Close to a century ago, researchers discovered that there are some questions in mathematics that cannot be answered. In his research project funded by the FWF START Award, Juan P. Aguilera wants to bring together different areas of mathematics in order to develop new logic tools. These should help to find out which questions actually have answers and which do not. In his FWF-START project “Proofs Beyond the Transfinite,” he combines proof theory, computability theory, and set theory to search beyond infinity for mathematical tools to determine whether mathematical questions have answers or not.
Juan P. Aguilera first studied applied mathematics and then completed his doctorate at TU Wien on the subject of infinity in mathematics. He has worked as a visiting scholar at Harvard University, Rutgers University, the University of Cambridge, and the University of Hamburg and has held a position at the University of Vienna. His contributions to mathematics have been recognized with several awards and in 2023 he completed his habilitation thesis on mathematical logic. He is currently working at TU Wien.