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51
votes
4answers
3k 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 ...
4
votes
4answers
230 views

Looking for a book similar to “Think of a Number”

Many years ago, I had read a book entitled "Think of a Number" by Malcolm E. Lines, and it was an eminently readable and thought provoking book. In the book, there were topics like Fibonacci numbers ...
85
votes
19answers
4k views

Good Physical Demonstrations of Abstract Mathematics

I like to use physical demonstrations when teaching mathematics (putting physics in the service of mathematics, for once, instead of the other way around), and it'd be great to get some more ideas to ...
75
votes
22answers
18k views
6
votes
6answers
2k views

Best Intermediate/Advanced Computer Science book

I'm very interested in Computer Science (computational complexity, etc.). I've already finished a University course in the subject (using Sipser's "Introduction to the Theory of Computation"). I know ...
3
votes
5answers
2k views

Where can I find a review of discrete math

I'm looking for course notes and assignments and hopefully some example exams for Discrete Math, I'm taking a placement exam in the subject after having taken it 4 years ago.
110
votes
29answers
38k views

Best book ever on Number Theory

Which is the single best book for Number Theory that everyone who loves Mathematics should read?
49
votes
28answers
22k views

Best Maths books for non-mathematicians

I'm not a real Mathematician, just an enthusiast. I'm often in the situation where I want to learn some interesting Maths through a good book, but not through an actual Maths textbook. I'm also often ...
79
votes
30answers
12k views

What is the single most influential book every mathematician should read?

If you could go back in time and tell yourself to read a specific book at the beginning of your career as a mathematician, which book would it be?
208
votes
29answers
15k views

A challenge by R. P. Feynman: give counter-intuitive theorems that can be translated into everyday language

The following is a quote from Surely you're joking, Mr. Feynman . The question is: are there any interesting theorems that you think would be a good example to tell Richard Feynman, as an answer to ...
13
votes
11answers
8k views

Which 4 maths courses to take as an Economics PhD student?

I am doing a PhD in economics and I have the chance of taking one subject a semester in the maths department (I would like to do more, but "unfortunately" I have to work on my thesis). I want to have ...
49
votes
19answers
4k views

Mathematical subjects you wish you learned earlier [closed]

I am learning geometric algebra, and it is incredible how much it helps me understand other branches of mathematics. I wish I had been exposed to it earlier. Additionally I feel the same way about ...
307
votes
35answers
35k 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 ...
18
votes
10answers
19k views

Real world uses of hyperbolic trigonometric functions

I covered hyperbolic trigonometric functions in a recent maths course. However I was never presented with any reasons as to why (or even if) they are useful. Is there any good examples of their uses ...
14
votes
8answers
4k views

How would you describe calculus in simple terms?

I keep hearing about this weird type of math called calculus. I only have experience with geometry and algebra. Can you try to explain what it is to me?
14
votes
4answers
5k views

What are some classic fallacious proofs? [duplicate]

If you know it, also try to include the precise reason why the proof is fallacious. To start this off, let me post the one that most people know already: Let $a = b$. Then $a^2 = ab$ $a^2 - b^2 = ...
39
votes
10answers
4k views

Paradox: increasing sequence that goes to $0$?

It is $10$ o'clock, and I have a box. Inside the box is a ball marked $1$. At $10$:$30$, I will remove the ball marked $1$, and add two balls, labeled $2$ and $3$. At $10$:$45$, I will remove the ...
97
votes
24answers
24k views

List of Interesting Math Blogs

I have the one or other interesting Math blog in my feedreader that I follow. It would be interesting to compile a list of Math blogs that are interesting to read, and do not require research-level ...
18
votes
6answers
6k views

Real world uses of Quaternions?

I've recently started reading about Quaternions, and I keep reading that for example they're used in computer graphics and mechanics calculations to calculate movement and rotation, but without real ...
34
votes
10answers
3k views

Real life usage of Benford's Law

I recently discovered Benford's Law. I find it very fascinating. I'm wondering what are some of the real life uses of Benford's law. Specific examples would be great.
26
votes
23answers
2k views

Can you recommend a decent online or software calculator?

I'm looking for an online or software calculator that can show me the history of items I typed in, much like an expensive Ti calculator. Can you recommend any?
29
votes
7answers
1k views

What is your favorite online graphing tool?

I'm looking for a nice, quick online graphing tool. The ability to link to, or embed the output would be handy, too.
50
votes
10answers
16k views

List of interesting math podcasts?

mathfactor is one I listen to. Does anyone else have a recommendation?