Exact Results in Quantum Theory

In searches for new phenomena in particle physics, we are often interested in observing tiny deviations from the Standard Model (SM) predictions. In consequence, the SM predictions must be known very precisely. This is often a challenge even in situations when purely perturbative calculations are sufficient. At present, the most powerful methods amount to expressing the observables of interest in terms of so-called Master Integrals (MIs). The MIs are not being evaluated directly but rather via solving systems of differential equations. In the process of finding the MIs via the Laporta algorithm, large numbers (often billions) of linear equations need to be generated and solved, with simplifications of complicated rational functions at each step. In consequence, even the most powerful present-day computer clusters are sometimes insufficient. The situation could radically improve is a clever mathematical solution of the considered algebraic problem could be found in general.