Happy International Women's Day. Today, I will handle one work of a female mathematician who died too early. Have any of you ever heard the name Maryam Mirzakhani? That mathematician died of cancer at the age of 40. The work of Maryam Mirzakhani handled hyperbolic surfaces. She was the first woman who win the Fields medal. The highest recognition in mathematics.
"Her earliest work dealt with “hyperbolic” surfaces. On such a surface, parallel lines arc away from each other rather than staying the same distance apart, and at every point, the surface curves in two opposing directions like a saddle. Although we can picture the surface of a sphere or doughnut, hyperbolic surfaces have such strange geometric properties that they’re impossible to visualize. But they’re also important to understand because such surfaces are ubiquitous in mathematics and even string theory." (QuantaMagazine, Years After the Early Death of a Math Genius, Her Ideas Gain New Life)
The ability to model those surfaces makes it possible to model the black holes. The black holes and wormholes can be a series of hyperbolic surfaces. Also, molecular, atomic, and subatomic bonds are the things that act like wormholes. There are many useful things in that kind of mathematical formula from information to engineering.
Or, we can think that those things are hyperbolic curves that are rolled into the tunnel-shaped structures. The hyperbolic surfaces and their interconnections can also shape the connections between black holes. And maybe those things can help researchers to make the models of the entropy in the black holes. The geodesic that illuminates the surface is the thing that can used to model the time loops. The time loop is the thing that forms an energy wave that travels back in time.
(QuantaMagazine, Years After the Early Death of a Math Genius, Her Ideas Gain New Life)
The reason why time travels in a certain direction is this. The past is in higher energy levels than in the future. That means information can travel to the past if the event's energy level is high enough. The time loop means that there is a thing that raises the energy level in the future higher than in the past. When information travels in a certain moment in time, outcoming effects will pump energy to them.
Then that energy causes time dilation that pushes information back in time. The problem is that the entropy mixes that information to a way, that denies us to understand it. The thing is that. The size of the quantum system determines entropy. But another thing is that the limited systems have limited entropy. Theoretically is possible to see things that happened in the past or even in the future.
But entropy causes a disorder in the information. That disorder makes information nonunderstandable by sorting it into a new order. The entropy is like whirls that disturb the information form. But if the entropy is limited that means it's possible to calculate those whirls backward. The system can put the pieces of information into the original form. That thing is possible only if the system calculator knows every movement and part of the system.
This kind of work will make fundamental things in chemistry, information technology, and maybe many other types of engineering and scientific work. The ability to model surfaces and curves makes it possible to create models about Hall fields. And that helps the system control information in the quantum tunnels.
https://www.quantamagazine.org/years-after-the-early-death-of-a-math-genius-her-ideas-gain-new-life-20250303/
https://en.wikipedia.org/wiki/Maryam_Mirzakhani
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