Let’s start with what’s probably the most tired, overused joke in math: A topologist is someone who can’t tell a coffee cup from a doughnut. Both, you see, have a hole in them. Topology is usually ...

Habituation, or loss of clinical benefit over time, is a frequent problem in spinal cord stimulation (SCS). Existing programming strategies such as waveform cycling or closed-loop stimulation try to ...

AI engineers often chase performance by scaling up LLM parameters and data, but the trend toward smaller, more efficient, and better-focused models has accelerated. The Phi-4 fine-tuning methodology ...

This study constructs a robust higher-order fitted operator finite difference method for a two-parameter singularly perturbed boundary value problem. The derivatives in the governing ordinary ...

mathematics number theory prime numbers twin primes conjecture All topics More than 2,000 years ago, the Greek mathematician Eratosthenes came up with a method for finding prime numbers that continues ...

“Math 55” has gained a reputation as the toughest undergraduate math class at Harvard—and by that assessment, maybe in the world. The course is one many students dread, while some sign up out of pure ...