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 ...

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 ...

The world of mathematics is full of unreachable corners, where unsolvable problems live. Now, yet another has been exposed. In 1900, the eminent mathematician David Hilbert announced a list of 23 key ...

The original version of this story appeared in Quanta Magazine. The world of mathematics is full of unreachable corners, where unsolvable problems live. Now, yet another has been exposed. In 1900, the ...

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 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 ...

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 ...

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, ...