The interactions between mathematics and mathematical physics studied by Atiyah led to the introduction of instantons - solutions, that is, of a certain nonlinear system of partial differential equations, the self-dual Yang-Mills equations, which were originally introduced by physicists in the context of quantum field theory. Drinfeld and Manin worked on the construction of instantons using ideas from algebraic geometry.
Ang mga pakikipag-ugnayan sa pagitan ng matematika at matematika physics-aral sa pamamagitan ng Atiyah na humantong sa pagpapakilala ng instantons - solusyon, iyon ay, ng isang tiyak na nonlinear sistema ng bahagyang kaugalian equation, ang self-doble Yang-Mills equation, na kung saan ang orihinal na nagpasimula ng physicists sa konteksto ng quantum field theory. Drinfeld at Manin nagtrabaho sa construction ng instantons gamit ang mga ideya mula sa algebraic geometry.