Corns are usually symptomatic of underlying problems- ill fitting shoes, constant rubbing from uneven distribution of pressure, walking habits etc. thick painful protrusion is just the response of the skin of the sole to the undue and uneven pressure.
Getting rid of the underlying cause is the first thing to do- better shoe measurements and finding right size shoes, soft insoles, silicone wedges to support the skin, all work. An already formed corn can be softened with foot products such as salicylate creams, soft Protectice corn plastersetc. Customised padding will also help to alleviate symptoms and slowly but surely eliminate the corn.
Speciality formulated liquid nitrogen will also 'freeze' the corn which will then get inflamed and extruded. Formal 'surgery' is not needed, as a podiatrist can cut away hard skin but this is usually only required for adults.