Difficulty of learning mathematics - Revision history

Issa Rice: /* Notes */

2019-02-13T02:39:51Z

Notes

← Older revision		Revision as of 02:39, 13 February 2019
Line 15:		Line 15:
	[http://colah.github.io/posts/2015-08-Backprop/ Christopher Olah]: "Derivatives are cheaper than you think. That’s the main lesson to take away from this post. In fact, they’re unintuitively cheap, and us silly humans have had to repeatedly rediscover this fact. That’s an important thing to understand in deep learning. It’s also a really useful thing to know in other fields, and only more so if it isn’t common knowledge."		[http://colah.github.io/posts/2015-08-Backprop/ Christopher Olah]: "Derivatives are cheaper than you think. That’s the main lesson to take away from this post. In fact, they’re unintuitively cheap, and us silly humans have had to repeatedly rediscover this fact. That’s an important thing to understand in deep learning. It’s also a really useful thing to know in other fields, and only more so if it isn’t common knowledge."

	https://www.facebook.com/vipulnaik.r/posts/10201718168211884 ; somewhat related is https://www.greaterwrong.com/posts/EByDsY9S3EDhhfFzC/some-thoughts-on-metaphilosophy/comment/Gh7S2NwJMeYjypDnH		https://www.facebook.com/vipulnaik.r/posts/10201718168211884 ; somewhat related are https://www.greaterwrong.com/posts/EByDsY9S3EDhhfFzC/some-thoughts-on-metaphilosophy/comment/Gh7S2NwJMeYjypDnH and https://www.greaterwrong.com/posts/de3xjFaACCAk6imzv/towards-a-new-decision-theory/comment/DRQciHjC8GMonBCFe

	[http://www.michaelnielsen.org/ddi/if-correlation-doesnt-imply-causation-then-what-does/ Michael Nielsen on Simpson's paradox]: "Now, I’ll confess that before learning about Simpson’s paradox, I would have unhesitatingly done just as I suggested a naive person would. Indeed, even though I’ve now spent quite a bit of time pondering Simpson’s paradox, I’m not entirely sure I wouldn’t still sometimes make the same kind of mistake. I find it more than a little mind-bending that my heuristics about how to behave on the basis of statistical evidence are obviously not just a little wrong, but utterly, horribly wrong."		[http://www.michaelnielsen.org/ddi/if-correlation-doesnt-imply-causation-then-what-does/ Michael Nielsen on Simpson's paradox]: "Now, I’ll confess that before learning about Simpson’s paradox, I would have unhesitatingly done just as I suggested a naive person would. Indeed, even though I’ve now spent quite a bit of time pondering Simpson’s paradox, I’m not entirely sure I wouldn’t still sometimes make the same kind of mistake. I find it more than a little mind-bending that my heuristics about how to behave on the basis of statistical evidence are obviously not just a little wrong, but utterly, horribly wrong."

Issa Rice: /* Notes */

2019-02-12T23:39:06Z

Notes

← Older revision		Revision as of 23:39, 12 February 2019
Line 28:		Line 28:

	https://news.ycombinator.com/item?id=7331775 "Mathematicians are chronically lost and confused. It's our natural state of being, and it's okay to keep going and take what insights you can."		https://news.ycombinator.com/item?id=7331775 "Mathematicians are chronically lost and confused. It's our natural state of being, and it's okay to keep going and take what insights you can."

			Nate Soares: https://www.greaterwrong.com/posts/w5F4w8tNZc6LcBKRP/on-learning-difficult-things

	==See also==		==See also==

Issa Rice: /* Notes */

2019-02-12T23:24:50Z

Notes

← Older revision		Revision as of 23:24, 12 February 2019
Line 26:		Line 26:

	[[Tim Gowers]]: "''Mathematics becomes hard.'' Every mathematician will be able to tell you rather precisely when it was that they found that mathematics had stopped being an easy subject that they could understand with very little effort and became a difficult subject that they had to struggle with if they wanted to get anywhere. It isn’t necessarily an advantage if this happens to you later rather than sooner. For example, some Cambridge students find the course difficult right from the start, whereas others largely coast through the first year and then find that they can’t coast through the second year. The people who found it hard in the first year may by this time have developed good study habits that the people who found it easy in the first year do not have." [https://gowers.wordpress.com/2011/09/23/welcome-to-the-cambridge-mathematical-tripos/]		[[Tim Gowers]]: "''Mathematics becomes hard.'' Every mathematician will be able to tell you rather precisely when it was that they found that mathematics had stopped being an easy subject that they could understand with very little effort and became a difficult subject that they had to struggle with if they wanted to get anywhere. It isn’t necessarily an advantage if this happens to you later rather than sooner. For example, some Cambridge students find the course difficult right from the start, whereas others largely coast through the first year and then find that they can’t coast through the second year. The people who found it hard in the first year may by this time have developed good study habits that the people who found it easy in the first year do not have." [https://gowers.wordpress.com/2011/09/23/welcome-to-the-cambridge-mathematical-tripos/]

			https://news.ycombinator.com/item?id=7331775 "Mathematicians are chronically lost and confused. It's our natural state of being, and it's okay to keep going and take what insights you can."

	==See also==		==See also==

Issa Rice: /* Notes */

2019-02-12T23:22:54Z

Notes

← Older revision		Revision as of 23:22, 12 February 2019
Line 24:		Line 24:

	Bill Thurston: https://mathoverflow.net/questions/38639/thinking-and-explaining		Bill Thurston: https://mathoverflow.net/questions/38639/thinking-and-explaining

			[[Tim Gowers]]: "''Mathematics becomes hard.'' Every mathematician will be able to tell you rather precisely when it was that they found that mathematics had stopped being an easy subject that they could understand with very little effort and became a difficult subject that they had to struggle with if they wanted to get anywhere. It isn’t necessarily an advantage if this happens to you later rather than sooner. For example, some Cambridge students find the course difficult right from the start, whereas others largely coast through the first year and then find that they can’t coast through the second year. The people who found it hard in the first year may by this time have developed good study habits that the people who found it easy in the first year do not have." [https://gowers.wordpress.com/2011/09/23/welcome-to-the-cambridge-mathematical-tripos/]

	==See also==		==See also==

Issa Rice: /* Notes */

2019-02-12T23:19:23Z

Notes

← Older revision		Revision as of 23:19, 12 February 2019
Line 22:		Line 22:

	https://www.lesswrong.com/posts/2TPph4EGZ6trEbtku/explainers-shoot-high-aim-low		https://www.lesswrong.com/posts/2TPph4EGZ6trEbtku/explainers-shoot-high-aim-low

			Bill Thurston: https://mathoverflow.net/questions/38639/thinking-and-explaining

	==See also==		==See also==

Issa Rice: /* Notes */

2019-02-12T23:18:17Z

Notes

← Older revision		Revision as of 23:18, 12 February 2019
Line 20:		Line 20:

	https://en.wikipedia.org/wiki/Monty_Hall_problem#Confusion_and_criticism		https://en.wikipedia.org/wiki/Monty_Hall_problem#Confusion_and_criticism

			https://www.lesswrong.com/posts/2TPph4EGZ6trEbtku/explainers-shoot-high-aim-low

	==See also==		==See also==

Issa Rice: /* Notes */

2019-02-12T23:16:48Z

Notes

← Older revision		Revision as of 23:16, 12 February 2019
Line 18:		Line 18:

	[http://www.michaelnielsen.org/ddi/if-correlation-doesnt-imply-causation-then-what-does/ Michael Nielsen on Simpson's paradox]: "Now, I’ll confess that before learning about Simpson’s paradox, I would have unhesitatingly done just as I suggested a naive person would. Indeed, even though I’ve now spent quite a bit of time pondering Simpson’s paradox, I’m not entirely sure I wouldn’t still sometimes make the same kind of mistake. I find it more than a little mind-bending that my heuristics about how to behave on the basis of statistical evidence are obviously not just a little wrong, but utterly, horribly wrong."		[http://www.michaelnielsen.org/ddi/if-correlation-doesnt-imply-causation-then-what-does/ Michael Nielsen on Simpson's paradox]: "Now, I’ll confess that before learning about Simpson’s paradox, I would have unhesitatingly done just as I suggested a naive person would. Indeed, even though I’ve now spent quite a bit of time pondering Simpson’s paradox, I’m not entirely sure I wouldn’t still sometimes make the same kind of mistake. I find it more than a little mind-bending that my heuristics about how to behave on the basis of statistical evidence are obviously not just a little wrong, but utterly, horribly wrong."

			https://en.wikipedia.org/wiki/Monty_Hall_problem#Confusion_and_criticism

	==See also==		==See also==

Issa Rice: /* Notes */

2019-02-12T23:15:42Z

Notes

← Older revision		Revision as of 23:15, 12 February 2019
Line 16:		Line 16:

	https://www.facebook.com/vipulnaik.r/posts/10201718168211884 ; somewhat related is https://www.greaterwrong.com/posts/EByDsY9S3EDhhfFzC/some-thoughts-on-metaphilosophy/comment/Gh7S2NwJMeYjypDnH		https://www.facebook.com/vipulnaik.r/posts/10201718168211884 ; somewhat related is https://www.greaterwrong.com/posts/EByDsY9S3EDhhfFzC/some-thoughts-on-metaphilosophy/comment/Gh7S2NwJMeYjypDnH

			[http://www.michaelnielsen.org/ddi/if-correlation-doesnt-imply-causation-then-what-does/ Michael Nielsen on Simpson's paradox]: "Now, I’ll confess that before learning about Simpson’s paradox, I would have unhesitatingly done just as I suggested a naive person would. Indeed, even though I’ve now spent quite a bit of time pondering Simpson’s paradox, I’m not entirely sure I wouldn’t still sometimes make the same kind of mistake. I find it more than a little mind-bending that my heuristics about how to behave on the basis of statistical evidence are obviously not just a little wrong, but utterly, horribly wrong."

	==See also==		==See also==

Issa Rice: /* Notes */

2019-02-12T23:14:47Z

Notes

← Older revision		Revision as of 23:14, 12 February 2019
Line 15:		Line 15:
	[http://colah.github.io/posts/2015-08-Backprop/ Christopher Olah]: "Derivatives are cheaper than you think. That’s the main lesson to take away from this post. In fact, they’re unintuitively cheap, and us silly humans have had to repeatedly rediscover this fact. That’s an important thing to understand in deep learning. It’s also a really useful thing to know in other fields, and only more so if it isn’t common knowledge."		[http://colah.github.io/posts/2015-08-Backprop/ Christopher Olah]: "Derivatives are cheaper than you think. That’s the main lesson to take away from this post. In fact, they’re unintuitively cheap, and us silly humans have had to repeatedly rediscover this fact. That’s an important thing to understand in deep learning. It’s also a really useful thing to know in other fields, and only more so if it isn’t common knowledge."

	https://www.facebook.com/vipulnaik.r/posts/10201718168211884		https://www.facebook.com/vipulnaik.r/posts/10201718168211884 ; somewhat related is https://www.greaterwrong.com/posts/EByDsY9S3EDhhfFzC/some-thoughts-on-metaphilosophy/comment/Gh7S2NwJMeYjypDnH

	==See also==		==See also==

Issa Rice: /* Notes */

2019-02-12T23:13:40Z

Notes

← Older revision		Revision as of 23:13, 12 February 2019
Line 14:		Line 14:

	[http://colah.github.io/posts/2015-08-Backprop/ Christopher Olah]: "Derivatives are cheaper than you think. That’s the main lesson to take away from this post. In fact, they’re unintuitively cheap, and us silly humans have had to repeatedly rediscover this fact. That’s an important thing to understand in deep learning. It’s also a really useful thing to know in other fields, and only more so if it isn’t common knowledge."		[http://colah.github.io/posts/2015-08-Backprop/ Christopher Olah]: "Derivatives are cheaper than you think. That’s the main lesson to take away from this post. In fact, they’re unintuitively cheap, and us silly humans have had to repeatedly rediscover this fact. That’s an important thing to understand in deep learning. It’s also a really useful thing to know in other fields, and only more so if it isn’t common knowledge."

			https://www.facebook.com/vipulnaik.r/posts/10201718168211884

	==See also==		==See also==