Mathematics Weekly Newsletter
Mathematics Weekly Newsletter

Top new questions this week:

Help me solve my father's riddle and get my book back

My father is a mathteacher and as such he regards asking tricky questions and playing mathematical pranks on me once in a while as part of his parental duty. So today before leaving home he sneaked …

(sequences-and-series) (puzzle)  
asked by Levix 55 votes
answered by johannesvalks 49 votes

What are some 'conceptualizations' that work in mathematics but are not strictly true?

I am having an argument with someone who thinks that it's never justified to teach something that is not strictly correct. I disagree: often, the pedagogically most efficient way to make progress is …

(soft-question) (examples-counterexamples) (teaching)  
asked by MGA 53 votes
answered by Dustan Levenstein 37 votes

How hard should a mathematician work?

Of course I would never compare myself to, and don't expect to be, one of the great mathematicians. However, I am curious as to how my work habits, dedication and passion differs from theirs. How …

(soft-question) (advice) (mathematicians)  
asked by JonHerman 30 votes
answered by Austin Stromme 23 votes

Is every factorial divisible by its sum of digits?

Denote by $\Sigma_d(t)$ the sum of digits in the decimal representation of the number $t$. Prove / disprove: $$\forall n\in \mathbb N:\ \ \Sigma_d (n!) | n!$$

(puzzle)  
asked by R B 19 votes
answered by Steven Charlton 38 votes

Mathematical Intuition Behind Schizophrenic Numbers?

Schizophrenic numbers (A014824) are numbers whose square roots "look" like rational numbers. They were first discussed in 2004 by Darling in the Universal Book of Mathematics (page 282), and I …

(soft-question) (recreational-mathematics)  
asked by ant11 18 votes
answered by Robert Israel 18 votes

Why is it that if I count years from 2011 to 2014 as intervals I get 3 years, but if I count each year separately I get 4 years?

I'm not a very smart man. I'm trying to count how many years I've been working at my new job. I started in May 2011. If I count the years separately, I get that I've worked 4 years - 2011 (year 1), …

(combinatorics)  
asked by bodacydo 16 votes
answered by N. S. 14 votes

Prove ${\large\int}_0^\infty\frac{\ln x}{\sqrt{x}\ \sqrt{x+1}\ \sqrt{2x+1}}dx\stackrel?=\frac{\pi^{3/2}\,\ln2}{2^{3/2}\Gamma^2\left(\tfrac34\right)}$

I discovered the following conjecture by evaluating the integral numerically and then using some inverse symbolic calculation methods to find a possible closed form: $$\int_0^\infty\frac{\ln …

(calculus) (sequences-and-series) (definite-integrals) (special-functions) (hypergeometric-function)  
asked by Vladimir Reshetnikov 16 votes
answered by David H 15 votes

Greatest hits from previous weeks:

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 any …

(puzzle)  
asked by user1092719 22 votes
answered by A.L 98 votes

Mathematicians ahead of their time?

In every field there's always that person who's just years ahead of their time. For instance, Paul Morphy (born 1837) is said to have retired from chess because he found no one to match his technique …

(soft-question) (math-history) (big-list) (mathematicians)  
asked by hb20007 57 votes
answered by MJD 55 votes

Can you answer these?

Upper bounding a Poisson Process with indicators of exponentials

Define $E_1,E_2,\ldots, E_i,\ldots E_n$ as i.i.d. exponentials with parameter $\lambda$. These define processes on some interval $[0,\delta]$ (think of $\delta$ as very small, it will come into play …

(probability-theory) (stochastic-processes)  
asked by Indigo 5 votes

Two question about how to compute this integral limit

Let $f: (-\pi,\pi]\to \mathbb R$ be continuous and let $p_x (u) = {(f(u+x) - f(x)) \cos ({u \over 2}) \over \sin ({u \over 2}) }$. I want to show that $$ \int_{-\pi}^\pi p_x(u) \sin (Nu) du \to 0$$ …

(real-analysis) (proof-verification)  
asked by blue 4 votes

Constructing a family of distinct curves with identical area and perimeter

Two recent questions were posed by Arjuba [1] [2] asking for counter-examples regarding whether two different figures could have the same perimeter and area. Responders quickly raised a number of such …

(analytic-geometry) (examples-counterexamples) (plane-curves)  
asked by Semiclassical 4 votes

New blog post:

Two points determine a line, three a quadratic — what has that got to do with CDs?

by Jyrki Lahtonen on Jul 24

In this post I describe how simple facts about polynomials are applied in correcting errors, for example scratches on compact disks.  The same technique is used in many other places, e.g. in the …

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