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8 votes
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Imaginary numbers may be essential for describing reality
5 votes -
Sounds of the Mandelbrot set
8 votes -
You could have invented Homology, part 1
6 votes -
A picture of Graham's Number
6 votes -
Why do Biden's votes not follow Benford's Law? Debunking an election fraud claim
24 votes -
Calculus explained and illustrated
6 votes -
Understanding hyperbolic geometry by illuminating it
3 votes -
The universal geometry of geology
10 votes -
Proving that 1=2, Bob Ross style
6 votes -
Decoding the mathematical secrets of plants’ stunning leaf patterns
6 votes -
The art of code - Dylan Beattie
7 votes -
Neutrinos lead to unexpected discovery in basic math
11 votes -
The complete idiot’s guide to the independence of the Continuum Hypothesis: part 1
9 votes -
How eugenics shaped statistics
9 votes -
Measuring the size of the Earth
3 votes -
How storytellers use math (without scaring people away)
4 votes -
What is 0 to the power of 0?
13 votes -
What is math? A teenager asked that age-old question on TikTok, creating a viral backlash, and then, a thoughtful scientific debate
12 votes -
I learned how to do math with the ancient abacus — and it changed my life
9 votes -
A math problem stumped experts for fifty years. This grad student from Maine solved it in days
19 votes -
There are forty-eight regular polyhedra
8 votes -
Terry Tao on what makes good mathematical notation
4 votes -
Division by zero in type theory: a FAQ
4 votes -
Why do prime numbers make these spirals?
12 votes -
The Monty Hall problem
22 votes -
Does anyone have resources for an introduction to semidefinite programming?
I'm interested in the subject, but don't know where to begin investigating it. I tried to look over the code for SeDuMi, but it is much more massive than I had realized. I have a background in...
I'm interested in the subject, but don't know where to begin investigating it. I tried to look over the code for SeDuMi, but it is much more massive than I had realized. I have a background in mathematics, if anyone can point me towards a textbook.
5 votes -
Bertrand Russell’s infinite sock drawer
8 votes -
A neat introduction to representation theory and its impact on mathematics
5 votes -
A surprising Pi and 5
3 votes -
Against Set Theory (2005) [pdf]
11 votes -
An inmate's love for math leads to new discoveries: Published in the journal Research in Number Theory, he showed for the first time regularities in the approximation of a vast class of numbers
8 votes -
At the limits of thought: Science today stands at a crossroads--will its progress be driven by human minds or by the machines that we’ve created?
3 votes -
Predictability: Can the turning point and end of an expanding epidemic be precisely forecast?
7 votes -
Periodic functions
Does there exist a function that does not include any trigonometric function in its definition that has similar properties (periodicity, for instance) as trigonometric functions? I can't think of...
Does there exist a function that does not include any trigonometric function in its definition that has similar properties (periodicity, for instance) as trigonometric functions? I can't think of any, and this strikes me as a bit surprising.
Edit: I thought of a simple answer: piecewise functions can achieve this!
6 votes -
COVID-19 kills renowned Princeton mathematician, 'Game Of Life' inventor John Conway in three days
26 votes -
Volume of a sphere
5 votes -
A parallelogram puzzle
3 votes -
Linear Algebra Done Right - Free electronic version
9 votes -
Extraordinary conics: The most difficult math problem I ever had to solve
6 votes -
Real Numbers - Why? Why not computable numbers?
Do we have any mathematicians in the house? I've been wondering for a while why math is usually focused around real numbers instead of computable numbers - that is the set of numbers that you can...
Do we have any mathematicians in the house? I've been wondering for a while why math is usually focused around real numbers instead of computable numbers - that is the set of numbers that you can actually be computed to arbitrary, finite precision in finite time. Note that they necessarily include pi, e, sqrt(2) and every number you could ever compute. If you've seen it, it's computable.
What do we lose, beyond cantor's argument, by restricting math to computable numbers? By corollary of binary files and therefore algorithms being countable, the computable numbers are countable too, different from reals.
Bonus points if you can name a real, non-computable number. (My partner replied with "a number gained by randomly sampling decimal places ad infinitum" - a reply as cheeky as the question.) Also bonus points for naming further niceness properties we would get by restricting to computables.
I've read the wikipedia article on computable numbers and a bit beyond.
10 votes -
17 Klein Bottles become 1 - ft. Cliff Stoll and the glasswork of Lucas Clarke
12 votes -
Fair dice (part 1/2)
4 votes -
The Ideal Mathematician
6 votes -
This is the (co)end, my only (co)friend
6 votes -
Mathematicians prove universal law of turbulence
9 votes -
Russian and Egyptian multiplication
5 votes -
This equation (the logistic map) will change how you see the world
11 votes -
Happy Universal Palindrome Day!
19 votes -
Big data+small bias << Small data+zero bias
5 votes