The abstract says:

The patenting of software-related inventions is on the increase, especially in the United States. Mathematical formulas and algorithms, though, are still sacrosanct. Only under special conditions may algorithms qualify as statutory matter: if they are not solely a mathematical exercise, but if they are somehow linked with physical reality. In this article, the best results are obtained if formulas and algorithms are only protected in combination with a proof that supports them. This argument is developed by conducting a thought experiment. After describing the development of algebra from the 16th century up to the 20th century (in particular, the solution of the cubic equation), the likely effects on the development of mathematics as a science are analyzed in the context of postulating a patent regime that would actually have been in force protecting mathematical inventions.

Laat points out the inconsistencies brought about in the US by limiting patent claims to applications of mathematics, citing the Karmakar and RSA examples. He then cites examples of advances in mathematical knowledge in renaissance times that were kept secret and that, according to Laat, would probably have been published earlier if there had been a patent system in place. Laat concludes

What lessons can be drawn from this thought experiment? If the results are any guide to present-day developments, they would argue for a BLANKET ACCEPTANCE of mathematical formula and algorithms as statutory matter for patent applications. Let us finally acknowledge that mathematics belongs not only to the 'liberal arts' but also the 'useful arts'. Let us abolish the 'pure-number condition'; even if it is all mathematical abstraction, this is acceptable. There is no need to specify links with 'physical elements' or 'process steps', with 'pre-computer' or 'post-computer process activity'. Even if nothing of the sort is specified, the claim is acceptable. Let us not bother that the claim 'wholly preempts' the use of the algorithm; let all possible commercial applications effectively become protectable. It should be stressed that noncommercial, in particular academic, use is to remain possible (experimental use exception). Actually, it is the development of both (pure) science and (applied) technology that the system is designed to foster. Such unconditional acceptance, however, should be carefully formulated as to what is protected and what is not. While the protection of formulas tout court is acceptal in societal terms, the best results seem to be obtained when algorithms and formulas are only patentable in combination with a supporting proof. That arrangements keeps avenues open for inventive mathematicians to develop alternative methods of proof.

Laat suggests that patent monopolies could have helped to incite pure mathematical research activity as long as that activity itself is patent-free. However he does not attempt to weigh the possible burden that these monopolies place on the overall economy. Although he correctly states that such a general patentability shifts the focus to the question of what kind of activities can constitute infringement and advocates that there should be clear restrictions concerning this, he does not propose any helpful criteria that could serve to clarify these restrictions in a consistent and meaningful manner. He does however issue some warnings about the possible consequences of his approach, saying e.g. that 16th century examples may not be adequate for analysing today's problems and that there is a danger that too burdensome monopolies could be imposed on society by this approach.