Todo gran legado comienza con un primer paso y ese inicio se dio el 1 de marzo de 1948. Hoy miles de historias llevan el nombre de la Universidad Industrial de Santander 💚
@MantillaIgnacio@ZahlenRMD En $\mathbb{C}$, del Teorema de Moivre, $1^{1/10}$, tiene diez soluciones, cada una de ellas de la forma $e^{i \frac{2\pi\cdot k}{10}}$ para k entero desde 0 hasta 9. Solamente cuando$ k=5$, tenemos &-1=e^{i \pi}$. En los demás casos, la igualdad mostrada no es cierta.
We congratulate Levent Alpöge and Tristan Buckmaster on their remarkable mathematical work.
We (the researchers and the agents) did not see any of their work through any means until they released it publicly — in particular, no specific user data was accessed in order to solve this problem.
While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models.
However, our proofs differ significantly and even the precise results proved are different in the Euler case (forced vs. unforced).
John Tukey the Fast Fourier Transform (FFT) inventor, who coined both "bit" and "software" died exactly 26 years ago today.
The Fast Fourier Transform (FFT), one of the most important algorithms in signal processing and data analysis, was introduced by Tukey & Cooley in 1965.
In 1805, Gauss - studying the orbits of asteroids Pallas and Juno - came up with a method to interpolate their trajectories from discrete samples. What he came up with was mathematically very close to the modern FFT but Gauss never published that work, and didn’t analyze its computational complexity. It predated even Fourier’s 1822 work on heat diffusion - but without the framing or generalization that Cooley & Tukey would bring 160 years later.
In 1965, Cooley & Tukey published their now-famous algorithm that reduced the cost of computing a Discrete Fourier Transform from 𝑂(𝑛²) to 𝑂(𝑛 log𝑛). This leap made real-time signal processing and digital media compression feasible.
From radio telescopes to JPEGs, from audio codecs to quantum mechanics - the FFT is everywhere. It’s one of the most important (and elegant) algorithms of the 20th century - rooted in the genius of Gauss, but brought to life in the computer age.
Tarski (in?)famously defined the truth predicate for the integers, then showed that it is undefinable. That is, if Def(ℕ) denotes the sets of integers definable by quantifying over integers then the truth predicate T is not in Def(ℕ). Nevertheless, T is definable over Def(ℕ).
Mortal Kombat cumple 30 años de su lanzamiento al mercado. El inicio de una saga que revolucionó la industria de los videojuegos con su estilo din��mico de combate, animaciones sangrientas y los legendarios Fatalities.
Cartagena, Colombia 🇨🇴
One of the worst "popular" cities in the Americas...
- Ugly beaches in city
- Annoying hustlers around every turn
- Overpriced
- All hotels + Airbnbs have "hostel-style" rules about guests
- Most women accept money for sex
- Unfriendly people overall
In 1964, C.P. Willans found this exact(!) formula for the primes.
Watch @ericrowland nicely explain how it works and why it's kinda useless...
https://t.co/uk1mqXpZ8z
Another Sier-tipsky Triangle. I used the midpoints to subdivide, but each of the resultant triangles is rotated a random angle (mean: 0°, SD: 5°).
#mathart#Mathematica
Cómo fueraaaa si Waze tuviera acento colombiano, tipo:
“Mano le dije que por la doble hijueputa esquina volteara, ahora tengo que volver a calcular por su culpa toche”
“[Proof by contradiction] is one of a mathematician’s finest weapons. It is a far finer gambit than any chess gambit: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.” – G.H. Hardy