Mathematics involves discovering and using patterns to formulate and prove conjectures, resulting in theorems. Defining new algebras or geometric characteristics with desired properties remains a challenge. Available approaches lack rigour and efficiency. During this internship, the student will work with scientists from IBM Research, UK and USA to advance the state-of-the-art methods for aiding the certifiability of mathematical results and streamlining the discovery process. Developed tools will be used to seek new connections between algebraic and geometric structures.