New answers tagged soft-question
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The signs "+" and "-" do not exactly correspond to positive and negative!
The negative of a number (or any element) in a group is just the inverse of that element with respect to the group operation.
We created $i$ as a solution to $x^{2} + 1 =0$ and extended the class of real numbers. However, this extended class had to be made into a group. So, $-i$ is ...
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I get a variant of this depressingly often when people find out I am an engineer. You might be surprised how many people think "engineering = math."
It's worse than you suggest. Being "bad at math" has actual consequences in life in ways being bad at music or history or poetry do not. Being bad at math means you likely make foolish decisions, especially ...
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Sometimes, the conversation never gets as far as "I was always bad at math." I was at a party with my wife while we were in graduate school. A guest asked her what she did, and my wife replied that she was a math teacher. The guest then turned and walked away, never saying a word in response, and never to be seen again. I think some people have some deep- ...
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I found this some time ago and I like the clear words:
http://thebestpageintheuniverse.net/c.cgi?u=math
Math doesn't suck, you do.
Every time I hear someone say "I suck at math," I immediately think
he or she is a moron. If you suck at math, what you really suck at is
following instructions.
Sucking at math is like sucking at cooking. I'm ...
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Since a vast majority of people are under the impression that mathematics is like the curricula they had in primary and secondary school, this is not too surprising.
Really they don't have any qualification to say they are bad at math. (I know I didn't see any real math until college.) They might have been bad at the curriculum, but that's understandable ...
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Finding some practical application for math can get people quite a lot more interested; helping them to feel like they have a mastery of the numbers; and thus of the world around them.
That most likely sounded like a paragraph of BS though, so what I'm really trying to advertise is the LOGO Programming Language; the story of Seymour Papert's Lisp-like ...
1
I think it depends on people. Beyond practicing, it's about logic, and sometimes about abstraction. I think a lot of people would find hard to put effort into it, because abstracion is a totally irregular way of thinking for an everyday people.
Just like anything else, math can be learnt anytime by anyone. Just have to begin it!
However, talking about it ...
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Oh good. This author solved two Millenium Prize problems in one short 5 page paper.
http://vixra.org/abs/1212.0137
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At the point where you say that you're a mathematician, that is then the most recent topic thrown into the "conversation pot", and the only connection most people have to that topic is that they were bad at it once upon a time. So that is all they can say, if they say anything at all.
That person you are speaking with was bad at math at a time when they ...
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Asserting you are a mathematician without immediately volunteering further details is just a bad thing. It's very closed.
The principle is simple: As soon as you mark yourself as part of a world that people are not part of and don't understand, you alienate them. Unless you give them something that relates to their own experience, you are going to have a ...
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I was never good at singing till a stranger at a wedding turned to my wife after the service and asked her "who was that bloke with the beautiful voice standing next to you?"
I once helped a person with their last chance at GCSE (high school) - they needed to pass to become a teacher. Looking at their work, they could do what they needed - indeed, over the ...
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Just ask what the student likes to do or does well. Then show that there is math in it. Then you can use this as a base to elaborate and cultivate an interest.
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I tend to nod agreeably and say that math isn't instinctive and takes a lot of time to learn, but that I was fortunate to have positive early experiences with math. Maybe I'll say a few words about what I think were key events (or key things that didn't happen--like never had a teacher who turned it into confusing drudgery), suggest that most people don't ...
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I respond with "what was your favorite subject?" If I was bad at it then I would say so. If I liked it even though I was bad at it, I would move the conversation to that topic. If I didn't like it, I would say so and ask "why was it your favorite subject?"
The "what do you do?" question is an attempt at finding a commonality and a mutually interesting ...
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To put a slightly different spin on this (before @Zev votes to close :) ). When folks ask me what I teach, I ask them to name their least favorite subject. Occasionally I do get English or history or science. But 90% of the time I get math ... to which I reply "bingo." :) I then engage them in a discussion about how math (generically) and history (for me and ...
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Math is hard for everyone. It takes long hours of practice to become competent. I think that's what people want to hear; and fortunately, it's true.
This reply has the advantage of steering the conversation in a somewhat more positive direction---in my experience, usually towards whatever it is that the person does like to do and has practiced long hours ...
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Edit: expanded
The purely formal process of combining axioms with laws of deduction to move from one "truth" to another "truth" is tautological.
But the meaning which we assign to mathematical statements exists outside of this formal system.
To illustrate the difference, consider the following thought experiment. Suppose there existed an oracle that told ...
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In addition to the other answers, which are valid and should be heeded, I found several other reasons not to submit a paper to vixra.
According to vixra itself, it is a parody of arXiv.
The individuals who run the vixra website don't provide their names, nor street addresses or other contact information or affiliation, merely a gmail address on the viXra ...
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There are some true gems on vixra. Ever wondered about $$\text{Heaven Breasts Structures,}$$ (some clarification: "From now on [...] double breasts are paired horizontally") or "The Creator's Question: If we substitute the expression (44) into the right-hand
side of the equation (28) or (32), does the solution (2) exist?"
This link contains all the relevant ...
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Look at the name of the analysis section
http://vixra.org/anal/
The website itself is an inducement to laugh
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Vixra is an absolute joke. It's where people send rubbish papers that can't pass the arXiv's very modest standards. I would strongly advise against this.
Yes, sadly true. It is unfortunate that it has become that. When I first heard about it, back in 2009, I thought it would be a good place to post early manuscripts for dissemination, particularly for ...
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I regularly use Arxiv since at least 1998. The first time I've heard about Vixra was reading your post a few minutes ago.
UPD: The paper titles in the Mathematical Physics section of Vixra are simply mind-blowing:
Calculate Universe 3 – Planck Units
Saint-Venant's Principle: Rationalized and Rational
Poster 6 for the Icm 2 Conference, CZ
The Structure of ...
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The arXiv is the natural place to send mathematics preprints. Many of the worlds mathematicians (ranging from the very top to undergraduate-level) send their preprints there. One can also submit a paper to the arXiv then subsequently update it.
Vixra is an absolute joke. It's where people send rubbish papers that can't pass the arXiv's very modest ...
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I will warmly recommend Mathematics: Its Content, Methods and Meaning, edited by Alexandrov, Kolmogorov and Lavrentiev, with contributions from many others. It's excellent and very affordable.
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This question does not have a unique answer. I will concur with Jonathan in that Jayne's "Probability Theory: the logic of science" is a great book.
This book changed my life as a scientist, converting me into a fervent Bayesian. For me it was a truly irreversible experience when I, for the first time, understood and comprehended that probability (as ...
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Perhaps the recent proof that there are infinitely many primes with a (fixed) bounded gap qualifies? (Although this story is not necessarily a happy ending for all, it has still caused quite the buzz!)
For those interested, I may as well add the actual work (subscription/campus IP/proxy required)
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I remember when Apéry's proof that $\zeta(3)$ is irrational appeared. There had been essentially no progress on values of
$$1+\frac{1}{2^n}+\frac{1}{3^n}+\frac{1}{4^n}+\cdots$$
for odd $n$ since the time of Euler.
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Smale's proof of sphere eversion and the proof of the Poincaré conjecture for dimensions 5 and higher were unexpected and completely out of the blue.
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I'm not sure this is correct, but I can't think of any precursors to Stephen Cook's invention of NP-completeness. With a single paper in 1971 he invented the idea of NP-completeness, previously unimagined, and showed that the satisfiability problem was NP-complete; this revolution has dominated the study of algorithms ever since. The same paper posed the ...
1
Without using π again, is it possible to add/subtract/multiply or
divide π by something to get just 3?
If you try such a thing, you would have to multiply by $3/\pi$, or divide by $\pi/3$ or add $3-\pi$ or minus $\pi-3$. These are all transcendental numbers, but there is an option.
Since $\pi=-i\ln\left(-1\right)$
So, you could multiply by ...
0
$\lfloor\lceil\lfloor\lceil\lfloor\lceil\lfloor\lceil\lfloor\lceil\lfloor \pi\rfloor + \pi\rceil - \pi\rfloor + \pi\rceil - \pi\rfloor + \pi\rceil - \pi\rfloor + \pi\rceil - \pi\rfloor + \pi\rceil - \pi\rfloor$...
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$$\sqrt{\dots \sqrt{6\sqrt{6\sqrt{6\sqrt{6\sqrt{6\sqrt{6\sqrt{6\pi-9}-9}-9}-9}-9}-9}-9}\dots }=3$$
(via iteration to find a fixed point in solving $(x-3)^2=0$.)
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Why not this?
$$3=\frac{\pi^2}{2\sum_{i=1}^{+\infty}\frac{1}{i^2}}$$
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Maybe that helps you playing aroung with the numbers some more $e^{i\pi} = - 1$.
Furthermore $-3e^{i\pi} = 3$.
EDIT
Of course $\lfloor \pi\rfloor = 3$.
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I guess the focus of the formula is not that you can evaluate certain integrals by plugging in function values, but that you can recover a function's values by an integral along a circle.
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Let $\pi$ be the prime-counting function.
Then $3 = \pi(5)$.
Or, to use $\pi$ twice, $3 = \pi(2\pi)$.
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Very late answer, but I figured I give it a shot, from the perspective of an economics graduate student.
There are clear connections between econ and math but the statement needs some qualification: Economics is about solving economics problem in the economics paradigm. How much math is involved in the solution depends on the subfield and the economist in ...
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$$3 \equiv \pi - 4 \times \left( \frac{1}{2 \times 3 \times 4} - \frac{1}{4\times 5\times 6} + \frac{1}{6\times 7\times 8} + ... \right) \\
= \pi + \sum_{n=1}^{\infty} \frac{(-1)^{n}}{(n)(2n+1)(n+1)}$$
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Once you get past precalculus, and maybe the basic calculus sequence, you might want to consider looking at the book "Concrete Mathematics" by Graham, Knuth, and Patashnik. The subtitle of the book is "A Foundation for Computer Science." The blurb on the back cover starts off "This book introduces the mathematics that supports advanced computer programming ...
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$$3 \cdot e^{2 k \pi i} ~ ~ ~ \text{for all} ~ k \in \mathbb{Z}$$
... maybe that is cheating.
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Higher abstract mathematics is probably going to be irrelevant to what you want to study. The most relevant mathematical topics for the typical programmer are some introductory mathematical reasoning, combinatorics, graph theory, calculus, differential equations, matrix algebra, and numerical analysis. Things like abstract algebra and analysis are not likely ...
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This is fun: $$\left\lceil \frac{\pi}{\sqrt[\pi]{\pi}}\right\rceil=3$$
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How about ... $$\lfloor{\pi}\rfloor$$
Or, perhaps ... $$-3 \cos(\pi)$$
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