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 Yearling
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1h
comment Math: A discovery or a creation?
That said, much of good mathematics seems to have an inevitable character about it that makes the definitions (rules of the game) seem to arise naturally.
1h
comment Math: A discovery or a creation?
I think of math as a game: We can make up the rules however we like, but once they are set the game is in motion and the winner and loser of a single playthrough are unambiguously determined by the rules. The game of chess is surely an invention, but it could be considered a "discovery" that a particular move gives a checkmate.
Apr
7
awarded  Yearling
Apr
7
comment Has lack of mathematical rigour killed anybody before?
You're not quite right that we have to prove the area formula for a rectangle. Area is something that's tricky to define properly, but we often start by defining the area of a rectangle to be the product of its side lengths, at least for certain rectangles - this is then used as a basis to define area more generally. You have to start somewhere.
Apr
6
comment Problem sets for Combinatorics?
Discrete math is an enormous subject, so you don't want to work on just any problems.
Apr
6
comment Problem sets for Combinatorics?
You should probably ask your instructor. S/he will give you problems that are more relevant to what you're working on in class.
Apr
2
comment How do we know this algorithm always generates a new prime?
It's not always prime.
Mar
23
answered Operations on polyhedra
Mar
4
comment Number of permutations of the sequence
@String: Ah, you are right. I read too quickly.
Mar
4
comment Number of permutations of the sequence
This is A174700 in Sloane's. It doesn't look like there's any nice formula or generating function.
Feb
28
comment Is $\sum_ix_iy_i=\sum_ix_i\sum_iy_i$?
Check it with $x_i = y_i = 1$. $(1)(1) + (1)(1) = (1+1)(1+1)$?
Feb
26
comment Integrating over a symmetric-group function (elements being permutations)
What's A? Isn't $\int_A^A dz = 0$?
Feb
24
comment What is your favorite online graphing tool?
Also, GeoGebra can output TikZ code so that you can generate nice graphs in TeX which is very useful.
Feb
23
comment What's the difference between list and sequence (as mathematical concepts not programming point of view)?
I don't think I've seen the term list actually defined in a math book, although it probably is somewhere. Its usage is usually more informal than sequence, and its meaning should be inferred from context.
Feb
13
answered Examples of open problems solved through short proof
Feb
9
comment What to answer when people ask what I do in mathematics
At some point they'll realize that you are screwing around with them and they'll be annoyed. It's not so bad if you are clearly goofing around, but if they asked the question they are probably interested in an honest answer.
Feb
9
answered What to answer when people ask what I do in mathematics
Feb
6
comment Shall I include my inventions in book or first publish them in some journal?
Generally the appendix to a math book is a refresher course on material that ought to be familiar to most of its readers. If the content is completely new to the mathematical community it should be part of the main text.
Jan
21
comment What is the number $p(n)$ of partitions of an abundant number $n$ into distinct, proper divisors of $n$?
@WillJagy Ah, I didn't notice that they needed to be distinct.
Jan
21
comment What is the number $p(n)$ of partitions of an abundant number $n$ into distinct, proper divisors of $n$?
See oeis.org/A018818