Ramanujan Auditorium

Results and Models : An Illustration through sum of cubes

Jean-Marc Deshouillers

University of Bordeaux

Number theory has the knack for phrasing easily understandable
statements which are hard to prove.

An archetype is Goldbach’s problem (1742), which is still unsolved :
_every even integer larger than 4 is a sum of two primes._

The root of the talk is Waring’s problem (1770), which states - for
cubes - that _every integer is a sum of at most 9 cubes. _It has been
proved in 1909-1912, but we expect much more, namely _every
sufficiently large integer is a sum of 4 cubes._

In the frame of this understantable question, we shall illustrate how
mathematicians _prove _weaker statements, lead _computation, _build
_models _to comfort their belief in statements they cannot prove.