👍 To support the channel, hit the like button and subscribe. 🐸 To learn how I make these animations using Grant Sanderson's (3Blue1Brown) program Manim, check out my quick intro to Manim on Skillshare: www.skillshare.com/r/profile/Kyle-B/344454857
I had a math teacher who seemed to believe math was basically solved except for some occasional really hard problems to be solved by geniuses. It was kind of weird because she had studied up to undergraduate topology, so surely she must have known some of the inventiveness of mathematics.
Unfortunately, grade school teaching is kind of considered the "failing out" of the math career pathway. I am a research mathematician, and absolutely hated my experience with grade school and high school math. It was only after studying physics in college that I started to understand that math is an art, not a stupid turn-crank process. It's a real shame...we pay grade school teachers so little that there isn't a lot of incentive for someone with real knowledge of math to choose that path.
@Kyle Broder it's all new, but people are studying how the deep neural networks can implement projections between high dimensional manifolds. it's not my field of work but a close friend of mine is currently at it. I'll ask him for a reference
Can anyone tell here..... Morethan telling i need help... How to write paper on differential equation (may be fluid mechanics or magneto hydro dynamics)i m having intersetd to do phd because of not clearing entrance... I m not able to join in my university... How to select a topic..... Could nay one... Or sir.. Plz help. Me out... Sir help me
It is not only about solving existing problems, but even more so about creating your own mathematical structures. In that sense mathematics research is highly creative.
Thanks for sharing, to be a research mathematician was my high school dream, but ended up taking BSEE since in the Philippines we are always told to take engineering when do well with math. Although I love my degree, after working for a semiconductor industry for almost 20 yrs, I felt something is really missing, my dream is still with me and I hope I can still achieve it.
Excellent explanation of what a researcher does.......step by step.........really couldn't be any clearer. You'll make a GREAT Professor if you go that route !! Wish I had a Mathematics Professor that was so methodical & clear.
How much math research costs? Not much I think! Given math's record of being useful in other areas after a discovery, I wish more was done because each $1 invested here generates $5 elsewhere. Math research needs a a major rampup!
This type of topic is useful to me as I am conducting a lay research project. I need to know how to structure or organize my tasks as an amateur researchist.
Can anyone tell here..... Morethan telling i need help... How to write paper on differential equation (may be fluid mechanics or magneto hydro dynamics)i m having intersetd to do phd because of not clearing entrance... I m not able to join in my university... How to select a topic..... Could nay one... Or sir.. Plz help. Me out
My mom had a similar situation where she was doing her phd research on a topic that someone else was just about to publish on. She ended up having to change topics a couple years in and stay in the program a few years longer than usual.
Amazing video thank you! What are your thoughts on choice of textbook and how to learn mathematics? Is it best to learn using a problem solving approach? I have a difficult time reading through the definition, theorem, proof style books. I am just not mathematically mature enough yet. You mentioned you look up a definition and try to generate some examples using those. Does it sometimes take you long to understand the definition? I find some definitions completely incomprehensible to the point I cant even start to think about what it is being defined. Anyway, if you can recommend any math textbooks which really showed you how to go about doing mathematics please recommend.
Can anyone tell here..... Morethan telling i need help... How to write paper on differential equation (may be fluid mechanics or magneto hydro dynamics)i m having intersetd to do phd because of not clearing entrance... I m not able to join in my university... How to select a topic..... Could nay one... Or sir.. Plz help. Me out
@@KyleBroder Thanks, nice video. I’m currently doing my masters and toying with the idea of doing a PhD. It sounds like a silly question but how do you know what area of maths you’re interested in? I’ve no idea how I’m going to come up with a proposal for a PhD.
@@KyleBroder I do 4 modules this year and a year long project (instead of the usual 6 modules). My project is a research project about the conjecture of Zaremba (number theory) but I’m not expected to discover anything - just researching it’s partial solutions so far. A lot of the project kind of goes into uniform distribution of sequences (as it is an application if it were true) and I’m not really interested in that. I don’t think I’d want to do this as a PhD.
@@Anteater23 Do your best to speak with as many mathematicians as you can (albeit, it is more difficult to do this in the present world circumstances). Expand your breadth of understanding in mathematics by going to talks/lectures, or even watching lectures online: the minimal model program might interest you (as there a vast number of open problems, especially in characteristic p) -- There are some great lectures online by Caucher Birkar, Frederic Campana, Christopher Hacon. You might also like the series of lectures given by Jim Borger on Witt vectors. All of these video lectures are available on UA-cam or easily found after a quick google search.
what do you do if the problem you chose to solve isn't solvable? how do you decide to carry on after 2 years of unproductive research? 5 years? 10 years? is it reasonable to spend 30 years 'researching' the same problem? for example, people researched fermat's last theorem for 150 years but the problem was actually solved overnight when some guy had a vivid mathematical dream that revealed the answer.............at what point does it make more sense to let higher order artificial intelligence systems do all future mathematical research since they are ubergenius level systems, or soon will be?
Can anyone tell here..... Morethan telling i need help... How to write paper on differential equation (may be fluid mechanics or magneto hydro dynamics)i m having intersetd to do phd because of not clearing entrance... I m not able to join in my university... How to select a topic..... Could nay one... Or sir.. Plz help. Me out
Msc output in 2013... How to gain knowledge... More... Plzzzplzzzzz🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻inform me plz..... But i m in touch with my math but nit fluid mechanics or magnetohydrodynamics
My Ph.D. is in complex differential geometry which is often concerned with analytic approaches to problems which are motivated by algebraic geometry, so a lot of my time has been spent studying algebraic geometry. I know nothing about algebraic geometry over fields which are not the complex numbers, however.
Do you need to be a pure mathematician for this ? or also applied mathematicians can do research ? And do you really need a PHD to do research ? Couldn't be enough a masters ?
There is more research being done in pure math, but there is absolutely research potential for those who enjoy applied math! To my knowledge, partial differential equations especially are what a lot of applied research mathematicians are focusing on. As well as inter-discinplary things like relating math to physics, biology, chemistry, computer science, etc. However, if you really want to stick to just math, then pure math is probably where you want to go for the best chance! To do academic research, you almost certainly need a Ph.D. Even most companies and the government normally require a Ph.D. for most positions (at many companies and the government you'd likely be stuck to applied math or concepts in pure math we are figuring out applications for like in computer science). However, for industry, a master's degree could be enough. Though you'll have a lot more responsibilities other than research and the jobs aren't as secure as a tenured faculty position (though they are more secure than thigns like post-docs or when you first become a professor) There are ups and downs to both, but tl;dr: Research exists in both applied and pure math, but more in pure math. Though most research positions require a Ph.D., it is technically possible to get a career in research with only a master's but is harder to do so!
@@soulsofwar8985 i want to ask you a question.. i am a high school student and i want to do a mathemaical research, but as you said i certainly need a ph.D. so how can i get a Ph.D help me in this, or if u know anyone could help me in this, i will be thankful.
There exists a finite magma such that x*y*y=0 && x*y |= 0 && z*y*y=y && limited associativity holds, i.e. for all a, b is valid a*(b*b)= (a*b)*b ? If so, then there is an exponentially fast algorithm for factoring integers. The time to factorize a number N is equal to Log N.
could you tell any material which lets you to familiarize with the notations and understandings how to derive equations, etc? I really don't understand how equations are derived, for example I work in medicine and we have equations too
Do you ever get the feeling that some concepts youre brain cant comprehend? Lol Im getting through the difficult maths again, but I love the abuse haha
2 equation with 2 unknown with the form a^x + b^y + c = 0 ... can u solve that :D my phd teacher university cant ... i can give this example (i guess it work or take any) : 4^x + 2^y = 32 and 3^x - 9^y = 1 ..... :D here :D maybe you can find how i should do it ... some1 said u can isolate x with ln ...but still cant solve completly ... and maybe if you want could you give me ur opinion on how far a good data scientist should know math ... (atlast discrete math/ stochastique ? , but u said u cant learn everything around math ... so.. not sure anymore :D ) thanks for your work and sry if i engrish , not my lang :D
👍 To support the channel, hit the like button and subscribe.
🐸 To learn how I make these animations using Grant Sanderson's (3Blue1Brown) program Manim, check out my quick intro to Manim on Skillshare: www.skillshare.com/r/profile/Kyle-B/344454857
I had a math teacher who seemed to believe math was basically solved except for some occasional really hard problems to be solved by geniuses. It was kind of weird because she had studied up to undergraduate topology, so surely she must have known some of the inventiveness of mathematics.
the more we learn about mathematics, the more problems we create
You can only believe mathematics is solved when you don't know mathematics.
Unfortunately, grade school teaching is kind of considered the "failing out" of the math career pathway. I am a research mathematician, and absolutely hated my experience with grade school and high school math. It was only after studying physics in college that I started to understand that math is an art, not a stupid turn-crank process. It's a real shame...we pay grade school teachers so little that there isn't a lot of incentive for someone with real knowledge of math to choose that path.
There are so many open problems in topology to the resch of a graduate student that is extremely they'd have that belief,
There's undergraduate topology?
Dude your field is what has the potential to explain all the deep learning that people implement without knowing what they're doing. Cool AF
There is a link between complex differential geometry and deep learning? I'd be very interested, do you have any references to point to?
@Kyle Broder it's all new, but people are studying how the deep neural networks can implement projections between high dimensional manifolds. it's not my field of work but a close friend of mine is currently at it. I'll ask him for a reference
@@raphaelcardoso7927 That'd be awesome, cheers!
@@raphaelcardoso7927 is this related to the PCA? or some extreme level thing?
Can anyone tell here..... Morethan telling i need help... How to write paper on differential equation (may be fluid mechanics or magneto hydro dynamics)i m having intersetd to do phd because of not clearing entrance... I m not able to join in my university... How to select a topic..... Could nay one... Or sir.. Plz help. Me out...
Sir help me
It is not only about solving existing problems, but even more so about creating your own mathematical structures. In that sense mathematics research is highly creative.
It's very creative, yes.
Thanks for sharing, to be a research mathematician was my high school dream, but ended up taking BSEE since in the Philippines we are always told to take engineering when do well with math. Although I love my degree, after working for a semiconductor industry for almost 20 yrs, I felt something is really missing, my dream is still with me and I hope I can still achieve it.
All love man
I found that very inspiring. It's not about remembering something but understanding something.
Excellent explanation of what a researcher does.......step by step.........really couldn't be any clearer. You'll make a GREAT Professor if you go that route !! Wish I had a Mathematics Professor that was so methodical & clear.
Excellent sensitive info on overcoming the point where you are really stuck.
Glad you liked the video!
How much math research costs? Not much I think! Given math's record of being useful in other areas after a discovery, I wish more was done because each $1 invested here generates $5 elsewhere. Math research needs a a major rampup!
Yeah you should do more contents like this! Can you make a video on career in mathematics? Would be waiting
This type of topic is useful to me as I am conducting a lay research project. I need to know how to structure or organize my tasks as an amateur researchist.
This is very interesting! I'm curious what is the end goal for your craeer? is it to teach or working finance?
I want to be a research mathematician.
@@KyleBroder best of luck!
@@Backshopgolf 🙏
Can anyone tell here..... Morethan telling i need help... How to write paper on differential equation (may be fluid mechanics or magneto hydro dynamics)i m having intersetd to do phd because of not clearing entrance... I m not able to join in my university... How to select a topic..... Could nay one... Or sir.. Plz help. Me out
@@justfocusonurdreams1317Just start. Do it. Use that problem solving ability.
11:57 you say right memory is not the problem understanding is important in mathematics if you understand the you can also derive that ❤❤❤❤
Best of luck on your research.......please upload the video of your defense and a simplified solution for us mortals....
Have you ever heard of phd students accidentally working on the same problem and one published before the other? Does that invalidate their phd?
My mom had a similar situation where she was doing her phd research on a topic that someone else was just about to publish on. She ended up having to change topics a couple years in and stay in the program a few years longer than usual.
@@pikeeper1 dang
You're a good speaker, well done!
Thank you!
The information's were worth listening
Really liked the Video bro, however i would appreciate it if the music was a bit more silent(sorry for bad english)
I would appreciate that too.
Aussie accent :O oh you're at usyd? Im over at UNSW. Not even studying maths but I'm going down a rabbit hole and I now I really wanna relearn maths 😂
Nice 💪 I have a terrible Australian accent haha
What do you study at UNSW?
@@KyleBroder Im doing a double major in psych and neuro :D so plenty of stats, which I actually really found to like :D
A very valuable information 👍
Amazing video thank you! What are your thoughts on choice of textbook and how to learn mathematics? Is it best to learn using a problem solving approach? I have a difficult time reading through the definition, theorem, proof style books. I am just not mathematically mature enough yet. You mentioned you look up a definition and try to generate some examples using those. Does it sometimes take you long to understand the definition? I find some definitions completely incomprehensible to the point I cant even start to think about what it is being defined. Anyway, if you can recommend any math textbooks which really showed you how to go about doing mathematics please recommend.
Spivak's Calculus is good, so is Trench's real analysis.
Qsm
Can anyone tell here..... Morethan telling i need help... How to write paper on differential equation (may be fluid mechanics or magneto hydro dynamics)i m having intersetd to do phd because of not clearing entrance... I m not able to join in my university... How to select a topic..... Could nay one... Or sir.. Plz help. Me out
Provide lectures on sieve theory
I have always wondered this!
Hi mate, hayya doin?
Keep goin on your interestin videos♡
It is a friend from Syria, I guess you're from Aussie, I adore Australia.
My greetings.
Great video!
Thanks!
really vibed with alot of the stuff u said, any criticism on the educational system?
Absolutely, the educational system struggles to help disabled people succeed to the same extent as non disabled people.
Really makes sense 🎉
Research in any subject of science doesn't mean that we are creating i believe its all about contributing specifically mathematics.
You should collab with 3b1b!
My favorite video
"Thanks for watching the video guys!"
5 solid minutes of nothing but music
I want to do research fellowship in maths
how are the kinds of research undergraduates do different?
What research do undergraduates do?
It attains maximum on compact interval
I'm surprised I took this long for someone to catch that. Nice work! 💪
@@KyleBroder Thanks, nice video. I’m currently doing my masters and toying with the idea of doing a PhD. It sounds like a silly question but how do you know what area of maths you’re interested in? I’ve no idea how I’m going to come up with a proposal for a PhD.
@@Anteater23 What was your masters on? Was it a masters by coursework, or a masters by research?
@@KyleBroder I do 4 modules this year and a year long project (instead of the usual 6 modules). My project is a research project about the conjecture of Zaremba (number theory) but I’m not expected to discover anything - just researching it’s partial solutions so far. A lot of the project kind of goes into uniform distribution of sequences (as it is an application if it were true) and I’m not really interested in that. I don’t think I’d want to do this as a PhD.
@@Anteater23 Do your best to speak with as many mathematicians as you can (albeit, it is more difficult to do this in the present world circumstances). Expand your breadth of understanding in mathematics by going to talks/lectures, or even watching lectures online: the minimal model program might interest you (as there a vast number of open problems, especially in characteristic p) -- There are some great lectures online by Caucher Birkar, Frederic Campana, Christopher Hacon. You might also like the series of lectures given by Jim Borger on Witt vectors. All of these video lectures are available on UA-cam or easily found after a quick google search.
You are a teacher of the Arabic curriculum. I have come from after I authorize
what do you do if the problem you chose to solve isn't solvable? how do you decide to carry on after 2 years of unproductive research? 5 years? 10 years? is it reasonable to spend 30 years 'researching' the same problem? for example, people researched fermat's last theorem for 150 years but the problem was actually solved overnight when some guy had a vivid mathematical dream that revealed the answer.............at what point does it make more sense to let higher order artificial intelligence systems do all future mathematical research since they are ubergenius level systems, or soon will be?
What a cool video
I have been pronouncing “Galois” wrong for at least 4 years and no one has corrected me
Absolute Value tshirt?
Well i have solved all of math, but i don't want to ruin your fun and spoiler you so i keep shut.
We appreciate it haha
No dislikes, wow!
Excellent
Can anyone tell here..... Morethan telling i need help... How to write paper on differential equation (may be fluid mechanics or magneto hydro dynamics)i m having intersetd to do phd because of not clearing entrance... I m not able to join in my university... How to select a topic..... Could nay one... Or sir.. Plz help. Me out
Msc output in 2013... How to gain knowledge... More... Plzzzplzzzzz🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻inform me plz..... But i m in touch with my math but nit fluid mechanics or magnetohydrodynamics
"Have all math problems been solved?"
No.
winky winky kitty face,
Kurt Gödel
The video is great, but I think your voice would be clearer without the background music.
Thank u anyway
I can never get the levels right.
Have you had to learn a lot of algebraic geometry?
My Ph.D. is in complex differential geometry which is often concerned with analytic approaches to problems which are motivated by algebraic geometry, so a lot of my time has been spent studying algebraic geometry. I know nothing about algebraic geometry over fields which are not the complex numbers, however.
@@KyleBroder That's pretty cool. Although it might be worth learning seeing where condensed mathematics comes from
so is math research all topology?
No.
Do you need to be a pure mathematician for this ? or also applied mathematicians can do research ? And do you really need a PHD to do research ? Couldn't be enough a masters ?
There is more research being done in pure math, but there is absolutely research potential for those who enjoy applied math! To my knowledge, partial differential equations especially are what a lot of applied research mathematicians are focusing on. As well as inter-discinplary things like relating math to physics, biology, chemistry, computer science, etc. However, if you really want to stick to just math, then pure math is probably where you want to go for the best chance!
To do academic research, you almost certainly need a Ph.D. Even most companies and the government normally require a Ph.D. for most positions (at many companies and the government you'd likely be stuck to applied math or concepts in pure math we are figuring out applications for like in computer science). However, for industry, a master's degree could be enough. Though you'll have a lot more responsibilities other than research and the jobs aren't as secure as a tenured faculty position (though they are more secure than thigns like post-docs or when you first become a professor)
There are ups and downs to both, but tl;dr: Research exists in both applied and pure math, but more in pure math. Though most research positions require a Ph.D., it is technically possible to get a career in research with only a master's but is harder to do so!
@@soulsofwar8985 i want to ask you a question..
i am a high school student and i want to do a mathemaical research, but as you said i certainly need a ph.D. so how can i get a Ph.D help me in this, or if u know anyone could help me in this, i will be thankful.
There exists a finite magma such that x*y*y=0 && x*y |= 0 && z*y*y=y && limited associativity holds, i.e. for all a, b is valid
a*(b*b)= (a*b)*b ? If so, then there is an exponentially fast algorithm for factoring integers. The time to factorize a number N is equal to Log N.
could you tell any material which lets you to familiarize with the notations and understandings how to derive equations, etc? I really don't understand how equations are derived, for example I work in medicine and we have equations too
the background music covers your voice up way too much.
I agree.
Hi. I really want to watch this video but it's hard for me to understand what your'e saying. It sounds really interesting so it's a shame.
Because of the music?
@@KyleBroder yes.
@@doontz111 I'll take this into account in the next video.
@@doontz111 Thanks for the feedback
@@KyleBroder thank you
Do you ever get the feeling that some concepts youre brain cant comprehend? Lol
Im getting through the difficult maths again, but I love the abuse haha
manim?
Yes, I use manim.
@@KyleBroder then I am subscribed!
But how do you earn money?
try "who funds pure math research" on google
UA-cam revenue obviously...
BY THE WAY….NOT ONE PROBLEM HAS BEEN SOLVED…
nice pen
Thanks.
2 equation with 2 unknown with the form a^x + b^y + c = 0 ... can u solve that :D my phd teacher university cant ... i can give this example (i guess it work or take any) : 4^x + 2^y = 32 and 3^x - 9^y = 1 ..... :D here :D maybe you can find how i should do it ... some1 said u can isolate x with ln ...but still cant solve completly ... and maybe if you want could you give me ur opinion on how far a good data scientist should know math ... (atlast discrete math/ stochastique ? , but u said u cant learn everything around math ... so.. not sure anymore :D ) thanks for your work and sry if i engrish , not my lang :D
Mathematician : Birth:Do Math:Die
❤❤❤❤
Aw owsome
If this is how the mathematics subject is explained. You have a special question: Are you a teacher or is this an experience from God Almighty?
Mh
I have a video about intruding into p=np, maybe i Will upload more.
Mathematicians have proven that mathematics isnt solvable lol
I think u dont understand Godel
@brainpower782 its potentially solvable but not provable
Pretty much everything with an analytical solution has been solved so, do not become a mathematician.