Applying pure mathematics: mathematics in the natural sciences

The book of nature is written in the language of mathematics. This quotation, attributed to Galileo, seemed to hold to an unreasonable1 extent in the era of quantum mechanics.

A playful side to twelfth-century mathematics

As editors of the book Lilavati's Daughters: The Women Scientists of India, reviewed by Asha Gopinathan (Nature 460, 1082; 2009), we would like to elaborate on the background to its title. Lilavati was a mathematical treatise of the twelfth century, composed by the mathematician and astronomer Bhaskaracharya (1114–85) — also known as Bhaskara II — who was a teacher of repute and author of several other texts. The name Lilavati, which literally means 'playful', is a surprising title for an early scientific book. Some of the mathematical problems posed in the book are in verse form, and are addressed to a girl, the eponymous Lilavati. However, there is little real evidence concerning Lilavati's historicity. Tradition holds that she was Bhaskaracharya's daughter and that he wrote the treatise to console her after an accident that left her unable to marry. But this could be a later interpolation, as the idea was first mentioned in a Persian commentary. An alternative view has it that Lilavati was married at an inauspicious time and was widowed shortly afterwards. Other sources have implied that Lilavati was Bhaskaracharya's wife, or even one of his students — raising the possibility that women in parts of the Indian subcontinent could have participated in higher education as early as eight centuries ago. However, given that Bhaskara was a poet and pedagogue, it is also possible that he chose to address his mathematical problems to a doe-eyed girl simply as a whimsical and charming literary device.

Mathematics, nature and cryptography: Insights from philosophy of information

One influential image that is popular among scientists is the view that mathematics is the language of nature. The present article discusses another possible way to approach the relation between mathematics and nature, which is by using the idea of information and the conceptual vocabulary of cryptography. This approach allows us to understand the possibility that secrets of nature need not be written in mathematics and yet mathematics is necessary as a cryptographic key to unlock these secrets. Various advantages of such a view are described in this article.

Segregating Discourse Segments from Engineering Documents for Knowledge Acquisition

The broader goal of the research being described here is to automatically acquire diagnostic knowledge from documents in the domain of manual and mechanical assembly of aircraft structures. These documents are treated as a discourse used by experts to communicate with others. It therefore becomes possible to use discourse analysis to enable machine understanding of the text. The research challenge addressed in the paper is to identify documents or sections of documents that are potential sources of knowledge. In a subsequent step, domain knowledge will be extracted from these segments. The segmentation task requires partitioning the document into relevant segments and understanding the context of each segment. In discourse analysis, the division of a discourse into various segments is achieved through certain indicative clauses called cue phrases that indicate changes in the discourse context. However, in formal documents such language may not be used. Hence the use of a domain specific ontology and an assembly process model is proposed to segregate chunks of the text based on a local context. Elements of the ontology/model, and their related terms serve as indicators of current context for a segment and changes in context between segments. Local contexts are aggregated for increasingly larger segments to identify if the document (or portions of it) pertains to the topic of interest, namely, assembly. Knowledge acquired through such processes enables acquisition and reuse of knowledge during any part of the lifecycle of a product.