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I have enjoyed math throughout my years of education (now a first year math student in a post-secondary institute) and have done well--relative to the amount of work I put in--and concepts learned were applicable and straight-to-the-point. I understand that to major in any subject past high school means to dive deeper into the unknown void of knowledge and learn the "in's and out's" of said major, but I really hate proofs--to say the least.

I can do and understand Calculus, for one reason is because I find it interesting how you can take a physics problem and solve it mathematically. It's applications to real life are unlimited and the simplicity of that idea strikes a burning curiosity inside, so I have come to realize that I will take my Calculus knowledge to it's extent. Additionally, I find Linear Algebra to be a little more tedious and "Alien-like", contrary to popular belief, but still do-able nonetheless. Computer Programming and Statistics are also interesting enough to enjoy the work and succeed to my own desire. Finally, Problems, Proofs and Conjectures--that class is absolutely dreadful.

Before I touch upon my struggle in this course, let me briefly establish my understanding of life thus far in my journey and my future plans: not everything in life is sought after, sometimes you come across small sections in your current chapter in which you must conquer in order to accomplish the greater goal. I intend to complete my undergraduate degree and become a math teacher at a high school. This career path is a smart choice, I think, seeing as how math teachers are in demand, and all the elder math teachers just put the students to sleep (might as well bring warm milk and cookies too). Now on that notion and humour aside, let us return to Problems, Proofs and Conjectures class.

Believe me, I am not trying to butcher pure math in any way, because it definitely requires a skill to be successful without ripping your hair out. Maybe my brain is wired to see things differently (most likely the case), but I just do not understand the importance of learning these tools and techniques for proving theorems, and propositions or lemmas, or whatever they are formally labelled as, and how they will be beneficial to us in real life. For example, when will I ever need to break out a white board and formally write the proof to show the N x N is countable? I mean, let's face it, I doubt the job market is in dire need for pure mathematicians to sit down and prove more theorems (I'm sure most of them have already been proven anyways). The only real aspiring career path of a pure mathematician, in my opinion, is to obtain a PHd and earn title of Professor (which would be mighty cool), but you really have to want it to get it--not for me.

Before I get caught up in this rant, to sum everything up, I find it very difficult to study and understand proofs because I do not understand it's importance. It would really bring peace and definitely decrease my stress levels if one much more wise than myself would elaborate on the importance of proofs in mathematics as a post-secondary education. More simply, do we really need to learn it? Should my decision to pursue math be revised? Perhaps the answer will motivate me to embrace this struggle.

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    "I'm sure most of them have already been proven anyways" For the record, 0% of all true statements have been proven. Formality aside, there are FAR too many known unsolved problems in math to list, all of which require proofs to settle.2012-04-09
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    Also, you seem to be asking two different questions: "How would being able to prove theorems make my life better?" and "Why are proofs an important part of mathematics?" Perhaps you could clarify for us which one you mean.2012-04-09
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    The ability to write proofs in mathematics is one of the foremost skills to have in order to become a mathematician. If you can't write a proof, or put ideas coherently together to form a proof, you can forget about being a mathematician.2012-04-09
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    Do you want to know how powerful proofs are? In the australian parliament people always squabble, like how the prime minister Julia Gillard squabbles with leader of the opposition Tony Abbott. The squables never end. Each person wants to be right. When you produce a rigorous proof, it ends all arguments. This is the true power of mathematical proofs.2012-04-09
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    Logic is the tool we use to discover truth, so the more skill in logic one has the easier it is to understand truth. If you don't value truth, then you probably won't care much about logic.2012-04-09
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    Primary and secondary mathematics education is largely about computation. So is first-year calculus, and even a lot of lineary algebra. Computation is important, but it’s not at the heart of mathematics: the heart is theorems and proofs. And I will be very blunt: I do not think that anyone who hates proofs ought to be teaching secondary school mathematics: the students would *not* be well served thereby.2012-04-09
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    I do have a few qualms with the amount of importance given to the axiomatic method, where most of the rigor, axioms and proofs are usually worked out after the fact. In A typical abstract algebra book the first few chapters are on notation, axioms etc (boring), the fascinating stuff comes later and rigor is built after the initial creative act. That being said, good for you if you instantly intuitively see the correctness of the many mathematical proofs without going through the formal derivation - i surely don't, and without the rigor, one cannot assert validity to another person.2012-04-09
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    Steven, I think the issue for you may be that you are still at the stage where the problems people ask you already have known solutions. In most fields where one would be expected to apply higher mathematical thinking, the goal is to solve a problem that has never been solved before and in order to do this, you need to be able to show that what you are doing is actually correct. That is where proof comes in. Intuition is well and good (and in fact most mathematicians are highly intuitive in their approaches to problems) but you need to be able to make it rigorous to be sure it is correct.2012-04-09
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    I think what you really want to do is engineering. That would suit your needs best.2012-04-09
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    If we take calculation as a jumping-off point, we can ask some questions ... How is it that we know that the methods we use for calculation always work? Having discovered a neat way of calculating something, can we apply it to the widest possible range of problems? The first question has to do with proof, the second with generalisation - a key feature of mathematics which hasn't yet made these comments.2012-04-09
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    You don't understand the importance of proofs, think we might as well do without them, _but_ want to become a high school math teacher? The mind boggles. Then you complain about teachers who put students to sleep -- presumably because they don't care about their subject -- all while explicitly planning to become such a teacher yourself? What is this I don't even2012-04-09
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    A high school math teacher typically has to prepare students for mathematics found in non-math majors and non-math careers. Perhaps it's exactly the focus on proof (irrelevant to high school students) that is soporific.2012-04-09
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    PLEASE do not become a maths teacher! You have no idea how much harm you can (and by the sound of it will) cause. Believe me, the job market us not in dire need of maths teachers who don't understand what mathematics is about.2012-04-09
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    Anyway, if you meant to ask a question, you better ask a question. This is just an (incredibly misguided) rant.2012-04-09
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    I voted to close because I feel the question is argumentative and the answer is overly subjective.2012-04-09
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    regarding the closure decision: what a shame. that this has been favourited 3 times suggests it is a valued question.2012-04-09
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    @Ronald: I apologize, I realize that my comment above might be read as saying that *your* answer is subjective. That is not what I intended. I was saying that in principle the collection of answers will include many subjective opinions, because I feel that the question is really a prompt for discussion.2012-04-09
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    @CarlMummert thanks :) that's understood. I don't take this personally!2012-04-09
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    I wish to echo Alex's statement: please steer clear of education. There are more than enough lackluster education majors--with their nearly incessant tantrums and whines of "Whaaaaah! When am I ever going to use this abstract algebra/topology/analysis/etc in real life?! **Whaaaaaaahhhhh!!**"--doing enough damage to K--12 math education. Do something else.2012-08-24
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    "If you can't write a proof, or put ideas coherently together to form a proof, you can forget about being a mathematician." I am not sure I can agree with that. I mean few people were born being able to write proofs.2013-12-08
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    Reminds me of: Is it unheard of to like math, but dislike numbers?2013-12-08
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    @MattGregory: I dont't care about "truth" and I like logic.2013-12-08
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    Now I read the entirety of Steven's question. I will probably have to calm down by proving some theorems.2013-12-08

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