Mathematicians Made of Silicon
A computer that independently formulates mathematical assumptions and also proves them - that's what many scientists dream of. New methods of artificial intelligence could bring the vision of the future a little closer.
"At some indefinite future date, mathematicians will be replaced by computers." The daring prediction is said to have been made by renowned mathematician Paul Cohen (1934–2007) in the 1970s. To this day, the statement has met with opposition from his colleagues. Cohen has always been a lateral thinker: his revolutionary methods in set theory earned him the Fields Medal, making him the first and only person to receive the coveted award for work in logic. He also argued controversially that all mathematics could be automated, including proof-making.
Contrary to what one might think from the experience of mathematics class, the work of a mathematician does not consist of calculating. Its main task is to provide irrevocable evidence for formal statements. A proof is a step-by-step logical argument that tests whether a conjecture is true. Once proved, a conjecture becomes a theorem (also called a theorem). In addition, evidence explains why a statement is valid-or false. Nevertheless, they are difficult to grasp because the arguments move in an extremely abstract world that has nothing to do with our everyday experiences. "We humans aren't cut out for the kind of task," says cognitive scientist Simon DeDeo of Carnegie Mellon University in Pittsburgh.
Up until now, computers have mostly been used to carry out large calculations. But mathematics requires something else. Conjecture arises from inductive reasoning, a person has to intuitively think about an interesting problem. Proofs usually follow a deductive, step-by-step logic. To do this, you often combine complicated connections in a creative way and then laboriously fill in all the existing gaps in your argumentation. Machines have not yet mastered such tasks.
Nevertheless, there are first approaches as to how algorithms can support the work of mathematicians…