Francisco A. Ocaña @faolmath

All Conic Sections in 20 Seconds

A spinning black hole does not just pull objects inward. It drags spacetime itself into a cosmic whirlpool. Around it, space twists, light bends, and time stops behaving the way we experience it on Earth. The Kerr Metric is the equation that describes this bizarre reality. Every symbol in it maps the geometry of a rotating black hole, where gravity becomes so extreme that even the fabric of the universe starts to spiral.

At room temperature, billions of gas particles are crashing around you at different speeds right now. Not randomly. Predictably. The Maxwell Boltzmann Distribution revealed the hidden pattern behind molecular motion and became one of the foundations of statistical physics.

How A Random System Can Actually Be Predictable #veritasium #science #physics #math

A German woman proved a single theorem in 1915 that quietly became the foundation of every law of physics on Earth. She taught for seven years without pay because the University of Göttingen refused to hire a woman. Then she fled the Nazis and died in Pennsylvania at 53. I started reading about her and could not believe how much of modern physics traces back to one woman the world refused to pay for her work. Her name was Emmy Noether. The theorem is called Noether's theorem. Every law of physics ever discovered. Conservation of energy. Conservation of momentum. The Standard Model. General relativity. Quantum field theory. All of them are direct consequences of a single mathematical insight she proved 110 years ago. And most physics students will graduate without ever hearing her name once. Emmy Noether was born in 1882 in Erlangen, Germany. Her father was a respected mathematician at the local university. The university would not allow women to enroll as students. So she audited classes from the back of the room and was not allowed to receive credit for anything she learned. She finished her PhD anyway in 1907. Then she could not get a job. For seven years she worked at the Mathematical Institute in Erlangen without a single paycheck. She supervised students. She published papers. She filled in for her aging father when he was too sick to teach. She did the work of a full professor and was paid nothing. There was no policy preventing her payment. There was simply no precedent for paying a woman. In 1915 David Hilbert and Felix Klein invited her to Göttingen, the most important mathematics department in the world. Hilbert wanted her there because he was working on Einstein's new general relativity and there was a problem nobody could solve. The philosophy faculty blocked her hiring. They argued returning soldiers should not learn from a woman. Hilbert stood up in the faculty meeting and said the line that has echoed for a century. He did not see how the sex of the candidate could be an argument against her admission, because the university senate was not a bathing establishment. She still was not hired. So Hilbert listed her courses under his own name on the official schedule. She taught them under his title. This is how the most important mathematician of the 20th century was forced to operate for years inside one of the most prestigious universities in the world. That same year she solved Hilbert and Einstein's problem. The puzzle was technical. In general relativity, energy did not seem to be conserved the way classical physics required. Einstein could not figure out why. Hilbert could not figure out why. Noether figured out why in a few months. Then, instead of just solving their specific problem, she proved a much deeper theorem that solved every problem of that shape forever. Her result was this. Every continuous symmetry in a physical system corresponds to a conservation law. If the laws of physics do not change over time, energy must be conserved. If they do not change with location, momentum must be conserved. The conservation laws were not separate facts. They were inevitable consequences of the symmetries underneath the universe. This single theorem is the foundation of every law of physics ever discovered after her. The Standard Model is built on it. The Higgs boson Nobel Prize is built on it. Quantum field theory is built on it. Einstein read her paper and wrote to Hilbert that he was astonished. He had never met anyone with her capacity for abstract thought. She finally got a paid teaching position in 1923. She was 41. She had been doing professor-level work for 16 years without compensation. While the German physicists kept getting credit for the consequences of her theorem, she quietly founded modern abstract algebra. The structures we now call Noetherian rings are named after her. Modern algebraic geometry, the math that powers cryptography and parts of machine learning, runs on her foundations. Then the Nazis came. In 1933 she was fired for being Jewish. Bryn Mawr College in Pennsylvania offered her a position. She took it. She taught there for two years that were among the most productive of her life. In April 1935 she went in for routine surgery to remove an ovarian cyst. Complications developed. She died four days later. She was 53. Einstein wrote a public letter to the New York Times the day after her death. He said she was the most significant creative mathematical genius thus far produced since the higher education of women began. Almost nobody reading that letter knew her name. She is buried in the courtyard of the library at Bryn Mawr College. The grave is small. Most students walk past it without noticing. The woman who built the mathematical foundation of modern physics was paid almost nothing for almost all of it. The world she worked in told her every single day that she did not belong there. She built it anyway.

David Blackwell (1919–2010) was one of the greatest probabilists and statisticians of the 20th century. Born in Centralia, Illinois, he earned his PhD in mathematics from the University of Illinois at just 22 under Joseph L. Doob. Despite facing racial discrimination, he became the first Black tenured professor at University of California, Berkeley. Blackwell made foundational contributions to probability, statistics, game theory, and decision processes. He is best known for the Rao–Blackwell Theorem (with Calyampudi Radhakrishna Rao), which improves statistical estimators using sufficient statistics. His work on Markov decision processes, dynamic programming, and repeated games deeply influenced modern probability theory and later areas like reinforcement learning and machine learning. Known for both brilliance and humility, Blackwell inspired generations of mathematicians and became a historic figure in American mathematics.

Happy Birthday to Claude Shannon, known by many as the “father of Information Theory.” Shannon was an American mathematician and electrical engineer. In 1948, he published A Mathematical Theory of Communication, which effectively created the field.

Some of the most beautiful improper integrals in mathematics From the Gaussian bell curve to the Lorentzian, sinc function, and damped cosine; each integrates over ℝ to a clean, elegant constant: ∫ e^{-x²} dx = √π ∫ 1/(x²+1) dx = π ∫ sin(x)/x dx = π ∫ cos(x)/(1+x²) dx = π/e Which one is your favorite?

🆕 EL OLIVAR FRANQUICIADO: ASÍ HAN CAMBIADO EL CAMPO LOS FONDOS DE INVERSIÓN 🌍 España, 1er productor de aceite del mundo 💶 Grandes capitales invierten en olivar en seto 💦 Costes mínimos, privilegios en el agua y pese a sus ganancias cobran PAC Hemos investigado quiénes son👇🧵

Basit ve güzel bir anlatımla " tüm çokgenlerin dış açılarının toplamının neden 360 derce olduğunun ispatı. Hiç bir çocuk bu şekilde anlatıldığında bunu unutmaz.

In 2015, physicists at the University of Rochester derived a formula for pi (the Wallis product) from calculations of the energy levels of a hydrogen atom. This discovery, published in the Journal of Mathematical Physics, showed a surprising and beautiful connection between pure mathematics and quantum mechanics.

🇸🇪 | El gobierno de Suecia ha decidido retomar el uso prioritario de libros físicos, papel y bolígrafos en las aulas para combatir el descenso en los niveles de comprensión lectora de los estudiantes. Esta transición, bajo el lema "de la pantalla a la carpeta", elimina la obligatoriedad de herramientas digitales en preescolar y busca reducir las distracciones, basándose en estudios que señalan que el uso excesivo de pantallas puede afectar el desarrollo cerebral y la concentración de los niños.

Today, April 15, 2026, marks the 319th birthday of the prolific Swiss mathematician Leonhard Euler. He introduced or popularized several key mathematical symbols and notations that are still used today.

Most things in life follow a curve—exam scores, reaction times, even measurement errors. This curve is called the Gaussian distribution, and it shows that the average value is actually the most common.

NASA scientists with their board of calculations, 1957.

keyboard_arrow_left Previous keyboard_arrow_right Next

Imperdible mensaje de Chistina Koch tras su vuelta del espacio. Oratoria 10/10. Contenido 10/10. Emoción 10/10. Gente que sí ♥️

Did you know that the man who helped invent probability theory also used mathematics to argue that believing in God is the smartest choice? Blaise Pascal was a brilliant thinker who made groundbreaking contributions to mathematics at a young age. At 31, he experienced a powerful and deeply personal mystical vision that shook him to his core. So profound was this moment that he wrote it down and stitched the note into the lining of his coat, keeping it close to his heart for the rest of his life. This experience transformed Pascal. He gradually shifted his focus from pure mathematics to philosophy and theology. But what makes his story remarkable is how he used the very tools of logic and probability he helped develop to form one of the most famous arguments for faith—now known as Pascal’s Wager. The idea is surprisingly simple. If God exists and you believe, the reward is infinite. If God does not exist and you believe, the loss is minimal. But if God exists and you do not believe, the loss could be everything. Even if the chance of God’s existence is small, the potential reward is so great that, from a mathematical perspective, belief becomes the rational choice. Pascal’s insight shows that sometimes, even life’s deepest questions can be approached through the lens of simple reasoning.

"Planet Earth: You. Are. A. Crew." Artemis II mission specialist Christina Koch reflects on what it means to be a "crew."