Mathematicians are chronically lost and confused (2014) • Hacker News Board

Re: Mathematicians are chronically lost and confused (2014)

#131

Post by goldenkey » Sat, Jun 11, 2016, 3:17 AM UTC

agentultra wrote: post #112

Nimitz14 wrote: post #51

Earlier quoted context omitted.

Yup. He's probably just unaware of how difficult and vast math actually is. Reminds me of comments I've read from programmers talking about learning 'advanced mathematics': Linear Algebra. Lol.

No, not completely unaware. I'm glad I've reminded you of something you find entertaining. I hope you discourage more people from learning something awesome.

Hes just being real. Ive been self learning group theory, and cardinality/ordinals, surreal numbers, VN universe, shit is hard. Foundation is key. In order to be profound one needs tools. Unlike programming, dedication to tightening ones toolbelt first, helps immensely later. Order in math progression is way more significant than programming by trial and error.

Re: Mathematicians are chronically lost and confused (2014)

#132

Post by Retra » Sat, Jun 11, 2016, 4:14 AM UTC

sn9 wrote: post #129

Retra wrote: post #123

Earlier quoted context omitted.

Sub-disciplines of mathematics don't blow up and become cornerstones of education if they don't have practical applications. Analysis, Topology, Algebra, Abstract Algebra, Linear Algebra, Statistics, Geometry... If something doesn't have a major practical use, it'll probably be named after somebody specific and studied in relative obscurity.

Number theory was a major field for centuries before people discovered there was a practical use for it.

Number theory has always had practical use. It used to just be called "Arithmetic", and it didn't become something else until that something else had demonstrated practicality.

Re: Mathematicians are chronically lost and confused (2014)

#133

Post by sn9 » Sat, Jun 11, 2016, 6:15 AM UTC

Retra wrote: post #132

sn9 wrote: post #129

Earlier quoted context omitted.

Number theory was a major field for centuries before people discovered there was a practical use for it.

Number theory has always had practical use. It used to just be called "Arithmetic", and it didn't become something else until that something else had demonstrated practicality.

The sort of number theory that mathematicians studied for centuries had no practical use until the development of cryptography and computing in the latter half of the 20th century.

That's why Hardy famously used it as his example of mathematics done with no consideration or hope of there ever being a practical application.

Re: Mathematicians are chronically lost and confused (2014)

#134

Post by taejo » Sat, Jun 11, 2016, 12:29 PM UTC

taejo wrote: post #84

abecedarius wrote: post #80

Earlier quoted context omitted.

I'm confused: [42] is an invertible matrix with integer coefficients, right?

I guess daniel-levin meant to say "invertible matrix with integer coefficients whose inverse also has invertible coefficients". The fact isn't too hard to see: * If M has integer coefficients, then det(M) is an integer. * det(inv(M)) = 1/det(M) * Since M has integer coefficients, det(M) is an integer * Since inv(M) has integer coefficients, det(inv(M)) is an integer * So det(M) and 1/det(M) are both integers, so det(…

s/invertible coefficients/integer coefficients/

Re: Mathematicians are chronically lost and confused (2014)

#135

Post by pathsjs » Sat, Jun 11, 2016, 1:19 PM UTC

nitwit005 wrote: post #96

laingc wrote: post #13

To me, this is about "mathematical maturity". My observation is that many programmers, especially those who have come of age by working in startups, tend to value ability and sometimes experience over formal education. This is a result, I believe, of noticing that they can outperform many people who have a classical education, and also seeing that many of the people to whom they look up also do not have much in the w…

I've seen some examples that don't seem to agree with that. Programmers often don't need advanced math, but the ones that do, such as video game engine developers, seem to get fantastically good at it. You need a lot of time to master any skill, and few jobs provide that for mathematics. At least, not with any diversity in problems. The degree provides some years of dedicated effort.

Videogame engine developers do not need advanced mathematics

Re: Mathematicians are chronically lost and confused (2014)

#136

Post by sullyj3 » Sat, Jun 11, 2016, 1:21 PM UTC

Nimitz14 wrote: post #51

yequalsx wrote: post #42

Earlier quoted context omitted.

Not knowing your level of mathematical insight and knowledge makes it hard to know if your belief about your mathematical talent is a self deception. I've never encountered anyone who understood typical second year graduate level mathematics without formal training. I know such people could exist. I've just never met any. I have met people who claimed to be self taught in mathematics and it was obvious that they didn…

Yup. He's probably just unaware of how difficult and vast math actually is. Reminds me of comments I've read from programmers talking about learning 'advanced mathematics': Linear Algebra. Lol.

Does anyone have like, a map or presentation or article or something that will give me an intuition of how vast maths is?

Re: Mathematicians are chronically lost and confused (2014)

#137

Post by nikofeyn » Sat, Jun 11, 2016, 4:00 PM UTC

sullyj3 wrote: post #136

Nimitz14 wrote: post #51

Earlier quoted context omitted.

Yup. He's probably just unaware of how difficult and vast math actually is. Reminds me of comments I've read from programmers talking about learning 'advanced mathematics': Linear Algebra. Lol.

Does anyone have like, a map or presentation or article or something that will give me an intuition of how vast maths is?

just go to the local university library and look at the math section. :P

to give a personal anecdote, i often commented with my fellow graduate students that our first two years in graduate school were spent merely getting to the 1950s in terms of mathematical technology. most people who graduate with a bachelor's in math only know math up until the late 1800s and early 1900s at best.

mathematics is the hardest intellectual activity i have done, and it has made my job as an engineer and software developer much, much easier. the ability to abstract yet get down and diry with details is something math beats out of you.

Re: Mathematicians are chronically lost and confused (2014)

#138

Post by throwawaysocks » Sat, Jun 11, 2016, 4:43 PM UTC

Bahamut wrote: post #67

laingc wrote: post #13

To me, this is about "mathematical maturity". My observation is that many programmers, especially those who have come of age by working in startups, tend to value ability and sometimes experience over formal education. This is a result, I believe, of noticing that they can outperform many people who have a classical education, and also seeing that many of the people to whom they look up also do not have much in the w…

How much difference is there between those who entered industry after their masters and those who hold doctorates? I personally haven't encountered much of a difference as a masters holder (spent 4 years in graduate school though, 2 to finish the masters, and 2 in a math PhD program before leaving), but I also haven't worked with many PhD holders.

My experience: not all masters degree holders are created equal.

There's a big difference between people who leave a funded phd program early with a masters, and people who enroll in a terminal masters program. Especially if the terminal masters program was a "professional", non-thesis program.

But there's much less difference between people who leave a Ph.D. early with a masters and those who stick it out.

Re: Mathematicians are chronically lost and confused (2014)

#139

Post by Retra » Sat, Jun 11, 2016, 5:07 PM UTC

sn9 wrote: post #133

Retra wrote: post #132

Earlier quoted context omitted.

Number theory has always had practical use. It used to just be called "Arithmetic", and it didn't become something else until that something else had demonstrated practicality.

The sort of number theory that mathematicians studied for centuries had no practical use until the development of cryptography and computing in the latter half of the 20th century. That's why Hardy famously used it as his example of mathematics done with no consideration or hope of there ever being a practical application.

I'm talking about education. Mathematicians work on useless stuff all the time. They don't teach it as part of their core curriculum.

Either way, Hardy was wrong. Number theory became relevant because of the work of people who thought it could be. There was hope for a practical application, even if Hardy couldn't see it.

Re: Mathematicians are chronically lost and confused (2014)

#140

Post by lostlogin » Sat, Jun 11, 2016, 8:14 PM UTC

sn9 wrote: post #133

Retra wrote: post #132

Earlier quoted context omitted.

Number theory has always had practical use. It used to just be called "Arithmetic", and it didn't become something else until that something else had demonstrated practicality.

The sort of number theory that mathematicians studied for centuries had no practical use until the development of cryptography and computing in the latter half of the 20th century. That's why Hardy famously used it as his example of mathematics done with no consideration or hope of there ever being a practical application.

> latter half of the 20th century.

Nitpick - latter half of the first half.