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Computer Scientists Invent an Efficient New Way to Count
By making use of randomness, a team has created a simple algorithm for estimating large numbers of distinct objects in a stream of data.
How Do Machines ‘Grok’ Data?
By apparently overtraining them, researchers have seen neural networks discover novel solutions to problems.
The Hidden Connection That Changed Number Theory
Quadratic reciprocity lurks around many corners in mathematics. By proving it, number theorists reimagined their whole field.
The Deep Link Equating Math Proofs and Computer Programs
Mathematical logic and the code of computer programs are, in an exact way, mirror images of each other.
How Many Microbes Does It Take to Make You Sick?
Exposure to a virus isn’t an all-or-nothing proposition. The concept of “infectious dose” suggests ways to keep ourselves safer from harm.
How Scientists Are Tackling the Tricky Task of Solar Cycle Prediction
Scientists have struggled to accurately forecast the strength of the sun’s 11-year cycle — even after centuries of solar observations.
Alan Turing and the Power of Negative Thinking
Mathematical proofs based on a technique called diagonalization can be relentlessly contrarian, but they help reveal the limits of algorithms.
How Genetic Surprises Complicate the Old Doctrine of DNA
For over a century, biologists have had to contend with a complicated picture of genetics, which they’ve only recently begun to understand.
How Math Achieved Transcendence
Transcendental numbers include famous examples like e and π, but it took mathematicians centuries to understand them.