The following question is a question that confuses my mind long since.  I'm sorry if it looks nonsense.     If mathematicians who had made important discoveries in mathematics such as Bernhard Riemann, Carl Friedrich Gauss, Évariste Galois, Joseph Fourier, Leonhard Euler, Niels Henrik Abel and others had joined today's mathematics olympiads ( for example , IMO)  would they all won the gold medal (perfect score) ?   Should the mathematician who did mathematical discoveries be an Olympiad winner in the past?  These questions can actually be dealt with in $1$ single question.     A person who has not joined IMO, can contribute to mathematics in the future?   Thank you and Best Regards.
I am extremely poor in solving a problem quickly, which leaves me doing badly in olympiads and other contests. But, if I just don’t give up on a problem, no matter how much time it takes, I usually end up solving it. To have a future in mathematics or physics, is it necessary for me to excel at contests, because these days children excelling at contests have an advantage over those who don’t (not complete advantage, but advantage nonetheless)?
How to control the coordinates in Tikz & Matrix? I use Tikz with Matrix because I need to draw arrows and write on and beside the matrix. However, I don´t control the coordinates well other than using trail and error. For instance in the matrix below I have put an X at (0,0) and it is not in the centre of the matrix. However, if the matrix is 4x4 than it is in the centre. Is there any convenient way to know the coordinates? \documentclass[border=1cm]{standalone}  \usepackage{tikz} \usetikzlibrary{matrix}   \begin{document}  \begin{tikzpicture} \matrix(m) [matrix of math nodes, nodes in empty cells, nodes={minimum size=1cm, outer sep=0pt, text height=1.5ex, text depth=.25ex}] {  36     &amp;   &amp; 32    &amp;   &amp; 33    &amp;   \\         &amp;   &amp;       &amp;   &amp;       &amp;   \\  10     &amp;   &amp; 8     &amp;   &amp; 7     &amp;   \\         &amp;   &amp;       &amp;   &amp;       &amp;   \\  12     &amp;   &amp; 17    &amp;   &amp; 16    &amp;   \\         &amp;   &amp;       &amp;   &amp;       &amp;   \\  23     &amp;   &amp; 15    &amp;   &amp; 16    &amp;   \\     &amp;   &amp;   &amp;       &amp;   &amp;       &amp;   \\ };  \draw (m-1-1.north west) rectangle (m-8-6.south east);    % Lineas horizontales \foreach \i in {2,4,6,8} {   \draw (m-\i-1.south west) -- (m-\i-6.south east); }  % Lineas verticales \foreach \j in {2,4,6} {   \draw (m-1-\j.north east) -- (m-8-\j.south east); }  % dual ui \node [font=\color{red}] at (3.5,3) {$\ge 10$}; \node [font=\color{red}] at (3.5,1) {$\ge 8$}; \node [font=\color{red}] at (3.5,-1) {$=4$}; \node [font=\color{red}] at (3.5,-3) {$=3$};  % dual vj \node [font=\color{red}] at (-2.5,-5) {$\le12$}; \node [font=\color{red}] at (-0.5,-5) {$=12$}; \node [font=\color{red}] at (1.5,-5) {$=6$};  \node [font=\color{red}] at (0,0) {X};  \end{tikzpicture}     \end{document} Positioning relative to page in TikZ Will Winterbash promote mass spamming due to its short time frame? Is there any concern that , due to their time-limited nature, will encourage mass spamming of posts? Cosmopolitan, for example, can only be achieved by posting to Meta. There are over one million users on Stack Overflow who may want this hat, and have only until January 4th to get it, and their only means of doing so is to invent some reason to post to Meta. in my mariadb i have replication, i tried to change the location of the binlogs by changing the configuration file as so: log-bin = /new/path/mysql-bin I also tried to change the index location as so: log_bin_index = /new/path/mysql-bin.index but every time when I restart I see that the location of the binlog files is /var/lib/mysql... i tried to check with mysqld --verbos --help | grep bin and I saw that the lob-bin parameter is mysql-bin and not what I wrote in the cnf... how to I make the MySQL to take the value of the log-bin from the cnf file? this is the cnf file of the MySQL for sure... A sequence includes $a_p=\sqrt2$, $a_q=\sqrt3$, $a_r=\sqrt5$ for some $1\leq p<q<r$. Can these be terms of an arithmetic progression? harmonic? How do I become a Werewolf? I've heard that one of (maybe the only?) secret races in this game is a werewolf.  How do I become a werewolf?  And by extension, how do I cure lycanthropy, that is, if there even is a cure? Creating intuition about Laplace & Fourier transforms I am going to start a phd at the US with an F1 visa. University told me that I could enter the US only 30 days before the date on I-20. Since English is not my first language (and this would be a big change in my life) I would like to go there by June.  The thing is that I have an European passport with a valid ESTA. My plan would be to arrive with this passport, stay 4-6 weeks , go to Canada for a short vacation (maybe flight maybe by land) and come back to the USA with F1 visa.  I have two questions about this:  1) is this possible?   2) If yes, how could I justify knowing I will lose my come-back flight during my first entry? (I would purchase round trip because one-way are too expensive, probably with less than 90 days difference) Why am I getting black photos when I use the Manual feature on my DSLR? I was taking photos a few days ago, and I had it set to Manual. After about four photos, the rest started coming out black. I could see through my eyepiece clearly, and it took the photo normally, but when I reviewed it they were all black. Formula between wire size and current Is there a mathematical formula between wire size, current, temperature and wire type(Or resistance)? I need to calculate the SQRT of  $x$ to $y$ decimal places. I'm dealing with $128$-bit precision, giving a limit of $28$ decimal places. Obviously, if $\,y &gt; 28$, the , which I'm currently using, becomes futile, as it simply doesn't offer $y$ decimal places.  My question to you is, can I calculate the Square Root digit-by-digit? For example, calculating the $n$-th digit, assuming I already have digit $\,n - 1$. I'm well aware this may be impossible, as I've not found any such method through Google yet, just checking here before I give up in search of arbitrary precision methods. How to write (La)TeX (with parentheses) [or any other TeX-related logo] Uniform integrability of a backward submartingale Let $\{\mathcal{F}_n\}_n$ be a decreasing sequence of sub-$\sigma$-fields of $\mathcal{F}$($\mathcal{F}_{n+1}\subset\mathcal{F}_n$) and let $\{X_n\}_n$ be a backward submartingale($E[|X_n|]&lt;\infty$, $X_n$ is $\mathcal{F}_n$ measurable and $E[X_n|\mathcal{F}_{n+1}]\geq X_{n+1}$).  If we know $l=\lim_{n\rightarrow\infty}E[X_n]&gt;-\infty$, how to prove that $\{X_n\}_n$ is uniformly integrable? Many thanks!  I have an idea, it is enough to show:    $\sup_nE[|X_n|]&lt;\infty$;  $\forall\epsilon&gt;0$, $\exists\delta&gt;0$ s.t. $\forall A\in\mathcal{F}$ such that $\mathbb{P}(A)&lt;\delta$, we have $\sup_nE[1_{A}|X_n|]&lt;\epsilon$.    For $|X_n|=2X_n^+-X_n$, we have  $$E[|X_n|]=2E[X_n^+]-E[X_n]\leq 2E[X_0^+]-l\leq 2E[|X_0|]-l$$  which implies $\sup_nE[|X_n|]&lt;\infty$.  Secondly, $\forall A\in\mathcal{F}$, we can suppose without loss of generality that $A\in\mathcal{F}_0$.  $$E[1_{A}|X_n|]=2E[[1_{A}X_n^+]-E[[1_{A}X_n]$$  Does someone have an idea for this term? Thanks a lot..... I'm fairly new to blender and not a graphics person by any stretch of the imagination. I've been having some success though modelling semi-reflective glass for a project I wish to build (physically) and I'm wondering if it is possible to model the effects of a lens. The lens I wish to model is a double-convex type. It has a diameter of 120mm and a focal-length of 301mm. Is this something that can be modelled in blender and if so, how? I'd like to be able to position the camera close to this lens and reproduce the magnifying effects of the lens on the scene behind the lens as well as depth-of-field effects.  Thanks a lot. One of the drivers behind the 'Rule of Two' is that with fewer Sith, the dark side will become more concentrated in those users and they will be more powerful as a result. Is there any indication that the same is true for Jedi? A while back, I read a story in a collection, but I don't remember very much. I know that it was about some missionaries on Mars. Eventually they found a bunch of spheres that apparently have escaped sin by leaving the material world. I don't remember anything else about it. Someone told me that it was in "The Martian Chronicles" by Ray Bradbury, but I checked my copy and couldn't find. I'm pretty sure that it was by Ray Bradbury though. Help would be greatly appreciated. Multiple forms in delphi Why don't I have this option?    here's my disk layout  sudo fdisk -l  Disk /dev/sda: 640.1 GB, 640135028736 bytes 255 heads, 63 sectors/track, 77825 cylinders, total 1250263728 sectors Units = sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes Disk identifier: 0x5b53cc54     Device Boot      Start         End      Blocks   Id  System /dev/sda1   *        2048      409599      203776    7  HPFS/NTFS/exFAT /dev/sda2          409600  1153767021   576678711    7  HPFS/NTFS/exFAT /dev/sda3      1216962560  1250050047    16543744    7  HPFS/NTFS/exFAT /dev/sda4      1250050048  1250261679      105816    c  W95 FAT32 (LBA)  Disk /dev/sdb: 4005 MB, 4005527552 bytes 32 heads, 63 sectors/track, 3880 cylinders, total 7823296 sectors Units = sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes Disk identifier: 0x20d8782d     Device Boot      Start         End      Blocks   Id  System /dev/sdb1   *          63     7822079     3911008+   c  W95 FAT32 (LBA) There's a story my grandpa use to tell me when I was younger, about the sole survivor of of an attack on a mining vessel in space. The man lives in space for months/years, ignored by the company he worked for and never rescued. Then when he thinks he is being rescued, it's actually another set of raiders who attack him and kidnap him.  He then wakes up in captivity in some sort of prison inside of an asteroid, and has a word tattooed on his forehead. My grandpa called him Ronin (that's what the tattoo on his forehead said) but I don't know what the character's real name is. Anyways, he learns that he has the ability to teleport after having a brush with death and decides to make his way back to Earth so that he can exact revenge on the mining company who abandoned him and left him floating to die.  Does anyone know what this story or book may be? My grandpa told it to me when I was little, he said that he got it from a book he use to love reading when he was younger. I'm assuming the book is very old (possibly pre 1940's as he was born in the 20s). I can't ask him as he is no longer alive. I'm also unsure as to whether or not all the details in the story he told me, are the same as in the original. I have a dataset with a large number of Yes/No responses. Can I use principal components (PCA) or any other data reduction analyses (such as factor analysis) for this type of data? Please advise how I go about doing this using SPSS.