In this paper we study generic complexity of undecidable problems. It turns out that some classical undecidable problems are, in fact, strongly undecidable, i.e., they are undecidable on every ...

The French scholar Pierre-Simon Laplace crisply articulated his expectation that the universe was fully knowable in 1814, asserting that a sufficiently clever “demon” could predict the entire future ...

His incompleteness theorems destroyed the search for a mathematical theory of everything. Nearly a century later, we’re still coming to grips with the consequences. In 1931, the Austrian logician Kurt ...

Research at the frontier between computer science and physics illustrates the shortcomings of the reductionist approach to science, which explains macroscopic behaviour using microscopic principles.

The spectral gap is one of the most important physical properties of a quantum many-body system, determining much of its low-energy physics. Gapped systems exhibit non-critical behaviour (for example, ...

Katie has a PhD in maths, specializing in the intersection of dynamical systems and number theory. She reports on topics from maths and history to society and animals. Katie has a PhD in maths, ...

Google has acquired small visual search-related startup Undecidable Labs for an undisclosed amount, putting the firm's founder Cathy Edwards (a former engineering director at Apple) in charge of its ...

Moral dilemmas are often undecidable. Which is to say, there are times when we lack solid rational grounds for choosing between two (or more) compelling courses of action. In those moments, after ...