This discussion board is a place to discuss our Daily Challenges and the math and science
related to those challenges. Explanations are more than just a solution — they should
explain the steps and thinking strategies that you used to obtain the solution. Comments
should further the discussion of math and science.
When posting on Brilliant:
Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.
Markdown
Appears as
*italics* or _italics_
italics
**bold** or __bold__
bold
- bulleted - list
bulleted
list
1. numbered 2. list
numbered
list
Note: you must add a full line of space before and after lists for them to show up correctly
# I indented these lines
# 4 spaces, and now they show
# up as a code block.
print "hello world"
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# 4 spaces, and now they show
# up as a code block.
print "hello world"
Math
Appears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3
2×3
2^{34}
234
a_{i-1}
ai−1
\frac{2}{3}
32
\sqrt{2}
2
\sum_{i=1}^3
∑i=13
\sin \theta
sinθ
\boxed{123}
123
Comments
You might not want to dive into much of this until you have the background to do so (that is, Linear Algebra, PDEs, Tensor Calculus (GR), Real Analysis [for operator theory, if you want to be rigorous], etc., etc.).
If you want to have brief, non-technical overviews, I'd recommend a bit of Greene's (e.g. "The Hidden Reality," "The Elegant Universe," but I'm no fan of String Theory, personally) stuff and some of Hawking's non-technical books--perhaps A Brief History of Time, which is one of the best of these kinds of books. I've grown to dislike many of these overviews, though, as they're very hand-wavy in some crucial cases.
If you really want to start on the historical developments, I'd very much recommend reading the original papers and working from there. I've been collecting Hawking's translations/commentaire of some of the landmark papers in Mathematics and Physics ("God Created the Integers," "The Dreams That Stuff is Made Of"), but they do require an extreme comfort with the mathematics presented, which could potentially be problematic.
Easy Math Editor
This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.
When posting on Brilliant:
*italics*
or_italics_
**bold**
or__bold__
paragraph 1
paragraph 2
[example link](https://brilliant.org)
> This is a quote
\(
...\)
or\[
...\]
to ensure proper formatting.2 \times 3
2^{34}
a_{i-1}
\frac{2}{3}
\sqrt{2}
\sum_{i=1}^3
\sin \theta
\boxed{123}
Comments
You might not want to dive into much of this until you have the background to do so (that is, Linear Algebra, PDEs, Tensor Calculus (GR), Real Analysis [for operator theory, if you want to be rigorous], etc., etc.).
If you want to have brief, non-technical overviews, I'd recommend a bit of Greene's (e.g. "The Hidden Reality," "The Elegant Universe," but I'm no fan of String Theory, personally) stuff and some of Hawking's non-technical books--perhaps A Brief History of Time, which is one of the best of these kinds of books. I've grown to dislike many of these overviews, though, as they're very hand-wavy in some crucial cases.
If you really want to start on the historical developments, I'd very much recommend reading the original papers and working from there. I've been collecting Hawking's translations/commentaire of some of the landmark papers in Mathematics and Physics ("God Created the Integers," "The Dreams That Stuff is Made Of"), but they do require an extreme comfort with the mathematics presented, which could potentially be problematic.
Cheers and good luck.
serway for saintist& engener