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A Retiree Discovers an Elusive Math Proof (2017)

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Re: A Retiree Discovers an Elusive Math Proof (2017)

#41

Post by tangentspace »

electricslpnsld wrote: post #39
n4r9 wrote: post #35

Earlier quoted context omitted.

People of that calibre are quite rare but they do exist. I've seen final year undergraduate courses pulled off without the lecturer once having to refer to notes. All proofs were completed in exacting detail on the whiteboard.

Sure, but those math profs have probably taught the same course 20+ times. Going through material that many times will permanently burn it into your brain.

Absolutely. And in mathematics, advanced structures and theorems are built up layers by layer upon more elementary material. A professor who has mastered presentation of undergraduate material on a topic also likely teaches a graduate course on it, and mentors students on it, and does research on it.

They can talk about their chosen topic at many levels to many different audiences, from general audience (who may provide funding to them), high school students (outreach and recruiting), university students, and peers. This flexibility is an important part of being a very successful mathematician, and you have to burn it into your brain to reach that level of fluency.

Re: A Retiree Discovers an Elusive Math Proof (2017)

#42

Post by jacobolus »

stealthmodeclan wrote: post #36

This is based on experience, i used to teach math. (~4000) And i found it easier to teach math to people whoes father, grandfather, great grandfather all had masters in math. So, i wonder if mathematical abilities are in genes and gene function changes when you bring a person with such genes into a math intense environment.

From observation, some of the people I know who were sharpest at learning new technical subjects and solving hard technical problems were way behind as undergraduates compared to folks who were not as good at problem solving but had been steeped in a technical culture from a young age, and as a result the newcomers had to work a lot harder to catch up.

“Easy to teach” comes from understanding your vocabulary and references, having seen similar material before, not being confused by severe misconceptions, coming in with similar mindset, etc., not necessarily from being the best at new research (or whatever other real work task).

Someone who is a 4th generation mathematician is going to be completely comfortable talking about mathematical topics in casual conversation, irrespective of any genetic differences.

Re: A Retiree Discovers an Elusive Math Proof (2017)

#43

Post by Ultimatt »

stealthmodeclan wrote: post #36

This is based on experience, i used to teach math. (~4000) And i found it easier to teach math to people whoes father, grandfather, great grandfather all had masters in math. So, i wonder if mathematical abilities are in genes and gene function changes when you bring a person with such genes into a math intense environment.

Not sure why you would even remotely assume genetics over just skills being passed down..? Pre war if you look at careers in census everyone used to do what their parents did. Its because its what they taught you!

Re: A Retiree Discovers an Elusive Math Proof (2017)

#44

Post by stealthmodeclan »

Ultimatt wrote: post #43
stealthmodeclan wrote: post #36

This is based on experience, i used to teach math. (~4000) And i found it easier to teach math to people whoes father, grandfather, great grandfather all had masters in math. So, i wonder if mathematical abilities are in genes and gene function changes when you bring a person with such genes into a math intense environment.

Not sure why you would even remotely assume genetics over just skills being passed down..? Pre war if you look at careers in census everyone used to do what their parents did. Its because its what they taught you!

> Not sure why you would even remotely assume genetics over just skills being passed down..?

There were also orphans who had never seen their parents or grandparents.

When genes are responsible for being lactose tolerate, why is it hard to hypothesise that only some people benefit from being raised in a math intense environment and not others?

Re: A Retiree Discovers an Elusive Math Proof (2017)

#45

Post by hyperpallium »

marcelluspye wrote: post #9

>“He had formulas that enabled him to pull off his magic,” Pitt said. “And I didn’t have the formulas.” The more I do pure mathematics, the more I realize just how important these kinds of insights are. Very often, solving a theoretical problem involves two key ingredients: 1. Rewriting your problem in a particular way, so that it is amenable to a certain suite of methods/looks like known results. 2. Apply a key bit…

\tangent does the formal proof make sense to a mathematician (as in, can they see it)?

Or is it more the hex of assembly of to the high level language of the intuition, in the semse that they can verify it, but not necessarily see it?

Re: A Retiree Discovers an Elusive Math Proof (2017)

#46

Post by mlevental »

electricslpnsld wrote: post #39
n4r9 wrote: post #35

Earlier quoted context omitted.

People of that calibre are quite rare but they do exist. I've seen final year undergraduate courses pulled off without the lecturer once having to refer to notes. All proofs were completed in exacting detail on the whiteboard.

Sure, but those math profs have probably taught the same course 20+ times. Going through material that many times will permanently burn it into your brain.

also they review the lecture before hand just like anyone delivering a speech does

Re: A Retiree Discovers an Elusive Math Proof (2017)

#47

Post by marcelluspye »

electricslpnsld wrote: post #39
n4r9 wrote: post #35

Earlier quoted context omitted.

People of that calibre are quite rare but they do exist. I've seen final year undergraduate courses pulled off without the lecturer once having to refer to notes. All proofs were completed in exacting detail on the whiteboard.

Sure, but those math profs have probably taught the same course 20+ times. Going through material that many times will permanently burn it into your brain.

I took a philosophy class with a professor who had taught it about that many times. Talked to a guy who had taken it before me, he said that the prof has literally word-for-word memorized certain parts of the lectures because he's figured out and internalized the wording he thinks is best. Mathematicians can certainly do the same.
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