How to defend Mathematics from "ignorant" people? Some of my friends are blaming me to stop talking about and studying Math. But I love Math so much and I do Math almost everyday. The problem is that some of my friends told me "go and get a life". I am asking this question because I would like to hear from experienced  and professional people what is wrong with these points (see below) and how to justify to people (like my friends) that Math is not only virtual things.
They told me a lot of things but I remember few of them now:


*

*How do $\pi$ being irrational helps you in your life? When did you use this in your whole life?

*Did you ever use or see in your life a matrix? 

*$A$ is singular. Great, and $\cdots$?

*Suppose you get the integral of a function $f$ and then what?

*$\cdots$.


I believe that Mathematics is used everywhere but I could not give argument to these friends. (Maybe for the integral I said that it measures an area and we use it in our life and somehow they are convinced).
Do you know a good reference that I must read so I can defend my beliefs about math? Or I have just ignore them and that's it?
Thanks.
P.S. I am doing a PhD on Theoretical Computer Science and I still do math (all kind of levels everyday). My friends are working in industry.
 A: In the actual world of smartphones and computer, I think that a good example of application of maths is the Fourier transform. I always introduce it as follow. First you ask the people to try to imagine how can your TV show a picture just by plugging a cable. There is something beautifully "magic" behind this fact. This is part of the signal processing which is (or was at least) almost completely based on the Fourier transform. This shows that without maths, no screen. And without screen, no cell phones, no computers, no playstation (I'm sure you'll find something that will concern directly your friends). Last thing to note is that Fourier probably wouldn't have found his results if he didn't knew how to compute an integral, what is pi and so on...
At the end, knowing how to determine whether $A$ is singular or not is as useful as knowing how to boil water. You don't need it until you're hungry and want to cook pastas.
A: Watch this and/or just ignore that sort of people. 
Use your energy for better, more pleasurable things.
A: Make the same argument about their job. If they're not farmers or something, probably what they do is more useless (well, I'd rather use redundant) than math.
Their objections are particulary stupid, too. I could understand if someone said something like "Zariski's topology, what the heck" , but really? The integral? Everything that they wear/use/eat makes use of integrals.
A is singular, well? Well the thing you're building may explode, have fun.
Also they should use matrices everyday in industries; if they don't, surely what clever people make them do does.
The $\pi$ question is the only one that kinda makes sense, however since it's a fundamental constant maybe knowing it's not a root of any polynomial is kinda useful. Since that polynomial would have awesome properties.
tl;dr change friends.
A: I take it your friends don't work in the kind of industry that uses math. Math and science are making themselves known behind the scenes in practically every aspect of our daily lives - what we eat, wear, drive, and do. It's in our electronic devices, our vehicles, our bank accounts. It's in the science-fiction-esque technology that allows us to go to the moon or map the sea's floor or see moving pictures on screens and hear things from holes in plastic devices or blow up entire cities instantaneously or map the universe through cosmic intervals of space and time - past, present, future, and lightyears of distance. Just because something seems tedious, dry, pointless, irrelevant doesn't mean it is to those who understand its significance and actively wield its power.
Savvy observers can distinguish between applied math and pure math, and ask what the latter has to say for itself. Like any hobby or passion or art or form of inquiry, it doesn't need to justify its existence with real-world use. (Personally, I've always taken to math as a form of escapism, as opposed to  something to tame life with.) But it does need to justify itself to society and government and corporations and comittees and citizens as something that requires our collective support - financially, culturally, bureaucratically. There is a spectrum or continuum of sorts between pure and applied, and everyone on this spectrum depends on their immediate neighbors for all sorts of insight, inspiration, understanding, experience and reference. Bolstering one end of the spectrum in the real world has run-off: it leaks strength into the other areas in education and hence industry.
There is also no telling when a serendipitous discovery fundamentally alters this spectrum, and turns something pure and applicationless into a staple of the modern world as we know it with global repurcussions. This has already happened for quantum mechanics with the nuclear bomb and logic with computers and number theory with crypto-security. Who knows what's next?
A: Well this is a social and personal question rather than a mathematical. I suppose the first thought I have is that if they are your friends, why are they not supporting you in what you want to do ? I think they are probably not so happy in their own life, so they want you to be just like them, it helps them to justify their own decisions.
It might be helpful to cultivate some new friendships with people already turned onto math. Finally, I think trying to justify your interest in math to other  does people is a waste of time, maybe when you are with these people focus on what you have in common, avoid math, and if math comes up treat it with a little humor. Take delight in knowing "useless" things. What does it do for you life ? It gives you pleasure.
