OpenAI claims its new reasoning model has produced an original mathematical proof disproving a famous unsolved conjecture in geometry, which was first posed by Paul Erdős in 1946. If this sounds ...

In a world where scientific breakthroughs often bring fame, wealth, and global recognition, Grigori Perelman chose a completely different path. The Russian mathematician stunned the academic world ...

Did our AI summary help? "No problem can be solved until it is reduced to some simple form. The changing of a vague difficulty into a specific, concrete form is a very essential element in thinking".

We may receive a commission on purchases made from links. Carrying out everyday home chores, such as cleaning, mowing, and cooking, consumes a large portion of the day, after which you are often left ...

Little progress had been made in solving Ramsey problems since the 1930s. Now, researchers have found the answer to r(4,t), a longstanding Ramsey problem that has perplexed the math world for decades.

In October 2024 I attended a workshop at Harvard University where mathematicians talked through the uses of artificial intelligence in their field. Most were less worried about the future of math than ...

A research team from HKU Engineering has pioneered a fundamentally new imaging strategy known as AIMED (Arbitrary illumination microscopy with encoded depth), which utilizes a sub-sampling approach.

After 80 years of fruitless struggle by human mathematicians, a major geometry conjecture has at last been solved—via a straightforward query to a chatbot. “No previous AI-generated proof has come ...

A generous influx of state resources from Gov. Kathy Hochul and a new tax on luxury second homes will help Mayor Zohran Mamdani balance a $125 billion budget. By Sally Goldenberg Dana Rubinstein and ...

Company says work on Paul Erdős planar unit distance problem shows advance in AI reasoning OpenAI has claimed a further advance in AI reasoning after its technology successfully tackled an 80-year-old ...