Tagged Questions
3
votes
2answers
156 views
Why demonstrations are important in mathematics? [closed]
Good evening, I'm studying math and would like to know how important are mathematical proofs in the world and particularly in a school of mathematics
Thanks for your help
35
votes
3answers
745 views
What are examples of unexpected algebraic numbers of high degree occured in some math problems?
Recently I asked a question about a possible transcendence of the number ...
20
votes
4answers
539 views
Is $\mathbb{N}$ impossible to pin down?
I don't know if this is appropriate for math.stackexchange, or whether philosophy.stackexchange would have been a better bet, but I'll post it here because the content is somewhat technical.
In ZFC, ...
0
votes
1answer
470 views
Philosophy of a Mathematician.
Introduction
I don't study Mathematics at university, and probably I don't have any chances to have a little understanding of what mathematics in all its aspects.
But I love to find structures and ...
116
votes
22answers
9k views
Is mathematics one big tautology?
Is mathematics one big tautology? Let me put the question in clearer terms:
Mathematics is a deductive system: it works by starting with arbitrary axioms, and deriving therefrom "new" properties ...
0
votes
2answers
126 views
Big Topics in Mathematics [closed]
My question is as follows: It is now the year 2013 as we know it, and I'm wondering what the "big topics" in mathematics are. What fields are of utmost interest and foundation in the modern era? How ...
19
votes
5answers
404 views
What does it mean for a set to exist?
Is there a precise meaning of the word 'exist', what does it mean for a set to exist?
And what does it mean for a set to 'not exist' ?
And what is a set, what is the precise definition of a set?
4
votes
2answers
161 views
Does $\mathsf{ZFC} + \neg\mathrm{Con}(\mathsf{ZFC})$ suffice as a foundations of mathematics?
I've heard people make the argument that:
$\mathsf{ZFC}$ suffices as a foundations of mathematics because almost all theorems in the mathematics literature can be proven using $\mathsf{ZFC}$, so ...
6
votes
6answers
873 views
What is this physicist saying?
I do not want to poison this forum with politics. But I want to understand, precisely, what is meant by the bolded statement. It is made by a physicist who used to work at Harvard regarding the ...
8
votes
3answers
260 views
What have been some of the most revolutionary philosophical shifts in perspective in mathematics?
Often times, great revolutions in mathematics come from shifts in philosophical perspective. The shift from extrinsic to intrinsic geometry yields manifolds (and much else). The shift in focus from ...
7
votes
3answers
140 views
Measure of how much information is lost in an implication
In an implication like $p \implies q$, is there some measure of how much information is lost in the implication? For example, consider the following implications, where $x \in \{0,1,\ldots,9\}$:
...
1
vote
2answers
116 views
Just a thought… defining “competition”?
Let's think about galaxies and animals. At first, they seem completely different.
But their behavior seems to be governed by (or at least arise from) the same rules.
Think about competition. ...
37
votes
13answers
3k views
Is there such a thing as proof by example (not counter example)
Is there such a logical thing as proof by example?
I know many times when I am working with algebraic manipulations, I do quick tests to see if I remembered the formula right.
This works and is ...
3
votes
1answer
118 views
Formality fades away in the air
I'm trying to study by myself mathematics, but I realized that I have only a naive notion of certains building blocks of mathematics; certain parts of the formalism. So I tried to start with logic, ...
1
vote
1answer
193 views
Is mathematics considered a science [duplicate]
Possible Duplicate:
what is the definition of Mathematics ?
I would like to know if mathematics is considered a science? I've searched the internet and asked many people for insight to no ...
6
votes
1answer
225 views
Age of Stochasticity?
Today I came across D. Mumford's 1999 article The Dawning of the Age of Stochasticity, which is quite remarkable even after more than a decade. The title already indicates the theme, but I copy the ...
1
vote
3answers
320 views
Looking for philosophical subject for my Bachelor Thesis
In may 2013 I have to write a Bachelor Thesis for my bachelor Mathematics. I prefer to choose a subject which involves philosophy. At the same time I have the feeling that my university wants me to ...
7
votes
5answers
451 views
Mathematics, Philosophy and writing.
Do you know of any famous mathematicians who were also philosophers? I have heard of Descartes, Plato and Leibniz. Are there other good examples, especially more modern examples?
Also welcome are ...
0
votes
1answer
112 views
Infinite versus unendlich and double-negation
The German term for infinite is unendlich, which transliterates as non-ending, or non-finite.
This is just word-play but from a constructive point of view, is the shift from a negative to a positive ...
8
votes
1answer
245 views
How do mathematicians think about the existence of numbers?
Question: How do mathematicians think about the existence of numbers? And how did Newton, Euler, and other famous mathematicians thought about this concept?
I know that existence of numbers is a ...
4
votes
2answers
73 views
On the existence of number systems, and the extent to which we can extend them
The more I think about math, the less I realize I know.
Learning about complex numbers has called me to re-evaluate how I think of negative numbers, or even natural numbers. I have to say the ...
-1
votes
2answers
85 views
Is math the measurement of motion? [closed]
I know that math can be used to measure motion, like where something will end up over a period of time, but is math itself 'in' motion. Take a look at how you use math: You scribble, type, draw ...
3
votes
5answers
406 views
How to interpret material conditional and explain it to freshmen?
After studying mathematics for some time, I am still confused.
The material conditional “$\rightarrow$” is a logical connective in classical logic. In mathematical texts one often encounters the ...
21
votes
5answers
741 views
How is a system of axioms different from a system of beliefs?
Other ways to put it: Is there any faith required in the adoption of a system of axioms? How is a given system of axioms accepted or rejected if not based on blind faith?
(PD: I'm not religious)
5
votes
3answers
377 views
What are the reasons for not supporting constructive mathematics
It is obvious that in constructive mathematics, you cannot use the law of excluded middle. What else would be the reasons for not adopting constructive stance in mathematics?
16
votes
1answer
631 views
What did Gauss think about infinity?
I have someone who is begging for a conversation with me about infinity. He thinks that Cantor got it wrong, and suggested to me that Gauss did not really believe in infinity, and would not have ...
6
votes
1answer
138 views
Hidden structures
There is a lot of talk about "hidden structures" in the realm of mathematics: hidden structures in the ZFC system, hidden structures in the natural number system, and so on. Saunders Mac Lane ...
5
votes
4answers
349 views
From continuity to differentiability and analyticity- what's next?
Continuity is an intuitive concept. I will not dwell on the precise definitions of continuity and the rest here. Note that differentiability is a more restrictive condition than continuity, while ...
9
votes
5answers
823 views
The status of high school geometry
Okay, so we've all seen Euclidean geometry in primary and high school. Back then, I really thought of points as indivisible entities in space and lines as 'breadthless lengths'. As far as I could ...
6
votes
6answers
843 views
Inherently discrete concepts
Are there any concepts which are naturally defined only for the integers and so far has resisted any attempts at extension to other fields such as rationals or reals?
Does not meet criteria:
...
5
votes
1answer
212 views
Generalisation of dualities, what concept do dualities represent?
Duality is a concept that pops up in different areas of mathematics as well as other science, but besides being a "woo isn't that nice?", is there anything more to duality (than loosely stated some ...
1
vote
0answers
219 views
Examples of mathematical coincidences that had great influence on other domains [closed]
I am looking for natural coincidences in math that had an unexpected but significant influence (positive or negative) in shaping up further developments in math or in other domains.
For example:
One ...
4
votes
2answers
390 views
Can one rigorously define “meaningful” versus “arbitrary” in math?
Often we regard certain mathematical expressions, or elements thereof, as arbitrary, in the sense that they have no apparent reason or cause, whereas more beautiful or natural seeming expressions feel ...
7
votes
2answers
374 views
How many different proofs can a theorem have?
I notice some problems has many different proofs, do all theorems have multiple proofs, is there some theorems which has only 1 way to prove it? $n$ ways? infinite?
7
votes
1answer
238 views
When can we say that a theorem has been proven?
I'm taking a Data Structures and Algorithms course for a CS program. The introductory material was all mathematics, mostly a series of formulas that we are to remember. I can work through the formulas ...
35
votes
17answers
3k views
What's the goal of mathematics?
Are we just trying to prove every theorem or find theories which lead to a lot of creativity or what?
I've already read G. H. Hardy Apology but I didn't get an answer from it.
2
votes
10answers
2k views
Does a negative number really exist?
Second Update:
I see that some answers that reference my image are more closely answering my question.
Here is a second image to clarify my point.
Take this image representing a checkerboard like ...
11
votes
9answers
860 views
Problems that are largely believed to be true, but are unresolved
Are there unsolved problems in math that are large believed to be true, but for reasons other then statistical justification?
It seems that Goldbach should be true, but this is based on heuristic ...
29
votes
16answers
2k views
Non-Scientific questions solved by mathematics
I have a general question about the applications of mathematics.
What are some applications of mathematics that are not scientific, perhaps maybe literary or philosophical, or political.
I am ...
7
votes
5answers
978 views
Common misconceptions about math
YARFMO (Yet another reposting from Mathoverflow) ;-)
The more you know about math the more you find conceptions previously thought correct to be false:
1.) math is not as exact as many believe - in ...
8
votes
5answers
554 views
Time in Mathematics
I claim that it is commonly believed that Mathematical objects can be seen as genuinely static, with no "Platonic" time in which they do genuinely evolve.
Nevertheless time has its place in ...
9
votes
6answers
841 views
What mathematical questions or areas have philosophical implications outside of mathematics?
Please list both the problem/area and justify why it is important philosophically. This question doesn't cover questions that are only important within the philosophy of mathematics itself.
11
votes
6answers
1k views
Why do statements which appear elementary have complicated proofs?
The motivation for this question is : http://math.stackexchange.com/questions/4066/rationals-of-the-form-fracpq-where-p-q-are-primes-in-a-b and some other problems in Mathematics which looks as if ...
7
votes
4answers
327 views
Are the computable reals finitary?
In the comment thread of an answer, I said:
The computable numbers are based on the intuitionistic continuum, and are not finitary.
To which T.. replied:
Computable numbers are not based on ...
9
votes
4answers
835 views
Why does Benford's Law (or Zipf's Law) hold?
Both Benford's Law (if you take a list of values, the distribution of the most significant digit is rougly proportional to the logarithm of the digit) and Zipf's Law (given a corpus of natural ...
40
votes
4answers
2k views
What is “ultrafinitism” and why do people believe it?
I know there's something called "ultrafinitism" which is a very radical form of constructivism that I've heard said means people don't believe that really large integers actually exist. Could someone ...
212
votes
33answers
18k views
Do complex numbers really exist?
Complex numbers involve the square root of negative one, and most non-mathematicians find it hard to accept that such a number is meaningful. In contrast, they feel that real numbers have an obvious ...
