In the philosophy of mathematics, mathematical constructivism asserts that it is necessary to find (or "construct") a mathematical object to prove that it exists. When you assume that an object does not exist, and derive a contradiction from that assumption, you still have not found it, and therefore not proved its existence, according to constructivists.
Constructivism is often confused with mathematical intuitionism, but in fact, intuitionism is only one kind of constructivism. Intuitionism maintains that the foundations of mathematics lie in the individual mathematician's intuition, thereby making mathematics into an intrinsically subjective activity. Constructivism does not, and is entirely consonant with an objective view of mathematics.
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2 Branches of constructivist mathematics
3 See also
Mathematicians that have contributed to constructivism
Branches of constructivist mathematics