Frontiers

The open problems (Riemann, Navier-Stokes, P vs NP) broken into what you need to even read them.

Lições

Advanced The Riemann Hypothesis Every non-trivial zero of the zeta function has real part ½, and with it, the primes obey their expected rhythm. Advanced Navier-Stokes existence and smoothness Do the equations of fluid flow always have smooth solutions, or can a fluid blow up in finite time? Advanced P versus NP If a solution can be checked quickly, can it always be found quickly? Advanced Goldbach's conjecture Every even number greater than 2 is the sum of two primes. Core The Collatz conjecture Halve it if even, triple-and-add-one if odd: does every start reach 1? Advanced The twin prime conjecture Are there infinitely many primes two apart, 3 and 5, 11 and 13, 101 and 103?

Nobody has solved these. Each page states the problem precisely, translates it into plain language, lists the exact prerequisites from the stages above, breaks it into the parts mathematicians actually work on, and says what is known. The point is not to solve them today; it is to be able to read them.

Mais lições

The Millennium Prizes

Millennium Prize Problems Navier–Stokes existence and smoothness P versus NP problem Hodge conjecture Birch and Swinnerton-Dyer conjecture Yang–Mills existence and mass gap Poincaré conjecture

Open questions in number theory

Goldbach's conjecture Abc conjecture Perfect number Riemann zeta function Prime number theorem Landau's problems

Solved, and how

Fermat's Last Theorem Four color theorem Classification of finite simple groups Hilbert's problems Kepler conjecture

Algumas destas lições são adaptadas a partir de textos abertos: Wikipedia. Cada página de aula nomeia sua fonte e licença.

Símbolos usados aqui

Toque em qualquer símbolo para a definição completa, uma imagem e o que cada letra nela significa.

Perguntas que as pessoas fazem

Can I actually work on these?

You can understand them, which is the honest first step and what these pages are for. Working on them means the full path through the stages above and then the research literature, but every person who has made progress started by reading the statement.

Why are they unsolved if so many people have tried?

Usually because the existing tools provably cannot work (the barriers in P vs NP), or because the problem mixes two structures mathematics handles separately (additive and multiplicative in Goldbach and Collatz). A solution needs a genuinely new idea.

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