Algero

alpha researcher @vibe_trading

[Algero @0xAlgero]

An hour of pure number theory that ends with the reason your credit card works. Free, filmed in a wood panelled hall in London, no paywall.

Robin Wilson takes the oldest subject in mathematics and walks it forward from Euclid to RSA without ever losing the thread.

Minute 7 is the proof that started everything. Assume you have every prime, multiply them all together, add one. The new number is divisible by none of them. Primes never run out, in three lines, twenty three centuries ago.

Minute 8 is the honest footnote. That trick doesn't always spit out a prime. 2·3·5·7 plus 1 gives 211, which is prime, but 2·3·5·7·11·13 plus 1 gives 30,031, which is 59 times 509. The proof still holds, and that's the elegant part.

Minute 16 is perfect numbers. 6, 28, 496, 8128, and then nothing at all until 33,550,336. Euclid found the recipe, Euler proved it catches every even one, and whether a single odd perfect number exists is still unknown today.

Minute 22 is where geometry and primes collide. You can construct a regular polygon with a ruler and compass only when the number of sides is a power of 2 times distinct Fermat primes, which Gauss proved as a teenager after drawing the 17 sided one. It also means a regular 100 sided polygon is impossible.

Minute 31 hands you every right triangle with whole number sides. a = x² − y², b = 2xy, c = x² + y². One formula, infinite triangles.

Minute 38 raises the exponent by one and the whole thing collapses. Cubes, fourth powers, nothing works, and it took 358 years and Andrew Wiles to close it in 1995.

Minute 46 is the party trick. When can February have five Sundays? Leap year, 365 leaves remainder 1 mod 7, the pattern repeats every 28 years, so 2004, 2032, 2060, 2088.

Minute 50 is my favourite. Shuffle a 52 card deck a certain way and every card at position x moves to 2x mod 53. Fermat's little theorem then guarantees the deck returns to its exact original order after 52 shuffles. Add two jokers and the answer drops to 20.

Minute 59 pays it all off. Two primes multiplied together, one public number that nobody can factor back, and every online payment you've ever made rests on that asymmetry.

Twenty three centuries of pure curiosity, no application in sight, and now it guards your bank account.

[Niko @0xNiko1]

https://t.co/9Vi8xgxrPX

[Algero @0xAlgero]

@0xDominiqq always

[Algero @0xAlgero]

MIT filmed a professor turning a drug boat's escape from the Coast Guard into a differential equation. On a chalkboard. In 2006.

The answer was a spiral.

This is 18.03, Lecture 4, taught by Arthur Mattuck. Free on MIT OpenCourseWare. The title sounds like nothing: substitution methods. Almost nobody watches it.

There are only two first-order differential equations you can always solve. Separable ones, and linear ones. That is the whole toolbox.

Every other one that can be solved is solved the same way. You disguise it. You change variables until it turns into one of the two you already know.

Then the boat. Caught in a lighthouse beam, it runs at a locked 45 degrees, hoping to slip the light before the helicopters come.

Mattuck writes out the slope. In normal coordinates it is an unreadable mess. He switches to polar, and the whole thing collapses to one line: r = C·e^θ.
An exponential spiral. The boat was always going to spiral.

His closing note: nobody could have set the problem up in polar from the start. But anyone who did would have gotten the answer instantly.

No formula sheet. His whole rule was learn the method, not the formula.

Just a smuggler, a spotlight, and a spiral.

[Niko @0xNiko1]

https://t.co/9Vi8xgxrPX

[Algero @0xAlgero]

MIT filmed a professor turning a drug boat's escape from the Coast Guard into a differential equation. On a chalkboard. In 2006.

The answer was a spiral.

This is 18.03, Lecture 4, taught by Arthur Mattuck. Free on MIT OpenCourseWare. The title sounds like nothing: substitution methods. Almost nobody watches it.

There are only two first-order differential equations you can always solve. Separable ones, and linear ones. That is the whole toolbox.

Every other one that can be solved is solved the same way. You disguise it. You change variables until it turns into one of the two you already know.

Then the boat. Caught in a lighthouse beam, it runs at a locked 45 degrees, hoping to slip the light before the helicopters come.

Mattuck writes out the slope. In normal coordinates it is an unreadable mess. He switches to polar, and the whole thing collapses to one line: r = C·e^θ.
An exponential spiral. The boat was always going to spiral.

His closing note: nobody could have set the problem up in polar from the start. But anyone who did would have gotten the answer instantly.

No formula sheet. His whole rule was learn the method, not the formula.

Just a smuggler, a spotlight, and a spiral.

[Algero @0xAlgero]

@isssa0x risk works until it doesnt

[Algero @0xAlgero]

@0xDezo true man

[Algero @0xAlgero]

An MIT professor opened his differential equations course by admitting that most differential equations cannot be solved, and then spent the whole hour teaching what to do about it.

The lecture is on MIT OpenCourseWare. Free, creative commons, first class of the semester. Almost nobody makes it to the end.

His point: He writes two equations on the board that look almost identical. One has the square on x, the other has the square on y. One you will learn to solve in a week. The other has no answer you can write down with elementary functions at all.

And equations like the second one are the rule, not the exception. Which means the entire skill you were trained in, isolate the variable and produce a formula, quietly stops working the moment the math describes something real.

Skip to 3:47, where he announces he will spend day one "not solving a single differential equation"and instead draws the geometry. The equation stops being a puzzle and becomes a map: At every point it tells you a slope, and the solution is just the curve that obeys those slopes all the way across.

Then at 36:39 he gives two rules that let you read that map: Solution curves cannot cross, and they cannot touch. Not by convention. Because a point can only have one slope, and existence and uniqueness makes it a theorem

No formula sheet. No answer key. A picture that tells you how the system behaves without ever telling you what it equals.

This is the actual literacy behind every dynamical model you have ever heard invoked. Climate, epidemics, orbits, interest rates, drug concentration in blood. None of it is solved. All of it is steered.

School sold you the closed form because closed forms are gradeable. The world runs on the picture, and the picture has been free for two decades.

[Algero @0xAlgero]

@andreysuperior true

[Algero @0xAlgero]

MIT filmed an exam review in 2007 and the best minute is at 47:26, after all the exam advice is over. 223 thousand views in 17 years.

it is free on YouTube. lecture 7 of 18.02, the first exam review, taught by Denis Auroux.

a student asks how to differentiate a dot product. the product rule survives: d/dt (r · r) = r' · r + r · r' = 2 r · r'.
now assume the length never changes. |r|² = r · r = constant. differentiate both sides. 2 r · r' = 0. so r ⊥ r'.

that is all of circular motion in one line. if a point is stuck on a sphere, its velocity is tangent to that sphere. no picture, no angles, no trig identities.

the rest of the review is built from two products in the same flat way. n = a × b is a normal to a plane. the line where two planes meet runs along n₁ × n₂. the area of a triangle is ½|a × b|. and Mx = 0 has a nonzero solution exactly when det M = 0, which is just the vectors being coplanar, said in algebra.

r · r' = 0 is what a gyroscope obeys. it is why a normalized quaternion stays normalized under its update. it is why the tension in a pendulum rod does no work: the force points along r, the motion does not.

the math is free and public. so is the lecture. what nobody can sell you is the reflex to differentiate a constraint instead of drawing a picture of it. that reflex is built over a semester, not one video.

[Niko @0xNiko1]

https://t.co/9Vi8xgxrPX

[Algero @0xAlgero]

MIT filmed an exam review in 2007 and the best minute is at 47:26, after all the exam advice is over. 223 thousand views in 17 years.

it is free on YouTube. lecture 7 of 18.02, the first exam review, taught by Denis Auroux.

a student asks how to differentiate a dot product. the product rule survives: d/dt (r · r) = r' · r + r · r' = 2 r · r'.
now assume the length never changes. |r|² = r · r = constant. differentiate both sides. 2 r · r' = 0. so r ⊥ r'.

that is all of circular motion in one line. if a point is stuck on a sphere, its velocity is tangent to that sphere. no picture, no angles, no trig identities.

the rest of the review is built from two products in the same flat way. n = a × b is a normal to a plane. the line where two planes meet runs along n₁ × n₂. the area of a triangle is ½|a × b|. and Mx = 0 has a nonzero solution exactly when det M = 0, which is just the vectors being coplanar, said in algebra.

r · r' = 0 is what a gyroscope obeys. it is why a normalized quaternion stays normalized under its update. it is why the tension in a pendulum rod does no work: the force points along r, the motion does not.

the math is free and public. so is the lecture. what nobody can sell you is the reflex to differentiate a constraint instead of drawing a picture of it. that reflex is built over a semester, not one video.

[Algero @0xAlgero]

An MIT professor opened his differential equations course by admitting that most differential equations cannot be solved, and then spent the whole hour teaching what to do about it.

The lecture is on MIT OpenCourseWare. Free, creative commons, first class of the semester. Almost nobody makes it to the end.

His point: He writes two equations on the board that look almost identical. One has the square on x, the other has the square on y. One you will learn to solve in a week. The other has no answer you can write down with elementary functions at all.

And equations like the second one are the rule, not the exception. Which means the entire skill you were trained in, isolate the variable and produce a formula, quietly stops working the moment the math describes something real.

Skip to 3:47, where he announces he will spend day one "not solving a single differential equation"and instead draws the geometry. The equation stops being a puzzle and becomes a map: At every point it tells you a slope, and the solution is just the curve that obeys those slopes all the way across.

Then at 36:39 he gives two rules that let you read that map: Solution curves cannot cross, and they cannot touch. Not by convention. Because a point can only have one slope, and existence and uniqueness makes it a theorem

No formula sheet. No answer key. A picture that tells you how the system behaves without ever telling you what it equals.

This is the actual literacy behind every dynamical model you have ever heard invoked. Climate, epidemics, orbits, interest rates, drug concentration in blood. None of it is solved. All of it is steered.

School sold you the closed form because closed forms are gradeable. The world runs on the picture, and the picture has been free for two decades.

[Niko @0xNiko1]

https://t.co/9Vi8xgxrPX

[Algero @0xAlgero]

A mathematician spent two hours answering a question a child could ask. How many ways can you wrap a 4-dimensional sphere around a 3-dimensional one? The answer is two.

Waterloo filmed it. It is free

His point: the question takes one line to ask and the heaviest machine in topology to answer. π₄(S³) = Z/2. Two elements. That is the whole answer.

He is William Gollinger. The talk is Serre Spectral Sequence II, from a seminar literally called "We Promise This Applies to Physics."

Skip to Example 4. He does not draw anything. He runs the spectral sequence and kills terms until a single group with two elements is left standing.

No pictures. No intuition. One machine, cranked to the end.

Then he goes further. A fibration hands you an exact sequence in homotopy but not in cohomology. He shows the cohomology version exists anyway, inside a range set by connectivity. Gysin sequences. Steenrod squares. Transgression.

That machinery is not decoration. Steenrod squares and Eilenberg-MacLane spaces are how physicists classify anomalies and topological phases of matter.

The seminar name is a joke that turned out to be true.

[Niko @0xNiko1]

https://t.co/9Vi8xgxrPX

[Algero @0xAlgero]

A physicist put his own face in front of a swinging bowling ball to prove one number never changes. The lecture is free. Almost nobody finishes it.

This is Walter Lewin at MIT, 8.01x, Lecture 10. Hooke's law, springs, pendulums, simple harmonic motion.

The idea is stubborn. A spring pulls back in proportion to the stretch, F = −kx. Out of that falls a period, T = 2π√(L/g). No mass in it, no amplitude. Swing it hard or soft, same time back.

Every system that hums sits on this. A bridge, a circuit, a clock, a market that overcorrects.

Watch him pull the ball to his chin, let go, and not flinch. He's betting his teeth on the math, not his nerve.

An engineer I know rewatches it before every resonance calculation.

Free on YouTube, chalkboard, one camera, subtitles on.

Some teachers say the period is independent of amplitude. He bets his face on it.

[Algero @0xAlgero]

A physicist put his own face in front of a swinging bowling ball to prove one number never changes. The lecture is free. Almost nobody finishes it.

This is Walter Lewin at MIT, 8.01x, Lecture 10. Hooke's law, springs, pendulums, simple harmonic motion.

The idea is stubborn. A spring pulls back in proportion to the stretch, F = −kx. Out of that falls a period, T = 2π√(L/g). No mass in it, no amplitude. Swing it hard or soft, same time back.

Every system that hums sits on this. A bridge, a circuit, a clock, a market that overcorrects.

Watch him pull the ball to his chin, let go, and not flinch. He's betting his teeth on the math, not his nerve.

An engineer I know rewatches it before every resonance calculation.

Free on YouTube, chalkboard, one camera, subtitles on.

Some teachers say the period is independent of amplitude. He bets his face on it.

[Niko @0xNiko1]

https://t.co/9Vi8xgxrPX

[Algero @0xAlgero]

@0xKonez apple tax exposed

[Algero @0xAlgero]

Edward Frenkel opened Berkeley's multivariable calculus in Lecture 1 with an idea most people think they already know. A curve. It's filmed, it's free, it sits on YouTube.

MATH 53. Multivariable Calculus. Curves in two and three dimensions. The first hour of the whole course.

Here's the claim. You think a circle is a shape. Frenkel says no. It's a motion.

A curve is a point moving in time. Write r(t) = (x(t), y(t)). As t runs, the point traces the path.

The circle is x = cos t, y = sin t. Flip one sign, y = −sin t, and the same picture runs backwards.

Same shape. Different journey. The parametrization carries direction and speed the picture alone can't show.

That's the seed of everything after. Velocity is the derivative. Arc length is the speed added up. It all starts here.

You're eight years late. The lecture is still free. What it teaches, seeing a shape as a motion instead of a drawing, is the thing no summary can hand you. It's built over a semester, not one video.

[Niko @0xNiko1]

https://t.co/9Vi8xgxrPX

[Algero @0xAlgero]

@0xNiko1 different path same result

[Algero @0xAlgero]

MIT filmed the hour that explains all growth and decay, and it fits on one chalkboard. Free, uncut, chalk only. Almost nobody watches it.

This is 18.01, Single Variable Calculus, Lecture 16, taught by David Jerison. Separation of variables.

For centuries, growth and decay looked like a hundred different problems. This lecture shows they're one equation wearing different clothes.

Every model of money, cooling, and radioactive decay rides on the move he makes here. Most people use those models daily and have never seen where they come from.

Watch the board in the middle. He takes dy/dx = ky. Splits it: dy/y = k dx. Integrates. Out falls y = A·e^(kx). Exponential growth, from one line of algebra.

An engineer I know rewatched it before building a decay model and said three tangled fields finally read as one equation instead of three.

You've been using the curve. You've never seen it earned.

[Algero @0xAlgero]

MIT filmed the hour that explains all growth and decay, and it fits on one chalkboard. Free, uncut, chalk only. Almost nobody watches it.

This is 18.01, Single Variable Calculus, Lecture 16, taught by David Jerison. Separation of variables.

For centuries, growth and decay looked like a hundred different problems. This lecture shows they're one equation wearing different clothes.

Every model of money, cooling, and radioactive decay rides on the move he makes here. Most people use those models daily and have never seen where they come from.

Watch the board in the middle. He takes dy/dx = ky. Splits it: dy/y = k dx. Integrates. Out falls y = A·e^(kx). Exponential growth, from one line of algebra.

An engineer I know rewatched it before building a decay model and said three tangled fields finally read as one equation instead of three.

You've been using the curve. You've never seen it earned.

[Niko @0xNiko1]

https://t.co/9Vi8xgxrPX

[Algero @0xAlgero]

Feynman stood at a Cornell blackboard in 1964. He drew a line every student and every AI lab still trips over. The BBC filmed it in black and white. Five minutes. It sits free on YouTube.

The clip is about knowing versus understanding. Between running the math and seeing what nature does. Every team cheering a model that gets the right answer stands on that line.

He was 46. Already a Nobel laureate. No slides. No jargon. One piece of chalk.

Here's the line. You can know a rule perfectly. You can plug in numbers and get the right answer every time. Feynman calls that knowing. It feels like mastery. It passes every test.

Then he twists it. Ask that person why. Ask what the symbols mean. Often the answer is nothing. They can compute the tide but can't say what pulls the water. They have the name, not the thing.

That's the whole distinction. Knowing is reproducing the answer. Understanding is rebuilding it when the problem shifts. One is memory. The other is sight.

Watch the middle. He splits the calculation from the comprehension. He's not insulting students. He's warning you about the sharpest illusion in learning.

The right answer that hides an empty head.

You're sixty years late. The lecture is still free. What it teaches, the gap between the answer and the why, is the one thing no shortcut hands you. It's built over years of asking "but why," not one clip.

[Niko @0xNiko1]

https://t.co/9Vi8xgxrPX