The main  research interest of Arianna Borrelli is on the emergenge of natural philosophical and scientific knowledge from the interplay of different methods of knowledge mediation: objects, words, symbols, numbers, procedures, images and much more. This approach tries to gain a "media perspective" on science studies.

Some ideas developed in Arianna Borrelli's publications concern:

• the astrolabe and medieval mathematical cosmology
• the observation and explanation of heat, cold and temperature from Antiquitiy to the present
• the interplay of mathematical formalism and experimental practice in the construction of classical and quantum mechanical notions of angular momentum
• the hybrid nature of key concepts in contemporary high-energy-physics, where mathematical  elements are inextricably interwoven with verbal narratives, giving rise to constructs like spontaneous electroweak symmetry breaking and the Higgs boson - a.k.a. “the God particle".

It is a fact that scientific knowing usually results both in new concepts and in new forms capable of expressing them and involves  any a priori limitation of this list would be regarded by many as non-scientific.
If knowledge is never independent from its modes and contexts of production and communication, the above list corresponds to an equally unlimited variety of knowing enterprises. At the same time, scientific knowing seems to be characterized by a drive never to rest in one medium, be it word, experimental set-up, number or operational definition. The result is a constant tension between theory and practice, an entanglement of materiality and abstraction whose richness grows with technical possibilities. Here lies a most promising focus for future research. Studies have brought insights on "paper tools", "thinking with objects", "artisan epistemology", "the mindful hand", and on the "trading zones" in which specialists from different disciplines communicate [1].

To proceed in this direction of research it is fruitful to take advantage both of methods and results of media studies, which are themselves an interdisciplinary enterprise questioning the borders between materiality and abstraction, production and communication. Media perspectives have helped see the "scientific" in the "artistic" - experiences in new media arts offer new perspectives on materiality and abstraction in techno-scientific research. Paths opened by media philosophers help grasp and compare internal and external histories of (scientific?) knowing of all ages and cultures. Those paths were most often followed in studies on life sciences, chemistry or early modern philosophy - less so  in analyses of the digital-symbolic-mathematical apparatuses interfacing subject and object in the exact sciences. Or in asking about the origin and gender of the purity of pure mathematics. Or in exploring measure and measures - from Chinese flutes to the Timaios, from “mathesis intensorum” to Lebesgue integrals, ISO norms and credit rating agencies.

Provided one takes into due account all the situated feature of the different cutlural-historical constellations, the tension between knowledge and its form can be investigated in different epochs and cultures.
References:
[1] D. Bertoloni Meli, Thinking with objects. The transformation of mechanics in the seventeenth century (Baltimore 2006)
P. Galison, Image and logic. A material culture of microphysics (Chicago 1997)
U. Klein, Experiments, models, paper tools. Cultures of organic chemistry in the nineteenth century (Stanford 2003)
L. Roberts, S. Schaffer and P. Dear (eds.), The mindful hand. Inquiry and invention from the late Renaissance to early industrialisation (Amsterdam 2007)
P. H. Smith, The body of the artisan. Art and experience in the scientific revolution (Chicago 2004)