Symplectic geometry is a relatively new field with implications for much of modern mathematics. Here’s what it’s all about. In the early 1800s, William Rowan Hamilton discovered a new kind of ...

The original version of this story appeared in Quanta Magazine. In October, a Falcon Heavy rocket is scheduled to launch from Cape Canaveral in Florida, carrying NASA’s Europa Clipper mission. The $5 ...

Transactions of the American Mathematical Society, Vol. 359, No. 1 (Jan., 2007), pp. 333-348 (16 pages) In this paper we study the behaviour of the Lefschetz property under the blow-up construction.

When two mathematicians raised pointed questions about a classic proof that no one really understood, they ignited a years-long debate about how much could be trusted in a new kind of geometry. In the ...

Russian-American mathematician and Wolf Prize laureate Yakov Eliashberg delivered a public talk at IIT Madras on Thursday, as part of the inaugural annual TNQ Distinguished Lecture in Mathematics. The ...

As their results began to crystallize, at first they didn’t notice the striking patterns emerging. But a colleague who reviewed their work spotted the famed Fibonacci numbers—a list whose entries have ...

In this paper we present rotational symplectic geometry for use in modern biomechanics of human motion. Generalized Hamiltonian formalism has been formulated on the configuration manifold consisting ...

A French-Russian mathematician has won the Abel Prize today for his work on advanced forms of geometry. The winner of the 6 million Norwegian kroner (US$920,000) prize, Mikhail Leonidovich Gromov, has ...

In a significant development, acclaimed Japanese mathematician Kenji Fukaya has left his post in the United States to take up a full-time professorship at China’s Tsinghua University. What Happened: ...