In an intuitionistic way.

A person who studies intuitionistic mathematics

(mathematics, logic) Dealing strictly in constructive proofs, abstaining from proof by contradiction

plural of intuitionist

(mathematics, logic) A type of logic which rejects the axiom law of excluded middle or, equivalently, the law of double negation and/or Peirce's law. It is the foundation of intuitionism.

plural of intuitionistic logic