Mathematics Weekly Newsletter
Mathematics Weekly Newsletter

Top new questions this week:

Why do we study real numbers?

I apologize if this is a somewhat naive question, but is there any particular reason mathematicians disproportionately study the field $\mathbb{R}$ and its subsets (as opposed to any other algebraic ...

(real-analysis) (soft-question)  
asked by MathematicsStudent1122 34 votes
answered by Jon Warneke 40 votes

Are there an infinite number of prime numbers where removing any number of digits leaves a prime?

Suppose for the purpose of this question that number $1$ is a prime number. Consider the prime number $311$. If we remove one $1$ from the number we arrive at the number $31$ which is also prime. If ...

(elementary-number-theory) (prime-numbers)  
asked by Farewell 28 votes
answered by Farewell 55 votes

Why do we classify infinities in so many symbols and ideas?

I recently watched a video about different infinities. That there is $\aleph_0$, then $\omega, \omega+1, \ldots 2\omega, \ldots, \omega^2, \ldots, \omega^\omega, \varepsilon_0, \aleph_1, \omega_1, ...

(cardinals) (infinity) (ordinals)  
asked by KKZiomek 27 votes
answered by jaska 25 votes

You have to estimate $\binom{63}{19}$ in $2$ minutes to save your life.

This is from the lecture notes in this course of discrete mathematics I am following. The professor is writing about how fast binomial coefficients grow. "So, suppose you had 2 minutes to save your ...

(combinatorics) (discrete-mathematics) (binomial-coefficients)  
asked by capablanca79 27 votes
answered by Carry on Smiling 32 votes

Are there theoretical applications of trigonometry?

I am a high school student currently taking pre-calculus. We have just finished a unit on analytic trig. I am curious to know if there are any purely theoretical uses for trigonometry. More ...

asked by Conan G. 26 votes
answered by David C. Ullrich 38 votes

Can you use both sides of an equation to prove equality?

For example: $\color{red}{\text{Show that}}$$$\color{red}{\frac{4\cos(2x)}{1+\cos(2x)}=4-2\sec^2(x)}$$ In high school my maths teacher told me To prove equality of an equation; you start on ...

(soft-question) (proof-writing)  
asked by BLAZE 22 votes
answered by Andrew D. Hwang 31 votes

How do we know the ratio between circumference and diameter is the same for all circles?

The number $\pi$ is defined as the ratio between the circumeference and diameter of a circle. How do we know the value $\pi$ is correct for every circle? How do we truly know the value is the same ...

(geometry) (pi)  
asked by Happy 21 votes
answered by shardulc 8 votes

Greatest hits from previous weeks:

A family has three children. What is the probability that at least one of them is a boy?

According to me there are $4$ possible outcomes: $$GGG \ \ BBB \ \ BGG \ \ BBG $$ Out of these four outcomes, $3$ are favorable. So the probability should be $\frac{3}{4}$. But should you take ...

asked by Niharika 17 votes
answered by lab bhattacharjee 88 votes

How many squares actually ARE in this picture? Is this a trick question with no right answer?

This is one of those popular pictures on sites like Facebook. I always see a huge variation of answers such as $8, 9, 16, 17, 24, 28, 30, 40, 41, 52,$ etc., yet I've never seen a definitive answer on ...

asked by user1092719 26 votes
answered by A.L 121 votes

Can you answer these?

Integer Triangle Radicals conjecture

An integer sided triangle has an area $A$. Heronian triangle areas have no radical, or radical 1. Otherwise, $4 A$ will always be of the form $a\sqrt{r}$, where $r$ is the squarefree radical of the ...

(geometry) (number-theory) (recreational-mathematics) (triangle)  
asked by Ed Pegg 11 votes

Measure on $\omega$ defined in the generic extension by an atomless measure algebra is atomless

Work in Cantor space with standard probability measure $m$. Suppose we are given a sequence of measurable sets $\bar{A}=\langle A_n : n\in \omega\rangle$ and a non-principal ultrafilter $U$ and the ...

(measure-theory) (set-theory)  
asked by Jing Zhang 4 votes

Abstraction and Genaralization

This is a (bit funny) ultra-soft question regarded to a type of thinking that is puzzling me. Suppose $a(p_{1}, p_{2}, p_{3}, p_{4}, ... , p_{n}, Q)$ denote: from the items $p_{i}$, find a common ...

asked by tpk 5 votes
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