Polynomial Interpolation is an approximation in which the value of a function at a position between two known data points is determined by determining a polynomial that passes between these points in an elegant, smooth manner. In that approach, the data positions are represented as coefficients on...
German mathematician David Hilbert first raised the fundamental idea behind KANs as one of 23 unsolved mathematical problems at the International Congress of Mathematicians in Paris in 1900. His 13th problem asked whether a function consisting of threevariablescould be expressed by combining the functions...
“Real” mathematics (or just mathematics) is the art of creating, understanding, and exploring the relationships between various mathematical* structures. Mathematics is the art ofmakingmathematics, by exploring and understanding mathematical structures. (Numbers are one such structure, but there are in...
String theory is only a mathematical model and still lacks concrete experimental evidence to prove its accuracy. Even so, the model provides an elegant description of the fundamental components that make up the universe. It also predicts the existence of 10 dimensions that the strings can vibrate ...
Ariel Procaccia has thought a lot about how to cut a cake over the last 15 years. As the father of three children, he knows how hard it is to divide a birthday cake to everyone's satisfaction. But it's also because Procaccia's work ...
But these kinds of demos always left a lurking question: How is this math? How does any of this actually help solve problems? It wasn’t until I saw the problem I’m about to show you, with its elegant and surprising solution, that I started to understand why mathematicians actually care...
This is of course an extremely inelegant proof, but elegance is not the point here; rather, that it is automated. (See also this recent article of Heather Macbeth for how proof writing styles change in the presence of automated tools, such as formal proof assistants.) The code is close ...
If this is considered the easiest path, then it looks a little grim. My crutch of using a Taylor/Wheeler lattice and making sure I dealt only with observables might not be at all elegant, but might at least guarantee that I can start and end a problem with invariants. From where I ...
In a world where we are increasingly reliant on devices with less computing power, such as mobile phones, ECC provides an elegant solution based on the obscure mathematics of elliptical curves to generate smaller keys that are more difficult to crack. ...
The beauty of the venture is that we stand to lose nothing. Elegance Something elegant. Beauty An outstanding or conspicuous example The golf shot was a beauty, stopping a foot from the hole. Elegance Grace, refinement, and beauty in movement, appearance, or manners. The bride was elegance ...