Gmili

[Millie Marconi @MillieMarconnni]

A Stanford mathematician spent 40 years watching brilliant students fail at hard problems.

Not because they were stupid.

Because nobody taught them what to do before they started solving.

His name is George Pólya.

His 1945 book has sold over a million copies and never gone out of print.

Marvin Minsky, the man who built the first neural network machine at MIT, said publicly that everyone should read it.

Most people have never heard of it.

The failure Pólya watched repeat itself for four decades was always the same.

A problem appears. The student feels anxiety. They immediately start calculating.

Not because calculating was the right move. Because it felt better than sitting with not knowing.

The calculation was almost always wrong.

Not from lack of skill. From lack of understanding what was actually being asked.

He called it the most neglected step in all of problem solving.

Step one is to understand the problem. Not skim it. Not assume you've seen something similar. Actually understand it.

His filter was one question: can you restate the problem in your own words without looking at it?

If you can't, you haven't understood it. You've only read it.

Most people skip this and spend hours stuck on a problem they never actually understood.

Step two is to make a plan. Not execute. Plan.

The pattern Pólya saw in every successful problem solver was the same. When something feels impossible, find a simpler version and solve that first.

Not because the simpler version is the goal. Because it gives you a method you can carry back.

He phrased it once with precision: if you cannot solve the proposed problem, try to solve a related one.

That question alone is worth more than most problem-solving courses ever taught.

Step three is to execute. Everyone thinks this is the whole game.

It is the third of four steps. Pólya spent the least time on it because it is the most obvious. Once you understand and have a plan, execution is mostly patience.

Step four is the one almost nobody does.

Look back.

Not to check the arithmetic. To ask: can I verify this with a different method? Can I use this method somewhere else? What would I do differently?

This is where the real learning lives.

Every expert Pólya studied had this habit. Every struggling student skipped from the answer to the next question, carrying nothing forward, starting from zero every single time.

His deepest insight was not a technique. It was a diagnosis.

Intelligent people feel bad at problem solving because they confuse reading a problem with understanding it. They confuse starting to work with having a method. They confuse getting an answer with having learned anything.

These are not the same things.

The students who get genuinely good at hard problems are not the ones who practice more.

They are the ones who slow down at the two moments every instinct tells them to rush.

The beginning and the end.

The problem was almost never as hard as it looked.

They just hadn't understood it yet.

[Chad Crowley @CCrowley100]

“If a man isn’t willing to take some risk for his opinions, either his opinions are no good or he’s no good.”

— Ezra Pound, following his arrest for treason

[Eddie©️🇧🇷🇺🇸 @SantoRosario100]

Padre Paulo Ricardo diz ficar impressionado quando escuta isso no confessionário.

[Gmili @vitor1984egg]

@OrlandoFvrioso @ThiagoWontLose @obobnunes Será q esse é o futuro da gen z? Ser mais burro e aniquilado socialmente? Pq tipo a nossa geração é mais burra q a dos nossos pais. Brutal

[Gmili @vitor1984egg]

@OrlandoFvrioso @ThiagoWontLose @obobnunes Entrei numa licenciatura e parece que piora, porque, a cada ano que passa, os calouros são mais burros. Eu não me tiro desse parâmetro, porque o pessoal que entrou antes de mim teve uma educação muito mais adequada. E, tipo, os caras só nasceram um ou dois anos antes de mim.

[Gmili @vitor1984egg]

@OrlandoFvrioso Based

[Gmili @vitor1984egg]

@rodrigotoworld @obobnunes A ignorância é uma benção

[Gmili @vitor1984egg]

@switchshot21 @AlenSael Entendi, obrigado

[Gmili @vitor1984egg]

@AlenSael 400 dólares

[Gmili @vitor1984egg]

@FlamingForge Deve ser pq ele tinha 2 metros e era muito forte

[Gmili @vitor1984egg]

@Anthony62067690 Então quer dizer q eu nunca irei pro momento antes de eu nascer? Aquele preto da nossa mente q nao existe nada? O vazio ? Então eu vou ser infeliz pra sempre?

[Gmili @vitor1984egg]

@Anthony62067690 QUE DESGRAÇAAAAAAAAAAAAAAAAAAAAAAAAAAAAA

[Gmili @vitor1984egg]

@AltRightEspan Inspiração pra alguma arte marcial

[Alt Right España 𝕏 @AltRightEspan]

Esto ha ocurrido en Barcelona. La cara de abusón que tiene no se la quita nadie.

[Gmili @vitor1984egg]

@opslima Mas a verdade é que ele ficou preso em 2016 kkkk

[Thiago Marques | Católico @ThiagoSMarques3]

O mundo dos confortos assépticos se escandaliza com a penitência porque perdeu o senso do sagrado.

[le.hl @0xleegenz]

Either you push your limits or suffocate in your comfort zone

[Gmili @vitor1984egg]

@ars_critica Preciso estudar pra concurso

[Gmili @vitor1984egg]

@apenasmojitos @ars_critica Também kkkkk