The formal verification of computer systems has become practical. It has an essential role in tech firms such as Amazon, AMD, Intel, Microsoft and Nvidia. In recent years, researchers have started asking whether verification technology could also benefit research mathematicians. Here, we explore every aspect of doing…
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We use distributed systems every day in the form of internet services. These systems are very useful, but also challenging to implement because networks are unpredictable. Whenever you send a message over the network, it is likely to arrive quite quickly, but it’s possible that it might be delayed for a long time, or…
Recently, somebody shared on Twitter a new proof of the irrationality of √2. Its claimed advantage is that “it requires no knowledge of mathematics above the definition of what it means for a number to be irrational, and can be written almost in one line.” These claims are dubious: the usual proof, which I’ve…