three-dimensional bodies, and optimizing it subject to constraints. Although the theory was conceived at the height of cold war tensions in the mid-1970's, it was instigated by a research paper published by a Soviet radar engineer. (The Soviets were not working on stealth technology.) It has its roots in theory developed by the Scottish physicist James Clerk Maxwell, more than a century ago.
The body shape of the F-117A was designed in the late 1970's, when computers were not as powerful as they are today. Software for minimizing radar cross-sections is based on approximating it by a pattern of triangles. The optimization routine is much more computationally intensive for round-surfaced bodies, which must use very small triangles in the approximation, than it is for flat-sided ones. Therefore, the F-117A has a flat-sided fuselage, with sharp edges where the sides join. Second-generation stealth technology, embodied for example in Northrop's B-2 bomber, uses more powerful computers, and so admits a more rounded shape.
It has been said that the shape of the F-117A aircraft, and hence also the mathematical theory and algorithms that produced it, are responsible for 85% of the fighter's low radar-visibility. The remaining 15% derives mainly from new materials and other engineering advances. Whatever the true ratio, there can be no doubt that stealth aircraft rely fundamentally on mathematical technology, for both their concept and design. Without adequate investment in mathematical science, including both training and high-level research, no country can be technologically competitive.
