In our Who's watching project we have been exploring the physics of observers. But observations also play a role in mathematics. We often get ideas about general results in mathematics by observing specific examples and specific examples also give us a feel for what a general result really means.
But unlike physicists, mathematicians don't need to "see" something to be certain it exists. Many mathematical proofs show that a mathematical object exists by logical necessity, without actually constructing them. Are these proofs really as valid as constructive proofs? And what happens if you try and avoid them? Find out with this collection of articles.
Background reading and further reading
This package is part of our Who's watching? The physics of observers project, run in collaboration with FQXi. Click here to see more articles and videos about questions to do with observers in physics.