Pubfred retweeted
In 1830, Liouville proved the area under the most important curve in mathematics has no formula. Not because nobody was clever enough - because the formula was never there to be found. Then somebody squared the problem, lifted it into a second dimension, and a circle walked into the exponent entirely on its own. The area is the square root of π - the same √π that normalizes every probability distribution inside every LLM and every diffusion model on every GPU cluster today.
The curve is e to the minus x squared - the bell curve De Moivre discovered in 1733 solving a coin-flip problem. One dimension and every integration method slides off it. Square the integral, rename one variable to y, and x² + y² appears in the exponent - Pythagoras hiding inside a function with no circles anywhere. Switch to polar coordinates and geometry hands you a free factor of r. The infinite hill collapses to π. That factor now sits inside every softmax normalization, every Gaussian noise layer in stable diffusion training, every loss function a transformer optimizes during backpropagation.
20 minutes. Bookmark & watch today. The proof that a circle was hiding inside a straight line the entire time.
Pubfred retweeted
Choose any positive integer and repeatedly apply two simple rules:
If n is even: n → n/2
If n is odd: n → 3n + 1
Start with 6: 6 → 3 → 10 → 5 → 16 → 8 → 4 → 2 → 1
Start with 27, and something unexpected happens.
Starting number: 27
Maximum reached: 9,232
Steps to reach 1: 111
Peak reached at: Step 77
The sequence climbs dramatically before eventually falling to 1.
This is the famous Collatz conjecture, which states that every positive integer eventually reaches 1 under these rules. Despite decades of research and extensive computer verification, no general proof is known.
Pubfred retweeted
Russian Kosmos 2612 and ICEYE-X36 (providing Ukraine military support) are now in perfect sync with each other. The Russian military satellite is intentionally stalking and tracking the Western radar satellite. Keeping a satellite "bumper-to-bumper" in this manner allows Russia to intercept or jam data transmissions, physically inspect Western technology, or quickly pivot to execute a kinetic or non-kinetic anti-satellite (ASAT) attack with very little warning or fuel expenditure.
Kosmos 2612 executed a series of highly precise, fuel-heavy maneuvers to force itself into a "coplanar" orbit—matching ICEYE-X36's exact altitude (~555 km), speed, and inclination (~97.8°). The ICEYE-X36 satellite is giving the Ukraine military support.
Pubfred retweeted
Quaternions turn multiplication into a directed path through four dimensions.
They extend the complex plane by adding j and k so that any number is q₀ + q₁i + q₂j + q₃k. The defining rules are i² = j² = k² = −1 together with ij = k, ji = −k and the cyclic partners. Order is no longer optional: swapping two factors can flip the sign of the result.
That single non-commutative property is what lets quaternions rotate three-dimensional space without the singularities that trap Euler angles.
The algebra remembers the sequence of turns, and that memory is exactly what keeps orientation continuous.
Pubfred retweeted
Thermodynamics has a clever way of turning difficult derivatives into quantities we can actually measure.
The Maxwell relations, derived from the mathematical structure of thermodynamic potentials, let us swap one hard to measure change for another. Combine them with the cyclic rule, and derivatives involving pressure, volume, temperature and entropy become connected to heat capacity, thermal expansion and compressibility.
The beauty is that a few mathematical relationships reveal how seemingly different properties of matter are tied together.
Pubfred retweeted
📊💰🪖🌎 Last year, global military spending amounted to $2.89 trillion. A third of this spending went to the United States, 55% to NATO countries.
Ukraine increased military spending faster than Russia (+20% versus +5.9%). Europe, as a whole, is breaking records in militarization: Spain (+50%), Germany (+24%), Poland (+23%), and Italy (+20%). It is significant that heavily indebted countries and the UK ignored this trend and did not significantly increase or even decreased their military spending.
LoW
Pubfred retweeted
MBS IS FINISHED: THE HOUSE OF SAUD FACES TOTAL COLLAPSE
Scott Ritter, former UN weapons inspector and Marine intelligence officer, warns that Mohammed bin Salman has entered a death spiral with no way out. A war launched in 2014 for quick military glory has become a 12-year nightmare that is now physically dismantling Saudi oil production. The American umbrella has failed, allies will not ride to the rescue, and the kingdom is losing decisively. The only remaining question is how fast the collapse arrives.
THE CORE VERDICT
➡️ Ritter states the demise of Muhammad bin Salman is inevitable.
➡️ “He’s finished.”
➡️ If lucky he catches the last gold-plated 747 out of Riyadh to a London hideaway or the United States.
➡️ If not, his head is removed by sword amid shouts of Allahu Akbar.
➡️ “It’s the end of the House of Saud.”
THE 2014 STRATEGIC ERROR
➡️ MBS tried to earn his military spurs with a fast victory over Ansar Allah.
➡️ The campaign turned into a 12-year nightmare.
➡️ His later decision to expand the war by striking Sanaa airfield only accelerated the destruction.
➡️ There is no political off-ramp left and no salvation coming.
THE OIL DESTRUCTION
➡️ Ansar Allah is no longer limited to blocking Bab el-Mandeb or hitting pipelines and storage.
➡️ They are now attacking production facilities and the wells themselves.
➡️ “This is the end of Saudi Arabia.”
➡️ Without oil the entire Vision 2030 fantasy collapses into what Ritter calls a Bedouin-infested sand pit with nothing left.
NO ALLIES WILL SAVE HIM
➡️ The American security umbrella proved nonfunctional.
➡️ Saudi forces are ineffective, overweight, proxy-driven and overmatched.
➡️ Pakistan faces massive Imran Khan protests and will not send tens of thousands of troops into a losing desert war.
➡️ Turkey has no interest in dying for the Saudis.
➡️ The Mecca Pact is a joke of maps and chalkboards with no real troop movement.
THE RIYADH PREDICTION
➡️ If MBS is removed and internal fighting follows, Ritter says Ansar Allah columns could drive through the streets of Riyadh.
➡️ Saudis have feared this outcome since 1990.
➡️ “Saudi Arabia is losing this war decisively. And there’s nothing that can be done to save them.”
➡️ The world will experience the same shock that hit when the Shah of Iran fell in 1979.
THE BOTTOM LINE
Scott Ritter sees MBS as toast and the House of Saud heading toward the same abrupt end that surprised everyone in 1979. Energy production is being dismantled, no outside force will intervene, and the collapse is already underway. History is about to deliver a shock that almost no one in the West has priced in.
#MBSFinished #HouseOfSaud #SaudiCollapse #AnsarAllah #YemenWar #OilCrisis #1979Shock
HT: YouTube Danny Haiphong - link in the comments
Pubfred retweeted
🇮🇷⚔️🇺🇸Secretary of the Supreme National Security Council: The fate of major powers that have tried to conquer Iran has been to become a footnote in history.
Trump has resorted to smuggling by employing a number of criminals operating in the Omani coastal waters.
He claims every day that the Strait of Hormuz is open, but I respond: You are engaged in smuggling, but the Strait is under Iranian control, and we manage it.
Over the past few months, we have targeted five ships used by smugglers every night in the Strait of Hormuz.
The commander of CENTCOM leads the smuggling operations, and he also uses the UAE military.
They use 5 or 6 small boats to transfer oil to larger tankers, but we also target 5 or 6 of them every night.
We are fully prepared to demonstrate new capabilities if the war restarts.
The United States has very valuable assets in the UAE and in the vicinity of the Strait of Hormuz, which we have not yet included among our targets.
If a war breaks out again, many cables, data centers, artificial intelligence facilities, and other sites in the region will be destroyed.
If another confrontation occurs today, we will definitely face the enemy with a much larger and more comprehensive plan.
The cables, data centers, and artificial intelligence facilities in the region are worth more than $2 trillion.
Tehran will not return to its past diplomatic practices.
We are facing a group of ignorant individuals in the United States.
We are dealing with a group of ignorant and foolish people in the United States who have not studied history and do not know the Iranian nation; as a result, we have reached this situation.
🇮🇷⚔️🇺🇸 Secretary of the Supreme National Security Council: A message for Rubio
General Rezaei: I have a message for the US Secretary of State: "The people are far greater than you. Throughout thousands of years, they have repeatedly dreamed of coming to Iran and conquering this country.
Various powers have dreamed of entering Iran, controlling it, and destroying the Iranian nation, but the Iranian nation has defeated them all.
Their names have now been erased from history, while the Iranian nation remains in the history books."
Let me be clearer: the more you try to fight against Iran, the more you will sink into a quagmire.
You mentioned history, and our history has many lessons for you. You will once again be forced to kneel before the Iranian nation, and in the end, you will contribute to the growth of the Iranian nation.
🇮🇷🇺🇸 The Secretary of the Supreme National Security Council addressed the United States: "Iranians will never surrender to you, and they will never back down from their demands until they reclaim their rights from you."
🇮🇷⚔️🇺🇸Secretary of the Supreme National Security Council: Bessent is known in the United States as a "liar."
The Trump Treasury Secretary has made statements and promises for over a year that he has failed to deliver on.
This man wants to confront the Iranian people and wage a war against their livelihoods. I am confident that he will experience a crushing defeat.
Just as the Americans failed in a military war, we will defeat them in an economic war as well.
We have already prepared our plans, and God willing, we will announce a series of economic defense measures.
🇮🇷⚔️🇺🇸Secretary of the Supreme National Security Council: We are considering the establishment of an "Economic War Council."
It is likely that such a council will be formed, and we will show Trump and Bessent what a real economic war means, and what position they will have in this conflict.
Our approach to diplomacy has changed, and we will not return to past diplomatic methods.
We held three rounds of negotiations, and in each round, the Americans abandoned the negotiations and attacked Iran. Therefore, we will not return to previous diplomatic patterns.
When someone signs an agreement and then withdraws from it, you naturally need to adopt a different approach to diplomacy with that person.
The Americans have responded to our 7 conditions, but we consider it insufficient.
Over the past two months, the Americans have approached us through three different channels: Pakistan, Qatar, and even Iraq, asking us to present our proposals to them.
About two weeks ago, we announced 7 conditions to the Americans and clearly stated that the Strait of Hormuz would not be opened to them, and no negotiations would take place, until these conditions were met.
The Americans have now responded; in their response, they have accepted some of our conditions, while others remain unclear.
We are no longer in the process of responding to the Americans; they have responded to us, and we consider their response insufficient. They need to clarify the issues that remain unclear to us.
Without Iran's management of the Strait of Hormuz, the Persian Gulf cannot be secure.
Control over the Strait of Hormuz represents a significant national asset and a major national wealth.
Our intention is not simply to block the passage and collect tolls. Our interests are much broader than that. Of course, we can certainly generate economic benefits from the Strait of Hormuz.
Farsna
Pubfred retweeted
Dans un champ du Berry, deux pylônes plus hauts que la tour Eiffel donnent l'heure à 200 000 horloges françaises.
Feux tricolores, parcmètres, panneaux des gares et des aéroports : ils se règlent sur ce signal.
C'est l'émetteur d'Allouis, dans le Cher. Ses deux pylônes mesurent 350 mètres, 20 de plus que la tour Eiffel.
Il entre en service en 1939, pour la radio.
Sous l'Occupation, les Allemands s'en servent. Notamment pour brouiller Radio Londres, la voix de la France libre.
En 1944, en se retirant, ils le font sauter.
Il faut des années pour le reconstruire. Il reprend du service en 1952.
Pendant des décennies, il diffuse France Inter en grandes ondes, bien au-delà des frontières.
En 1977, il reçoit une nouvelle mission. Diffuser l'heure légale française, réglée sur une horloge atomique.
La radio s'arrête le 31 décembre 2016.
L'heure de la France part encore de ce champ, à chaque seconde.
Pubfred retweeted
Each coordinate of a closed outline has its own real Fourier series: x(t) = ∑ (aₖ cos kt + bₖ sin kt), and the same for y.
A cosine and sine of frequency k make one arm of length √(aₖ² + bₖ²) turning k times per lap. One chain sets x, one sets y, and the pen sits where their guides cross. With N harmonics per axis the knight is off by 30.2 % of its height at N = 1, 0.70 % at N = 50.
At N = 1 both coordinates are pure sinusoids: an ellipse.
Pubfred retweeted
Samsung open-sourced a method that shrinks 13B parameter LLM into less than 1 GB.
It's called "LittleBit"
Instead of storing AI weights as standard numbers, they used latent factorization to crush them down to extreme sub-1-bit levels.
In some configurations, they hit 0.1 bits per weight.
But here is where the architecture gets crazy.
When you compress an AI this much, you can stop doing math.
Instead of forcing the hardware to do heavy floating-point multiplication, LittleBit replaces the core computation with a bitwise XOR operation.
It swaps complex matrix math for basic sign flips.
The results rewrite the rules of model deployment:
• Unlocks a massive 11.6x inference speedup relative to standard FP16 models.
• Radically reduces memory footprint and loading bandwidth.
• Maintains robustness in extreme sub-0.5 bit regimes where previous compression methods catastrophically fail.
This is not a clever optimization.
It is the blueprint for running massive, state-of-the-art AI locally on cheap, resource-constrained devices.
Pubfred retweeted
It's the beauty of pure math that a problem about factoring integers became a method for securing the information.
One of the cleverest ideas in number theory became the basis of public-key cryptography:
Take two large primes, p and q, and multiply them:
n = pq.
Multiplication is easy. But if only n is known, recovering p and q can be extremely difficult when the primes are large.
That asymmetry is the mathematical heart of RSA: the public information can be shared openly, while the prime factors remain secret and are used to recover the private key.
Pubfred retweeted
As a teenager, Bernhard Riemann reportedly borrowed Legendre’s 859-page Theory of Numbers from his school director.
He returned it one week later, saying it had taken him the whole week to master.
Two years afterward, he chose the same book for his graduation examination and answered every question correctly, despite not having looked at it in the meantime.
Source: Stephen Hawking (ed.), God Created the Integers.
Pubfred retweeted
Around AD 900, the mathematician Abu Kamil was already asking a question that feels strikingly modern:
Not just does a problem have a solution? but how many solutions does it have?
He wrote of problems with one solution, several solutions, no solution at all, and one remarkable problem for which he found 2,678 valid answers.
That shift, from finding a solution to understanding the entire solution set, is one of the great habits of mathematics.
Source: David Wells, The Penguin Book of Curious and Interesting Mathematics.
Pubfred retweeted
One of the strangest constants in number theory is
ζ(3) = 1 + 1/2³ + 1/3³ + 1/4³ + ⋯ ≈ 1.202056903159594…
Euler found elegant formulas for ζ(2), ζ(4), ζ(6), … in terms of powers of π. But the odd values proved far more mysterious.
Then in 1978, Roger Apéry unexpectedly proved that ζ(3) is irrational. His argument was initially surprising because it relied on sequences that looked unlikely to have the required integer properties, yet the proof held.
Even today, ζ(3) stands as a reminder that the odd zeta values behave very differently from the even ones.
Pubfred retweeted
In 1900, Max Planck was trying to solve a stubborn problem: the spectrum of radiation emitted by a hot body.
The mathematics led him somewhere unexpected.
He found that the observed spectrum could be explained if energy were exchanged not continuously, but in discrete packets:
E = hν
Here, ν is frequency and h is the constant now bearing his name.
Planck initially treated quantization as a mathematical necessity rather than a complete new picture of nature. But the small constant h became one of the defining constants of modern physics.
Einstein soon pushed the idea further by treating light itself as quantized.
A problem about thermal radiation had opened the door to quantum theory.
Source: Nobel Prize, historical account of the development of quantum theory and Planck’s 1900 work.
Pubfred retweeted
“Well, Papa, can you multiply triplets?”
According to William Rowan Hamilton’s later recollection, his sons kept asking him this question at breakfast in early October 1843.
He was trying to find suitable multiplication rules for triples of numbers. Each morning, he had to admit that he could only add and subtract them.
Then, on 16 October, while walking with his wife along Dublin’s Royal Canal, the breakthrough came. His new system, the quaternions, used four components.
Hamilton recalled taking out a knife and carving its fundamental relation into a stone of Brougham Bridge:
i² = j² = k² = ijk = −1
The algebra had a remarkable feature: multiplication depended on order. For example, ij = k, but ji = −k.
The inscription eventually disappeared. The mathematics survived.
Sometimes progress means changing the kind of answer you are looking for.
Source: Hamilton’s letter to his son Archibald, 5 August 1865, reproduced by Trinity College Dublin.
Pubfred retweeted
Henry Briggs was so impressed by John Napier’s invention of logarithms that he travelled from London to Edinburgh simply to meet him.
When they finally came face to face, the two mathematicians reportedly stood looking at one another for nearly fifteen minutes without speaking. Briggs had come to understand how Napier had conceived an idea that now seemed astonishingly natural. He then stayed at Napier’s home for a month. Mathematical Circles
Sometimes a mathematical idea is so beautiful that the first response is silence.
Source: Howard W. Eves, In Mathematical Circles.
Pubfred retweeted
Coup de gueule du week-end.
En 2022, on nous vendait "l'économie de guerre" à grand renfort de fanfare. En 2026, le clairon se tait et personne ne s'en émeut.
Les Forges de Tarbes sont la seule usine française capable de fabriquer les corps creux des obus de 155 mm du canon #CAESAr. Selon BFM Business, elles ont tout arrêté entre mi-août et mi-septembre. Les matières premières n'arrivent plus depuis mars, les machines en fin de vie tombent en panne et les salaires arrivent en retard. Plusieurs des 60 salariés témoignent sans donner leur nom, dans un climat de peur. Certains s'attendent déjà à ne plus être payés.
Les commandes, elles, existent. KNDS, seul client, annonce 60 000 à 150 000 corps creux sur 2026-2028. Pourtant, l'usine n'arrive pas à produire. Son actionnaire, Europlasma, tient grâce à des obligations convertibles, un financement que l'AMF associe aux sociétés sans autre solution. Le groupe affiche 35,6 millions d'euros de perte en 2025 et a vendu les murs de l'usine en mars. En avril, il annonçait des négociations exclusives pour céder sa branche défense à un investisseur français resté anonyme. Depuis, silence complet.
Et l'État ? Il a avancé 7 millions d'euros en 2022 et 2023 pour moderniser l'outil, puis il a tourné la tête. Nous ne voyons ni plan de sauvetage, ni réponse claire du ministère des Armées, ni industriel de la BITD qui lève la main.
Pendant ce temps, les Allemands et les Polonais produisent pour eux et pour leurs alliés sans se poser mille questions. Nous, grand pays d'artillerie et de métallurgie, nous confions un maillon unique à un montage financier bancal.
Bravo, la France invente l'économie de guerre à flux tendu : un site unique, un client unique, un actionnaire sous perfusion et zéro marge. Elle se tire une balle dans le pied, puis s'étonne de boiter. La profondeur industrielle, c'est pourtant simple : une seconde source, des stocks de matières premières et un propriétaire à la hauteur. Tant que l'État ne tranche pas, il organise lui-même la défaillance.
