Michael Friedman

How can one frame recent AI-based geometrical achievements like AlphaGeometry within the broader trajectory of the mechanization of geometry in the 20th century? This paper examines the historical marginalization of material, hand-drawn diagrams in the framework of such mechanization, arguing that mechanized geometric problem-solving has systematically displaced embodied visual reasoning. Indeed, between the 1930s and 1970s, the push to mechanize geometry marginalized physical diagrams by translating them into algebraic or coordinate systems; these foundational efforts established a precedent where diagrammatic reasoning was either bypassed entirely or outsourced to computers. In this framework, 21st century AI systems like Google’s AlphaGeometry represent the culmination of this trend: these technologies operate in quantitative regimes outside human sense perception, generating diagrams only retroactively – if at all – for human readers rather than using them as material tools for discovery. This marks a profound epistemological shift, which may replace geometry as an embodied, material practice with opaque algorithmic encodings.