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
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*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"
# I indented these lines
# 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
He was a great mathematical mind indeed.
What truly is logic? Who decides reason? My quest has taken me to the physical, the metaphysical, the delusional, and back. I have made the most important discovery of my career - the most important discovery of my life. It is only in the mysterious equations of love that any logic or reasons can be found. I am only here tonight because of you. You are the only reason I am. You are all my reasons. Thank you.
For me, the biggest impact of John Nash's work has had on my world view is that Pareto thing, "Not the Pareto Optimal thing to happen". First, Nash proved that in any non-cooperative game, there always exists at least one equilibrium point where the players see no benefit in changing their strategy. Next, he proved that there could be and usually more than one such point, of which not all and even most aren't even optimal. In other words, players in a game can easily get stuck in a rut and not ever "move" to a better place to be. Doesn't this describe a lot of what we're seeing today? Adam Smith's "Wealth of Nations" seems to imply that the "unseen hand" of the free market will unerringly guide it to the most optimum strategies. And that is the entire argument pushed by those that want the least government or regulatory interference. But, as Nash's work points out, not only this won't necessarily happen, it isn't even likely to happen.
Too often, when we see things stuck in an useless rut, like the current US Congress, what it needs is a swift kick in the pants to get it out of the rut.
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# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"\(...\)or\[...\]to ensure proper formatting.2 \times 32^{34}a_{i-1}\frac{2}{3}\sqrt{2}\sum_{i=1}^3\sin \theta\boxed{123}Comments
He was a great mathematical mind indeed.
What truly is logic? Who decides reason? My quest has taken me to the physical, the metaphysical, the delusional, and back. I have made the most important discovery of my career - the most important discovery of my life. It is only in the mysterious equations of love that any logic or reasons can be found. I am only here tonight because of you. You are the only reason I am. You are all my reasons. Thank you.
For me, the biggest impact of John Nash's work has had on my world view is that Pareto thing, "Not the Pareto Optimal thing to happen". First, Nash proved that in any non-cooperative game, there always exists at least one equilibrium point where the players see no benefit in changing their strategy. Next, he proved that there could be and usually more than one such point, of which not all and even most aren't even optimal. In other words, players in a game can easily get stuck in a rut and not ever "move" to a better place to be. Doesn't this describe a lot of what we're seeing today? Adam Smith's "Wealth of Nations" seems to imply that the "unseen hand" of the free market will unerringly guide it to the most optimum strategies. And that is the entire argument pushed by those that want the least government or regulatory interference. But, as Nash's work points out, not only this won't necessarily happen, it isn't even likely to happen.
Too often, when we see things stuck in an useless rut, like the current US Congress, what it needs is a swift kick in the pants to get it out of the rut.
So sad, a life so important cut short by an accident.
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I wouldn't say cut short TBH. He was 86.
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Cut short in the sense, with out the accident it would have been longer.
True He will be remembered as the greatest genius of our generation. one with a beutiful mind.
RIP John Nash
Rest in Peace. Must be hard being schizophrenic
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If I could accomplish what he has accomplished, I don't think I'd mind being schizo.
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I cannot even imagine that. It must be hard that who you thought to be your friends did not go away or die but even worse never existed.
A beautiful mind
Rest in peace, John Nash :(