There's no single "world's hardest" math question, as difficulty is subjective, but prominent unsolved problems include the Collatz Conjecture, the Riemann Hypothesis, the Navier-Stokes Existence and Smoothness problem, and the P vs NP problem, all of which are Millennium Prize Problems offering $1 million for solutions. These problems are incredibly complex, often deceptively simple to state but requiring profound new mathematical insights to solve, with some, like Collatz, baffling experts for decades.
Of the original seven Millennium Prize Problems listed by the Clay Mathematics Institute in 2000, six remain unsolved to date:
The 3x + 1 problem or Collatz Conjecture, also known as the 3n + 1 problem, is a famous unsolved problem in mathematics that has puzzled mathematicians for over half a century. The problem is deceptively simple to state, but it has resisted all attempts to solve it.
As much as we would like to have an answer for "what's 1 divided by 0?" it's sadly impossible to have an answer. The reason, in short, is that whatever we may answer, we will then have to agree that that answer times 0 equals to 1, and that cannot be true, because anything times 0 is 0.
Fraction = 1 / 12 = 0.0833333333333 | Desmos.
This is an easy one. The square root of 8, √8, can be denoted as √(2×4) which calculates to √(2×2×2)=2√2 which is an “irrational” number (decimal fraction: 2.82843 rounded to 5d. p).
The correct answer is 16.
Anyone who argues it's 1 is definitely wrong—and clearly isn't using PEMDAS correctly!
The conclusion is that while mathematics (resp. logic) undoubtedly is more exact than any other science, it is not 100% exact. We cannot be 100% sure that a mathematical theorem holds; we just have good reasons to believe it. As any other science, mathematics is based on belief that its results are correct.
Because 0.999... cannot be bigger than 1 or smaller than 1, it must equal 1 if it is to be any real number at all.
Science history: Russian mathematician quietly publishes paper — and solves one of the most famous unsolved conjectures in mathematics — Nov. 11, 2002. Mathematician Grigori Perelman solved the Poincaré conjecture, and then rejected the $1 million prize that came with it.
The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved mathematical problems, the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Riemann hypothesis, Yang–Mills existence and mass gap, and the Poincaré ...
The P versus NP problem is a major unsolved problem in theoretical computer science. Informally, it asks whether every problem whose solution can be quickly verified can also be quickly solved.
"I love you" in math often uses numerical codes like 143 (I=1, love=4, you=3 letters) or mathematical expressions, like graphing the equation 3sin(x)−2sin(2x)+sin(3x)=03 sine x minus 2 sine 2 x plus sine 3 x equals 03sin(𝑥)−2sin(2𝑥)+sin(3𝑥)=0 to draw the words, or representing infinity as 1/∞1 / infinity1/∞ for endless love, showing love through unique formulas, functions, or codes.
PEMDAS term is used mainly in the US but in India and the UK, we call it as BODMAS. But there is no difference between them.
If we know the prime factorization of 32, we can write the simplest radical form of the square root of 32. Thus, the prime factorization of 32 is 2 × 2 × 2 × 2 × 2. If it is written in the radical form, then the simplest radical form of the square root of 32 is 4√2. Square Root of 32 in Radical Form: 4√2.
A 'correct answer' is defined as a response that accurately reflects the right solution to a question, contributing to the total score in a testing scenario, as exemplified by the calculation of maximum possible correct answers in a group of questions.
You simply have to do the math. 2/3 becomes a decimal if you actually divide 2 by 3. The result will be 0.666, so about 0.67. Now, if you want to go the opposite way, knowing the place values becomes important.
There is no correct answer. The problem is an anomaly caused by writing division horizontally and following it with multiplication without clarifying what the denominator is. The left to right rule is an arbitrary attempt to compensate for subtraction and division not being Commutative.