How much of a math nerd are you?

For the discussion of math. Duh.

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How much of a math nerd are you?

Postby nurd.gurl » Mon May 05, 2008 1:26 am UTC

When I am bored, I either write Pascal's Triangle (about 15 rows) and then write out the whole "a, a+b, a^2+2ab+b^2" thing or count in binary. So I would consider myself reasonably high on the math nerd scale.

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Re: How much of a math nerd are you?

Postby nurd.gurl » Mon May 05, 2008 1:38 am UTC

So, I guess what I meant to ask is, "What astoundingly nerdy things do you do?"

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Re: How much of a math nerd are you?

Postby krilitor » Mon May 05, 2008 2:04 am UTC

-Counting in trinary on my hand (0=finger down, 1=finger bent, 2=finger extended, total 39365)
-Doing math in binary, trinary, and hex
-Reading books on math
-Doing physics problems for fun (ie How much power would be required to crash the moon into Earth in 1 minute)
-Other things I can't think of right now.

My hand hurts now from counting....
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Re: How much of a math nerd are you?

Postby Robin S » Mon May 05, 2008 2:13 am UTC

krilitor wrote:Doing physics problems for fun (ie How much power would be required to crash the moon into Earth in 1 minute)
If you were also a gaming nerd, you'd probably modify that to "72 hours".
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Re: How much of a math nerd are you?

Postby Xanthir » Mon May 05, 2008 2:49 am UTC

krilitor wrote:-Counting in trinary on my hand (0=finger down, 1=finger bent, 2=finger extended, total 39365)
-Doing math in binary, trinary, and hex
-Reading books on math
-Doing physics problems for fun (ie How much power would be required to crash the moon into Earth in 1 minute)
-Other things I can't think of right now.

My hand hurts now from counting....

That's why you don't do trinary! You just can't maintain it for any length of time.

Now, *binary*, you can do. I do all my finger-counting in binary. I have a calculator at hand too often to have learned fast binary math on my fingers, but I like being able to count to 1k easily. I've found that I can only reliably get two digits out of each foot, though (big toe, then rest of toes).
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Re: How much of a math nerd are you?

Postby Mathmagic » Mon May 05, 2008 3:08 am UTC

The only things I ever do is prove things for fun (I derived an expression for the amount of area swept out by an elliptical trajectory, not realizing Kepler did it first :razz:), and looking up maths and physics concepts on Wikipedia. I'll also apply physics and math to everyday scenarios, and subsequently get poked fun at for being such a math/physics nerd. :razz:
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Re: How much of a math nerd are you?

Postby Bassoon » Mon May 05, 2008 3:25 am UTC

I regularly get math problems generated in my head. For example, I figured out that the 3D diagonal of a rectangular prism is Sqrt(a2+b2+c2) I also figured out that the height of an isosceles is Sqrt(.75) * a, where a is the length of the two sides that are equal.

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Re: How much of a math nerd are you?

Postby Robin S » Mon May 05, 2008 3:33 am UTC

You mean an equilateral triangle.
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Re: How much of a math nerd are you?

Postby skeptical scientist » Mon May 05, 2008 3:51 am UTC

  • I am a graduate student in mathematics working on his PhD.
  • I read math books and papers in unrelated fields just for the hell of it.
  • I own and regularly wear math-related T-shirts, and have done so since I was 11.
  • I travel as far as China to attend mathematics conferences.
  • I get annoyed at the mistake on Star Trek when Wesley Crusher refers to a "Rianaman" tensor field.
  • When I need to procrastinate from my studies or otherwise take a break, I do math on internet forums.
  • I recently gave a seminar talk on some of the recreational math I did on said internet forums, and received compliments* on the quality of the talk.
  • I have several times mistakenly referred to a summer REU as a "recreational experience for undergrads" because research and recreation are the same thing.
  • I entered my first state-wide mathematics competition in 5th grade. I won it.
Do I win?
*I mistakenly typed that as "complements" because the latter occurs more often in my writing.
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Re: How much of a math nerd are you?

Postby antonfire » Mon May 05, 2008 3:52 am UTC

I once proved unique prime factorization. Rigorously. Took up 42 handwritten pages.

I also hand-calculated all indefinite binary quadratic forms (up to equivalence) up to discriminant 200 or so.

And, yes, I also procrastinate by doing math on forums.
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Re: How much of a math nerd are you?

Postby Mathmagic » Mon May 05, 2008 4:01 am UTC

skeptical scientist wrote:When I need to procrastinate from my studies or otherwise take a break, I do math on internet forums.
antonfire wrote:And, yes, I also procrastinate by doing math on forums.

For what it's worth, this applies to me too. I just figured that it was implied, since we're all here in the first place. :razz:
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Re: How much of a math nerd are you?

Postby skeptical scientist » Mon May 05, 2008 4:02 am UTC

mathmagic wrote:
skeptical scientist wrote:When I need to procrastinate from my studies or otherwise take a break, I do math on internet forums.
antonfire wrote:And, yes, I also procrastinate by doing math on forums.

For what it's worth, this applies to me too. I just figured that it was implied, since we're all here in the first place. :razz:

Yeah, that's basically an xkcd math forum universal property*. :P

*Feel free to demonstrate your math nerdiness by explaining why this is not an example of a universal property.
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Re: How much of a math nerd are you?

Postby Robin S » Mon May 05, 2008 4:15 am UTC

Clearly, xkcd forumites are not structurally identical; therefore, there do not exist isomorphisms between them, and so no universal property can possibly apply.
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Re: How much of a math nerd are you?

Postby Mathmagic » Mon May 05, 2008 4:47 am UTC

Robin S wrote:Clearly, xkcd forumites are not structurally identical

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Re: How much of a math nerd are you?

Postby Shakleton » Mon May 05, 2008 7:28 pm UTC

I usually write down random formulae including or solving for Pi. Or I draw a golden rectangle...or or or
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Re: How much of a math nerd are you?

Postby barysnikov » Mon May 05, 2008 7:50 pm UTC

I count in binary, write up paper scripts to show people how binary works. Like 8-4-2-1, each digit represents that and you add them up.

At one of those "guess how many peanut m&m's are in the jar" contest, i measured one of the m&m's measured the jar, then got within 20 m&m's of the actual number.

Um...and oddly enough, i actually do calculate which path to my destination will be the quickest.

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Re: How much of a math nerd are you?

Postby Robin S » Mon May 05, 2008 8:25 pm UTC

Shakleton wrote:I usually write down random formulae including or solving for Pi. Or I draw a golden rectangle...or or or
Was anyone else bothered by this repeated use of "or" without listing any operands?
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Re: How much of a math nerd are you?

Postby Shakleton » Mon May 05, 2008 8:34 pm UTC

Robin S wrote:
Shakleton wrote:I usually write down random formulae including or solving for Pi. Or I draw a golden rectangle...or or or
Was anyone else bothered by this repeated use of "or" without listing any operands?


I'm sorry but to my defense the direct translation is a very common way of saying you could list sooo much things in addition in Germany.

Let's do it like this:

[*]OR count in Binary
[*]OR do funny Math-Exercises I invented
[*]OR Think of two random numbers and a random operator and do the calculation in my head for training
[*]OR think of algorithms for my BASIC-Programms at home.

Or or or or
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Re: How much of a math nerd are you?

Postby Likpok » Mon May 05, 2008 10:39 pm UTC

I once proved unique prime factorization. Rigorously. Took up 42 handwritten pages.


I think you're doing it wrong... We did this in my class last semester, and it definitely didn't take that much space... (then again, I don't know where you started from, what theorems you took as given)

I'm majoring in computer engineering.

But I'm taking enough math courses for a math degree (or I was, the last time I checked).

I would get a double-major, but it would require me to take additional gen-eds.

I routinely look up new math on wikipedia.

I inform my friends of mathematical paradoxes.
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Re: How much of a math nerd are you?

Postby Sir_Elderberry » Mon May 05, 2008 10:45 pm UTC

Robin S wrote:
krilitor wrote:Doing physics problems for fun (ie How much power would be required to crash the moon into Earth in 1 minute)
If you were also a gaming nerd, you'd probably modify that to "72 hours".


Hah! No. Skull Kid failed because of that. I don't care how hard you play any ocarina, no Inverted Song of Time will give you time to stop that thing in one minute.

(Personally, I was always irritated that Terminus didn't suffer tidal effects from the descending moon, but, y'know, magic.)
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Re: How much of a math nerd are you?

Postby Likpok » Mon May 05, 2008 11:05 pm UTC

Sir_Elderberry wrote:(Personally, I was always irritated that Terminus didn't suffer tidal effects from the descending moon, but, y'know, magic.)


Clearly the moon was massless. :P

I mean. It had a face. How weird was that?
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Re: How much of a math nerd are you?

Postby Sir_Elderberry » Mon May 05, 2008 11:30 pm UTC

Likpok wrote:
Sir_Elderberry wrote:(Personally, I was always irritated that Terminus didn't suffer tidal effects from the descending moon, but, y'know, magic.)


Clearly the moon was massless. :P

I mean. It had a face. How weird was that?


I played that game this weekend for the first time in years, and I have to wonder how that didn't bother me as a child. I mean, it's really a pretty freaky thing, and nobody really seems to care that much iirc.
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Re: How much of a math nerd are you?

Postby antonfire » Mon May 05, 2008 11:44 pm UTC

Likpok wrote:I think you're doing it wrong... We did this in my class last semester, and it definitely didn't take that much space... (then again, I don't know where you started from, what theorems you took as given)
No, no. Rigorously.

Well, all right, I started with Z is a commutative ring with identity together with a nonempty well-ordered subset closed under multiplication and addition (the positive integers) and satisfying the trichotomy property.

After that, I didn't skip any steps, including applications of associativity, commutativity, and the like.
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Re: How much of a math nerd are you?

Postby skeptical scientist » Tue May 06, 2008 12:49 am UTC

Likpok wrote:
I once proved unique prime factorization. Rigorously. Took up 42 handwritten pages.


I think you're doing it wrong... We did this in my class last semester, and it definitely didn't take that much space... (then again, I don't know where you started from, what theorems you took as given)

I agree. Taking the basic properties of arithmetic on the natural numbers as axioms:
Spoiler:
  • (a + b) + c = a + (b + c)
  • 0 + a = a + 0 = a
  • a + b = b + a
  • (ab)c = a(bc)
  • 1a = a1 = a
  • ab = ba
  • a(b + c) = (ab) + (ac)
  • 0a = 0
  • 1 > 0
  • a > 0 or a=0
  • a < b and b < c => a < c
  • For any pair a,b, exactly one of a = b, a < b, and a > b holds.
  • a < b => a + c < b + c
  • a < b and c > 0 => ac < bc
  • a < b => a + 1 < b or a + 1 = b

I will also use the well-ordering principle of the natural numbers as well as induction.

Defn: We say a divides b, and write a|b, if b=ac for some number c. If a|b, we say a is a divisor of b.

Defn: We say p is prime if p>1, and p has no divisors among the natural numbers other than p and 1.

Lemma 1: 1 has no divisors among the natural numbers other than itself.
Proof: If c>1, a>0, ac>a, so ac ≥ a+1 ≥ (0+1)+1=2 > 1. Therefore if c>1, c does not divide 1.

Lemma 2: Let a and b be natural numbers, and let S be the set S={x : x is a natural number and a|bx}. Then for some k, S={nk : n is a natural number}.
Proof: Certainly a|ba, so a|bx for some x>0. By the well-ordering principle, a|bk for some least k>0. (In fact, k is at most a.) Certainly a|b(nk) for each natural number n, since there is some factor c with ac=bk, so a(nc)=b(nk), so S is contained in {nk : n is a natural number}. Suppose x is some other member of S, and k does not divide x. Then (easy proof by induction) x=mk+l for some 0<l<k. We know that a|bx, and bx=bmk+bl, so a|(bmk+bl), and therefore bmk+bl=ra. Since a|bk, bk=sa, so bmk=msa, and therefore bl=ra-msa=(r-ms)a, so a|bl contradicting the minimality of k. So k divides x.

Lemma 3: If a|bc, and a is prime, then a|b or a|c.
Proof: Let a|bc, and let S={x : x is a natural number and a|bx}. By the previous lemma, S={nk : n is a natural number} for some natural number k, and since both a and c are elements of S, k|a and k|c. If k=1, then a|b and we're done. Otherwise, since a is prime and k|a, k=a, and k|c, so a|c and we're done.

Lemma 4: If p|q1...qn and p is prime, then p|qi for some i.
Proof: By induction on n. If p|q1, then certainly p|q1. Now assume the result for n-1, and suppose p|q1...qn. By lemma 3, p|q1...qn-1 or p|qn. By the inductive hypothesis, p|qi for some i.

Lemma 5: If n>1 is a natural number, then n has a factorization as a product of primes.
Proof: By induction on n. If n=2, then n=2 is a prime factorization of n. If n>2, then if n is prime, n=n is a prime factorization. If n is not prime, then n=ab for some a,b<n. By the inductive hypothesis, both a and b have prime factorizations a=p1...pr and b=q1...qs. Then n=p1...prq1...qs is a prime factorization of n=ab.

Theorem: If n>1 is a natural number, then n has a unique factorization as a product of primes.
Proof: By lemma 5, the factorization exists, so we need only show that it is unique. We go by induction on n, noting that the result is true when n is prime. If n=p1...pr=q1...qs are two prime factorizations, then p1 occurs in the first factorization. By lemma 4. p1|qi for some i, and hence p1=qi, since qi is prime. So both factorizations are p1 times some prime factorization of n/p1; by induction, the latter is unique, so n admits a unique factorization as a product of primes.


That's about as rigorous as you can ask for. Since you specifically mentioned explicit applications of e.g. the commutative property, it seems like what you want is a formal derivation in first order arithmetic, which doesn't actually exist, since unique factorization is not a sentence of first order arithmetic, let alone a theorem. The best you can do is a sentence for each n asserting that if x has a prime factorization of length n, then this is unique. Since to capture unique factorization in first order arithmetic you need infinitely many theorems, you can't actually derive all of them in 42 pages.
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Re: How much of a math nerd are you?

Postby antonfire » Tue May 06, 2008 1:31 am UTC

skeptical scientist wrote:That's about as rigorous as you can ask for.
Only if you have low standards.

I started from a slightly different place than you did, but anyway, quick list a few of the many things you skipped, assuming you want to start from where I did (and most apply to where you started as well):

Define ">". Define "≥". Prove that if a>0, b>c, then ab>ac and various other properties of > and ≥ and |. (e.g., a>0, b|a => a≥b, used implicitly in the proof of Lemma 5.) If you prefer to start where you did, fine. Define "subtraction". When is it defined? Prove that it's well-defined in those cases. Prove various useful properties of it.

Prove induction from well-ordering or vice versa (why make more assumptions than you need?). Better yet, just use well-ordering everywhere, it generally looks better anyway.

Justify each "certainly" (this adds up to a lot). You have no idea how many times you've associated during all that until you check.

Define "p1...pn". Oh, wait, since, y'know, that's bad notation, use pi notation instead. Define pi notation. Prove that pi notation actually works. Prove various useful properties of it.

Define "factorization as a product of primes". Define "unique factorization as a product of primes" ("up to reordering"? "in ascending order"?). Don't play fast and loose with ordered sequences.


All the stuff you skipped adds up to a lot, and I wasn't exactly trying to squeeze every square inch out of every page. And, yes, I took a slightly longer path than you gave, since I also wanted to prove some nice-ish lemmas along the way.


And, no, I'm not talking about a proof in first order arithmetic. I'm talking about a formal proof1 that any ring that satisfies the conditions above (commutative ring with identity and a well-ordered non-empty subset closed under *, + satisfying the trichotomy property) has unique prime factorization. And, yes, that needs to be stated more precisely before it makes sense.

For example, applications of the commutativity property are just uses of the assumption that our ring is commutative.


1 Allowing defined terms and even, *gasp*, defined notation like a*b and f(x).
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Re: How much of a math nerd are you?

Postby skeptical scientist » Tue May 06, 2008 2:12 am UTC

There's a difference between being formal and being anal. When you ask me to justify "certainly a|ba" you're being anal. Explicitly stating every use of commutativity and associativity is also being anal - once I've stated that my set is a commutative ring, if I want to write abc instead of (ab)c and state that it is divisible by b (without specifying left-divisible or right divisible, and without proof), that should be reasonable under any level of rigor. Unless you actually want a formal line-by-line derivation, which nobody ever does except possibly the three formal derivation exercises they are given when they first learn what one is.

When you are writing mathematics, you should take into account that you are talking to a human, reasonably smart reader, and should try to follow the golden rule. As a reader, I would want someone to say "a|ba" or "a|bk, so a|bnk" without justification, since the justification is so obvious that reading it is a waste of my time. So while you should only use a phrase like "certainly" when the thing really is obvious, don't waste the reader's time by proving the obvious. (And when I say obvious, I really do mean obvious, and not "obvious" in the sense of the old joke of the mathematician who spends 15 minutes working something out before concluding, "oh yes, it is obvious".)

And yes, I would have done pi notation, except I'm trying to respect the users of the old skin by not using texmath when I don't have to.
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Re: How much of a math nerd are you?

Postby antonfire » Tue May 06, 2008 2:19 am UTC

skeptical scientist wrote:that should be reasonable under any level of rigor.
I never claimed my level of rigor was reasonable. In fact, I think I implied the opposite. Isn't that the point of this thread? "Feats" of unreasonable nerdhood?

It was never really meant to be read by anyone. It was a (useful) exercise, and I learned a thing or two from it. I was not "doing it wrong", unless by "doing it wrong" you mean "doing it very very rigorously".

skeptical scientist wrote:Unless you actually want a formal line-by-line derivation, which nobody ever does except possibly the three formal derivation exercises they are given when they first learn what one is.
Well, now you know that that last bit is wrong. (Well, okay, not quite, I stopped writing "commutativity" and "associativity" and "definition of subtraction" after a while and just wrote long chains like a(b-c)=a(b+-c)=ab+a(-c)=ab+-ac=ab-ac.)
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Re: How much of a math nerd are you?

Postby pkuky » Tue May 06, 2008 3:40 pm UTC

the point of writing math is getting the other guy to understand. I've frequently lost points on tests and competitions by assuming the tester knew what the hell he was talking about and just needed to be shown that I knew, rather then needed everything explained step-by-step.

I once stayed up till 230 doing discrete math. next morning at 730, I started getting up, the nrelized that by derivation of a slimy green strechable function over it's n! (or something combinatoricy which I don't remember) options, you can conclude that I would take far to long to get up for school and that there was no point in budging from the bed. so I rolled over and got back to half sleep.
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Re: How much of a math nerd are you?

Postby antonfire » Tue May 06, 2008 3:51 pm UTC

I did something very similar.

"Because the cardinality of the set of times between now and when I have to be in class is the same as that between a few minutes later and when I have to be in class, sleeping more can't actually make me any later. Back to sleep."
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Re: How much of a math nerd are you?

Postby Robin S » Tue May 06, 2008 3:55 pm UTC

Shakleton wrote:I'm sorry but to my defense the direct translation is a very common way of saying you could list sooo much things in addition in Germany.
Ah, I see. In English "etc." is more standard.

Sir_Elderberry wrote:I played that game this weekend for the first time in years, and I have to wonder how that didn't bother me as a child. I mean, it's really a pretty freaky thing, and nobody really seems to care that much iirc.
It freaked me out a fair bit when I first saw it.

antonfire wrote:"Because the cardinality of the set of times between now and when I have to be in class is the same as that between a few minutes later and when I have to be in class, sleeping more can't actually make me any later. Back to sleep."
You're assuming certain things about the nature of time there.
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Re: How much of a math nerd are you?

Postby Macbi » Tue May 06, 2008 4:16 pm UTC

I draw fibbonaci spirals (with circular arcs as approximations), doodle proofs of pythagoras' theorem (and occasionally think up one.), and draw out steps of cellular autonoma with various rules. I also play a mean game of Dots and Boxes.
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Re: How much of a math nerd are you?

Postby 3.14159265... » Tue May 06, 2008 4:41 pm UTC

1 -> Life -> Math -> 1
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Re: How much of a math nerd are you?

Postby BeetlesBane » Tue May 06, 2008 4:54 pm UTC

Robin S wrote:
Shakleton wrote:I'm sorry but to my defense the direct translation is a very common way of saying you could list sooo much things in addition in Germany.
Ah, I see. In English "etc." is more standard.
...

The same construction is used informally in American English. Unlike "etc.", it does indicate the nature of the conjoining.

My own nerd credentials? I memorized a small table of logarithms in high school. I had a collection of slide rules, this included a geared circular slide rule from the late 1800's. I have a graduate degree in math...

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Re: How much of a math nerd are you?

Postby pkuky » Tue May 06, 2008 8:40 pm UTC

someone just sent me a "happy indipendence day" poem that was aired on channel 101. my reply was "happy indipendence day to you too. 101 is prime. hooray for 101! hooray for all primes! hooray for factorials!..."
I went on for three lines describing various types of numbers to congratulate. and all this was sent to a non-mathy person.
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Re: How much of a math nerd are you?

Postby headprogrammingczar » Tue May 06, 2008 11:33 pm UTC

Not so much a math nerd as a logic/compsci nerd, but I try to make people solve this puzzle:
They refer to themselves in the plural third person. Who are they?
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Re: How much of a math nerd are you?

Postby Fafnir43 » Tue May 06, 2008 11:57 pm UTC

I tend to use words like "trivially" in everyday conversation. With non-mathematicians. Unintentionally.

I also got so hacked off at the poor level of exposition and rigour given at A Level when talking about matrices (they would literally just prove deep, general theorems for 2x2 and 3x3 matrices only and that by algebraic expansion) that I got hold of a few books and learned linear algebra. That was sort of when I realised I was a mathematician at heart...
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Re: How much of a math nerd are you?

Postby z4lis » Wed May 07, 2008 12:07 am UTC

headprogrammingczar wrote:They refer to themselves in the plural third person. Who are they?


You? O_o
What they (mathematicians) define as interesting depends on their particular field of study; mathematical anaylsts find pain and extreme confusion interesting, whereas geometers are interested in beauty.

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Re: How much of a math nerd are you?

Postby BeetlesBane » Wed May 07, 2008 12:18 am UTC

headprogrammingczar wrote:Not so much a math nerd as a logic/compsci nerd, but I try to make people solve this puzzle:
They refer to themselves in the plural third person. Who are they?

Just to display my weirdness credentials I'll answer "a group of clones of G. Julius Caesar."

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Re: How much of a math nerd are you?

Postby Sir_Elderberry » Wed May 07, 2008 2:59 am UTC

headprogrammingczar wrote:Not so much a math nerd as a logic/compsci nerd, but I try to make people solve this puzzle:
They refer to themselves in the plural third person. Who are they?


Anyone? Just because "you" is a solution that fits, doesn't mean it's the solution. Anyone who refers to themselves in the plural third person would be referred to in the same way.
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Re: How much of a math nerd are you?

Postby antonfire » Wed May 07, 2008 3:04 am UTC

Indeed. Another valid answer is "they".
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