This might be a very stupid question but comes to mind when we encounter each and every topic of pure maths. Why we are studying this, what are the applications of this etc etc. The topics in the pure maths are abstract unlike applied mathematics. What will be the best answer satisfy a student of mathematics, to the question application of mathematics? Actually our mathematics teachers generally dont focus on applications in mathematics. Does this mean that mathematicians are more interested in the extension/generalization of previously known field or results rather than their applications?
I am trying to think/know about something, but I don't know if my base premise is plausible. Here we go.  Sometimes when I'm talking with people about pure mathematics, they usually dismiss it because it has no practical utility, but I guess that according to the history of mathematics, the math that is useful today was once pure mathematics (I'm not so sure but I guess that when the calculus was invented, it hadn't a practical application).  Also, I guess that the development of pure mathematics is important because it allows us to think about non-intuitive objects before encountering some phenomena that is similar to these mathematical non-intuitive objects, with this in mind can you provide me historical examples of pure mathematics becoming "useful"?
Can I safely uninstall games purchased from Steam? Can I uninstall purchased games from my computer and then later download them through Steam without having to re-purchase if I'd like to?   I'm running short on space on my laptop, looking to free up some space and wanted to be sure that I can safely re-download anything at a later time similar to how you can with the Xbox Live marketplace. Random errors on various sites when viewing main page Occasionally (very occasionally) when returning to the main page of a site by clicking on the logo I get the following message:     It was not possible to perform this tag search at this time due to an unexpected error.   This is odd because I'm not performing a tag search.  So far this has happened on both Movies &amp; TV and Cooking.  I have heard that others are getting this same message. I followed  to create a soccer ball.  Now I want to texture it in a way that every pentagon has an image inside itself and the exagons are white, but I also want everything to be a little glossy. I managed to successfully UV Map the ball and paint the texture in photoshop but now I am having big problems in applying the texture material to the mesh.    I've created a new material in Blender Render mode with Diffuse and the texture applied to it. I also set the Texture mapping to UV. I've gone in edit mode, selected all the mesh and applied the material. Unfortunately in Texture View Mode I see just a white ball and while rendering I see everything's black.      If I try to do this in Cycles Render and use a Mix Shader with the FAC set to the texture image I get what I want in the Texture View Mode but while rendering I just see everything black and white of my colored images.        I hope I've been clear enough and that someone will help me in this easy/difficult task! Thank you in advance i want to create new event in SharePoint calendar list in which I have some custom columns,i tried below code but it is not working      function bookingRoomForMeeting() {         var ctx = new SP.ClientContext(appWebUrl);//Get the SharePoint Context object based upon the URL           var list = ctx.get_web().get_lists().getByTitle("MyCalendarList"); //Get the List based upon the Title         var listCreationInformation = new SP.ListItemCreationInformation(); //Object for creating Item in the List         listItem = list.addItem(listCreationInformation);         listItem.set_item('Title', $("#txt_Title").val());         var date = $("#txt_startTime").val();         var dateTime = moment(date, 'DD/MM/YYYY HH:mm a').format("MM/DD/YYYY HH:mm a");         listItem.set_item('EventDate', dateTime);         var enddate = $("#txt_endTime").val();         var enddateTime = moment(enddate, 'DD/MM/YYYY HH:mm a').format("MM/DD/YYYY HH:mm a");         listItem.set_item('EndDate', enddateTime);         listItem.set_item('EmailId1', $("#txt_EmailId1").val());         listItem.set_item('EmailId2', $("#txt_EmailId2").val());         listItem.update();         ctx.load(listItem);         ctx.executeQueryAsync(             Function.createDelegate(this, success),             Function.createDelegate(this, fail)            );     } function success() {     alert("Completed"); } function fail() {     alert("operation failed"); }   list am using is SharePoint hosted app list,can any one tell me where am going wrong? We are familiar with the nifty fact that given the Fibonacci series $F_n = 0, 1, 1, 2, 3, 5, 8,\dots$ then $0.0112358\dots\approx 1/89$. In fact,  $$\sum_{n=0}^{\infty}\frac{F_n}{10^n} = \frac{10}{89}$$  How do we prove that, more generally, for $p &gt; 1$ then,  $$\sum_{n=0}^{\infty}\frac{F_n}{p^n} = \frac{p}{p^2-p-1}$$  (The above simply was the case $p = 10$.) Run multiple instance of a program in parallel How does evolving relate to CP? How can I convert JPG into PDF easily? Is there any way to batch convert .jpg files into single .pdf files? Font characters displayed as squares in Ubuntu 18.04 Recently, on my Ubuntu 18.04 I have noticed that at least on gnome-calculator and chromium browser the fonts are displayed as squares. I have followed instructions  and , the calculator is fixed, but the problem on chromium still exists when I open a dialog to search for a file.  Not sure if this happens on other applications as well, I haven't checked all my apps, but File managers nemo and nautilus are working fine.  Also, before few months ago, I have included some windows fonts for my libre office shown . I used the copy (cp) method, not the link (ln -s). But, was working fine until yesterday. Haven't done any major change or update, at least on my Linux partition (dual boot). But, I don't think that this has anything to do with that.  Any idea how can I fix this issue?  . Command to move a file to Trash via Terminal I would like to know if there is a command I can issue in a terminal so I do not classically remove (rm) the file, but instead move it to trash (i.e. Nautilus Move to Trash behavior).  In case there is such a command, I would also be interested in knowing what it is. Why there isn't a feature that lets any user on SO to request other user to answer their question? When I browse through other questions to find my answer, sometimes I'll find answers similar to what I'm looking for, and though they don't exactly answer my question, the author might be able to do so. Could we have a feature on SO that will let me request that another user answer my question, in case I find someone who could potentially answer my question? Irreducible cyclotomic polynomial I want to know if there is a way to decide if a cyclotomic polynomial is irreducible over a field $\mathbb{F}_q$? Cast ray to select block in voxel game Remove all packages installed from a PPA? I have installed LibreOffice 4 using PPA. I was using LibreOffice 3, then  I had upgraded to LibreOffice 4, because I was somewhat eager to try a new version.   Now since I found that LibreOffice 4 has some issues, including handling my native language, I want to move back to LibreOffice 3.  This question  has already some answers which has some similarity with my above mentioned issue, but it does not solve my problem. This question talks about downgrading from a specific version of LibreOffice, namely from 4.0 to 3.6. The solutions mentioned are not the ones I am looking for. They will work, but the  solutions suggest either downloading .deb files for LibreOffice 3.6 or adding PPA for them. Furthermore, some of the answers put out-of-proportion~(applicable for the solution, however) stress on use of , not general command-line-solution.     I want a general solution without using PPA or downloading .deb files. All I want is to move back from the (higher) PPA version to the (lower) official version.  Anyway, in order to accomplish this, I removed the LibreOffice config directory from my home and then purged LibreOffice from my machine.  sudo apt-get purge libreoffice-*   Then I removed the relevant PPA's using the sudo apt-add-repository --remove command. And then ran sudo apt-get update.  Now, when I try to install LibreOffice using the command  sudo apt-get install libreoffice   I get an avalanche of output about unmet dependencies, something like,   The following packages have unmet dependencies:  libreoffice : Depends: libreoffice-core (= 1:3.5.7-0ubuntu4) but it is not going to be installed (snipped)    If I dig the issue further, by using the command,  sudo apt-get install libreoffice-core   I get    The following packages have unmet dependencies:  libreoffice-core : Depends: libreoffice-common (&gt; 1:3.5.7) but it is not going to be installed                 Depends: libexttextcat0 (&gt;= 2.2-8) but it is not going to be installed                 Depends: ure (&gt;= 3.5.7~) but it is not going to be installed E: Unable to correct problems, you have held broken packages.    Could you please tell me how do I install LibreOffice 3 in my machine?  I am using Ubuntu 12.04 LTS.    EDIT  Before receiving , I was wondering, at this very moment, if I take a fresh computer, and install Ubuntu 12.04, LibreOffice installation will work without a hitch. Then why I can not install LibreOffice in my 12.04 machine today from simple command line?  Then the accepted answer clarified everything. I need to use ppa-purge so that this resets all packages from a PPA to the standard versions released for my distribution.  Basically it is like a way to restore my system back to the way it was before my installed packages from a PPA.  further elaborates the idea.    worked perfectly for me. Actually, this was an education for me since it taught me how do downgrade a package that was added via PPA. And I realized that the answer actually teaches us to "move from PPA installation  of a package to official lower version package." Showing a function on $[0,1]$ is the zero function Is there a string math evaluator in .NET? If I have a string with a valid math expression such as:  String s = "1 + 2 * 7";   Is there a built in library/function in .NET that will parse and evaluate that expression for me and return the result? In this case 15. I know that it is defined such that there is no more than one y-value output for any given x-value input, but I"m wondering WHY it is defined that way? Why can't we apply everything we know about functions to equations that have more than one y-value output for any given x-value input?   In short, what is the benefit or reason to define a function this way?  At the same time, a little historical context would also be appreciated (i.e., when the concept originated and why).  Thanks,  Moshe Where to ask Question that can be flagged too broad or opinion based When asking a new question and typing in the title we get a list of similar questions named     Questions that may already have your answer     That suggestions contains posts across all tags. Like the example in the screenshot it returns similar questions for Python, jQuery, SQL, C#, Java, C++, ...  This makes the list less useless unlikely people find a question that already answers theirs. If people actually find a similar question in that list many duplicates could be avoided.  So can tags I entered below the question be considered to update the list? And can the tag textbox maybe put above the question title? An example of a sequence of Riemann integrable functions $(f_n)$ that converges pointwise to a function $f$ that is not Riemann integrable.