First of two articles on software patents

In 1997 the U.S. Patent and Trademark Office granted Amazon.com a patent for "one-click shopping"--a system that lets customers make purchases without having to go through an online checkout. The patent started a fierce debate in both the business and the technical press. Critics felt the Amazon.com patent was the poster child for everything that was wrong with software patents, charging that such patents allowed obvious applications of existing technology to be wrapped up in intellectual property monopolies.

The Amazon.com patent is no fluke. Consider the following recently issued patents:

**Method and system for solving linear systems (U.S. Patent No. 6078938)** .

**Cosine algorithm for relatively small angles (No. 6434582)** .

**Method of efficient gradient computation (No. 5886908)** .

**Methods and systems for computing singular value decompositions of matrices and low rank approximations of matrices (No. 6807536)** .

The arcane details of these patents are not relevant. What is relevant is that these patents are for purely mathematical algorithms, and for centuries prior to the 1990s, mathematics was not patentable. So how did these patents come to be granted?

By U.S. law, scientific principles may not be patented. Electromagnetism, the theory of relativity, and a menagerie of quantum particles were all discovered after the inception of the U.S. Patent and Trademark Office, now based in Alexandria, Va. Yet none of these discoveries could have received patents, because until the early 1990s it was universally agreed that mathematical algorithms were in the category of scientific principles that could not be owned by an individual.

What has changed is that mathematics has become increasingly reliant on machines. Abstract algorithms that involve inverting large matrices or calculating hundreds of coefficients in a sequence are routine today and of only limited use without physical computers to execute them.

Conversely, devices such as video drivers, network interface cards, and robot arms depend on algorithms for their operation. Because of the machine-intensiveness of modern mathematics and the math-intensiveness of modern machines, the line between mathematical algorithms and machinery is increasingly blurred. This blurring is a problem, because without a clear line delimiting what is patentable and what is not, creative entrepreneurs will eventually be able to claim sole ownership of abstract mathematical discoveries. But how do we draw a line that would ensure that mathematical algorithms are not patentable while innovative machines are?

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