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General acceptance of a mathematical proposition $P$ as a theorem requires convincing evidence that a proof of $P$ exists. But what constitutes convincing evidence? I will argue that, given the types of evidence that are currently accepted as convincing, it is inconsistent to deny similar acceptance to the evidence provided for the existence of proofs by certain randomized computations.
This paper describes in basic terms what a Thin Group is, as well as its uses in various subjects.
Quantum simulators are devices that actively use quantum effects to answer questions about model systems and, through them, real systems. Here we expand on this definition by answering several fundamental questions about the nature and use of quantum
We consider idealized parton shower event generators that treat parton spin and color exactly, leaving aside the choice of practical approximations for spin and color. We investigate how the structure of such a parton shower generator is related to t
We discuss a generalization of logic puzzles in which truth-tellers and liars are allowed to deviate from their pattern in case of one particular question: Are you guilty?
This paper aims at providing a global perspective on electromagnetic nonreciprocity and clarifying confusions that arose in the recent developments of the field. It provides a general definition of nonreciprocity and classifies nonreciprocal systems