# I'm a mathematician, AMA.



## hauntology

Hey! I'm a mathematician working towards a PhD in topology and comparative media at MIT. Ask me anything about anything!


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## Metalize

Hi Star Buxxx

Why are some people suck at math and others not


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## hauntology

Metasentient said:


> Hi Star Buxxx
> 
> Why are some people suck at math and others not


Oh my... 
The one time I'm trying to be serious and... yeah.
Probably the same reason some people suck at say, cleaning. Or paper mache. Or a great many number of things.
(i sUCK at cleaning and paper mache and cleaning up paper mache)


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## Psychophant

Do you believe criticisms that Charles Babbage lied about Lovelace's contributions to the Analytical Engine?

Hey.. I was here first.


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## Metalize

Well my question doesn't count since it wasn't really math-related

I just saw StarBux and wanted to comment


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## hauntology

Yomiel said:


> Do you believe criticisms that Charles Babbage lied about Lovelace's contributions to the Analytical Engine?
> 
> Hey.. I was here first.


Even if there was slight fabrication, the sources we have still hold that she was the only one to recommend a Bernoulli numbers program. Also, the program is far different in structure than anything Babbage himself wrote, from an analytical viewpoint.


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## Psychophant

Space Junkie said:


> Even if there was slight fabrication, the sources we have still hold that she was the only one to recommend a Bernoulli numbers program. Also, the program is far different in structure than anything Babbage himself wrote, from an analytical viewpoint.


Are you saying this as an observer of the programs? Btw, that just popped into my head since I saw your avatar (obviously) and I read part of a book on the two and then noticed the criticism noted on her wiki page. I have no idea if it's true or not.

I'm actually curious about a few things. A) Why topology? And did you have a second choice? B) do you have an idea of what your thesis is/have started writing it, and if not, does it stress you out that you have to add some new idea to the field of mathematics? Does anyone make it to that level and simply fail to come up with anything? Because that pretty quickly turned me off the idea of becoming a PhD, not that I really ever was considering it.


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## hauntology

Yomiel said:


> Are you saying this as an observer of the programs? Btw, that just popped into my head since I saw your avatar (obviously) and I read part of a book on the two and then noticed the criticism noted on her wiki page. I have no idea if it's true or not.
> 
> I'm actually curious about a few things. A) Why topology? And did you have a second choice? B) do you have an idea of what your thesis is/have started writing it, and if not, does it stress you out that you have to add some new idea to the field of mathematics? Does anyone make it to that level and simply fail to come up with anything? Because that pretty quickly turned me off the idea of becoming a PhD, not that I really ever was considering it.


1 (ada lovelace.) Yes, I have observed the programs!
A.) Why topology? My passion is the overlap of art and math, and it seemed like the most logical and passionate choice for me. My second would have been pure algebra.
B.) My thesis plan and research covers using literacy and visual correlation to teach children abstract mathematical concepts and push for more minorities in STEM fields. It scares me a bit, but it mostly exhilarates me to know I can make an impact.


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## Psychophant

Space Junkie said:


> 1 (ada lovelace.) Yes, I have observed the programs!
> A.) Why topology? My passion is the overlap of art and math, and it seemed like the most logical and passionate choice for me. My second would have been pure algebra.
> B.) My thesis plan and research covers using literacy and visual correlation to teach children abstract mathematical concepts and push for more minorities in STEM fields. It scares me a bit, but it mostly exhilarates me to know I can make an impact.


Good luck.


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## Polymaniac

Any recommendations for someone planning to dual major in math and cog-sci with an emphasis in computational modeling?


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## FakeLefty

What interests you about the field of mathematics in general?


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## He's a Superhero!

What's the chance of Abiogenesis occurring on a life-less planet that is otherwise very similar to earth?


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## zara1

Maths is great subject but i dont like long tail logics


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## zara1

i like to solve and practice algebra instead


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## zara1

What is the importance of theorem?
i think it is wrong to include in our course mainly students cheat to learn theorem they are totally useless


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## Donkey D Kong

Why did the chicken cross the Mobius Strip?


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## hauntology

JPS said:


> Any recommendations for someone planning to dual major in math and cog-sci with an emphasis in computational modeling?


expect to have zero free time, pirate the shit out of your textbooks, keep track of all the work you do to write a good resume, and try to get an internship during your third or fourth year.
(don't take 20 hours a semester, also.)


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## hauntology

FakeLefty said:


> What interests you about the field of mathematics in general?


It's the very building blocks of all dimensions above and below ours, and ours itself. It is the language of logic and science, but also of philosophy and art. It's permeating everything I know, so it seemed to be the best thing to study.


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## hauntology

He's a Superhero! said:


> What's the chance of Abiogenesis occurring on a life-less planet that is otherwise very similar to earth?


Not my field of expertise, sorry. I'm quite clueless when it comes to xenobiology.


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## hauntology

Donkey D Kong said:


> Why did the chicken cross the Mobius Strip?


to get to the same side!


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## nolemonplease

Do you have an Erdös number?

Any cool people that you are linked to in the Mathematics Genealogy tree?


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## runnerveran

http://plato.stanford.edu/entries/nominalism-mathematics/

1. mathematical nominalism or platonism?

2. Some prominent philosophers and mathematicians think that statistics should be taught earlier and more emphasized in high school and college, given that it will be of more use to the typical person (compared to say geometry). Richard Carrier is one person who thinks this, but I've heard it from many other academics as well. Thoughts?

3. Your thoughts on frequentism vs Bayesianism. Should both approaches be taught ? Just one? Usually a frequentist approach is taught in stats 101, to my knowledge at least.


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## Purrfessor

Will you marry me?

Also not a question but I just want to say since you seem to be into the learning process of mathematics... I was a natural at math - I didn't have to try to ace tests all throughout high school. I learned so fast and completely that people always called me a math genius. However when I first struggled in math when I was in college to be an engineer, it only hit me harder when I hit a bump in the road. I dropped out because I didn't have faith in my abilities due to my lack of discipline toward learning math. I look back and think about how powerful of a mathematician I could have been and wonder what could have been. Just so the same thing doesn't happen to another person, can you not feed the egos of those who are young and natural talent? I think it would have been good for me to hear that I didn't have it easy.


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## Nightmaker81

Hell yeah I'm a physicist(but also majored in math in undergrad), and working towards my PhD in physics.

Have you done a course on general relativity and using tensors? That's the thing that I'm most nervous/excited about in grad school


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## HAL

Out0fAmmo said:


> I've been brushing up on my math in preparation for engineering. What was the most difficult mathematical concept for you to understand, and do you have any suggestions for overcoming such obstacles?


I'm a physics student and have done all the required bits of mathematics to be considered as 'knowing enough maths to be a physicist', according to the Institute of Physics. (I mean, there's loads more to learn, but I've done all the required core modules for being an official physicist - I now just need to learn the application of the maths, in the realm of physics, in future modules. I think in the US they'd call it Calc IV).

The hardest thing for me was grasping vector calculus. Div, Grad and Curl was fine, but line and surface integrals was a pain. Things like, "A solid is bound by x=1, y=ln(x), z=2x+2y , find the surface area of the shape using a suitable surface integral." I don't know how I managed it. Got a First, though! However I admit I'm still clueless on the topic. Luckily I've changed to another university and one of my upcoming modules happens to go over vector calculus again, so I'll get a whole other semester to work on it. I'm sure it'll be fine next time around. Definitely one thing that needs focus, though.

Also, I found it strangely hard using calculus to work out moments of inertia.

Oh and Fourier Transforms. No idea. I can _do_ them, but I never fully grasped what was going on. I'm ashamed of that.

Anyway yeah I got pretty good marks after all my exams, but these are the bits that stand out as the toughest.


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## Nightmaker81

HAL said:


> I'm a physics student and have done all the required bits of mathematics to be considered as 'knowing enough maths to be a physicist', according to the Institute of Physics. (I mean, there's loads more to learn, but I've done all the required core modules for being an official physicist - I now just need to learn the application of the maths, in the realm of physics, in future modules. I think in the US they'd call it Calc IV).
> 
> The hardest thing for me was grasping vector calculus. Div, Grad and Curl was fine, but line and surface integrals was a pain. Things like, "A solid is bound by x=1, y=ln(x), z=2x+2y , find the surface area of the shape using a suitable surface integral." I don't know how I managed it. Got a First, though! However I admit I'm still clueless on the topic. Luckily I've changed to another university and one of my upcoming modules happens to go over vector calculus again, so I'll get a whole other semester to work on it. I'm sure it'll be fine next time around. Definitely one thing that needs focus, though.
> 
> Also, I found it strangely hard using calculus to work out moments of inertia.
> 
> Oh and Fourier Transforms. No idea. I can _do_ them, but I never fully grasped what was going on. I'm ashamed of that.
> 
> Anyway yeah I got pretty good marks after all my exams, but these are the bits that stand out as the toughest.


To add on to that, I'm not sure what your specialization in engineering, but I also have to add complex analysis.

That was by far the hardest math subject I've done. Hell analysis classes in general are annoying, but the complex plane isn't intuitive at all and will take a lot of studying, but once you get it down, it becomes so damn useful.

One of the my favorite things with complex analysis is the residue thm. There are infinite integrals you can't do in the real plane. Take them into the complex plane. Once there, there are "tricks" to get the residue, but the most obvious/direct way is finding the taylor series of the function and to bring out the coefficients where they begin to align and that'll be your residue.

Pop it into the residue thm, and boom. An impossible integral in the real plane is now down: 
https://en.wikipedia.org/wiki/Residue_theorem


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## Vahyavishdapaya

Do you think that maths has ontological reality, or do you believe it is only a man-made abstraction?


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## bender477

Nightmaker81 said:


> analysis classes in general are annoying,


that's an understatement
I'm just at the beginning of my training but I'm really curious how an understanding of math can translate over into more applied, science disciplines.
recently have been looking at how diffeq can be used to find algorithms to model population growth.
can I with good conscience avoid these upper-level theoretical classes because cannot be bothered? is there any connection at all between, say, abstract algebra and big data studies? thanks.


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## Vahyavishdapaya

Could you please explain in layman's terms the Euler Formula, Godel's Incompleteness theorem, and the Fourier transform?


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## Nightmaker81

bender477 said:


> that's an understatement
> I'm just at the beginning of my training but I'm really curious how an understanding of math can translate over into more applied, science disciplines.
> recently have been looking at how diffeq can be used to find algorithms to model population growth.
> can I with good conscience avoid these upper-level theoretical classes because cannot be bothered? is there any connection at all between, say, abstract algebra and big data studies? thanks.


Analysis in general sets up the math laws so math can be used effectively. The thing about math is that it has to work so the physics work and so the engineering can work.

Real analysis with calculus proves calculus which is really huge, because if we don't know if it works or if we find cases if it works, then pretty much any science or engineering with it falls a part. 

Learning abstract algebra isn't going to have a direct effect with learning biology, but proving the math is essential so we can use the math in other fields.

If you go into quantum mechanics and for some reason the Hermitian space doesn't exist. Well crap there goes an entire field.


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## Nightmaker81

Spitta Andretti said:


> Could you please explain in layman's terms the Euler Formula, Godel's Incompleteness theorem, and the Fourier transform?


Euler's formula is huge because it relates the complex plane to the real plane. The base formula is e^itheta=cos(x)+isin(x)

in many cases e^ix is an eigenfunction which means it has a related eigenvalue/eigenvector. Which is huge. In linear algebra and later quantum mechanics, you work with Hermitian spaces that allow QM to work on a more simplistic level and it'd be impossible if you didn't have the eigenvalues/eigenvectors, because eigenvectors do not change under any kind linear transformation

Overall it's one of the most amazing formulas because it has so many applications, both as an eigenfunction and making the complex and real plane easy to interchange

Fourier transform is great because it takes any continuous function into a sinusoidal function. Sines and Cosines are easy functions. Many other functions are not. As long as your function is continous, you can use a fourier transform to change into something much, much more easy to calculate

Not sure on the middle one though


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## bender477

Nightmaker81 said:


> so math can be used effectively.


I guess I'm trying to figure out how much I have to know in order to use it effectively in, say, biomedical applications.
I feel a bit conficted about this because I suspect I have a strong aptitude for math and especially 'higher' eschelons of it but I what I really want to do with solve lupus or diabetes or something. I sense there are some real answers in combining the two but I'm trying to figure out the right balance esp as time and energy are limited atm.


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## Nightmaker81

bender477 said:


> I guess I'm trying to figure out how much I have to know in order to use it effectively in, say, biomedical applications.
> I feel a bit conficted about this because I suspect I have a strong aptitude for math and especially 'higher' eschelons of it but I what I really want to do with solve lupus or diabetes or something. I sense there are some real answers in combining the two but I'm trying to figure out the right balance esp as time and energy are limited atm.


I think for the whole part you don't have to deal with that much proof based mathematics. It'll be nice to enter a mathematician's mind, but I don't think it's necessary.

However, complex analysis is the one analysis class I do advocate. Complex numbers are everywhere, and I'm sure you'll run into them in your field. Knowing complex analysis makes math much easier to deal with, especially with my real life situations.


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## Psychophant

Nightmaker81 said:


> Euler's formula is huge because it relates the complex plane to the real plane. The base formula is e^itheta=cos(x)+isin(x)
> 
> in many cases e^ix is an eigenfunction which means it has a related eigenvalue/eigenvector. Which is huge. In linear algebra and later quantum mechanics, you work with Hermitian spaces that allow QM to work on a more simplistic level and it'd be impossible if you didn't have the eigenvalues/eigenvectors, because eigenvectors do not change under any kind linear transformation
> 
> Overall it's one of the most amazing formulas because it has so many applications, both as an eigenfunction and making the complex and real plane easy to interchange
> 
> Fourier transform is great because it takes any continuous function into a sinusoidal function. Sines and Cosines are easy functions. Many other functions are not. As long as your function is continous, you can use a fourier transform to change into something much, much more easy to calculate
> 
> Not sure on the middle one though


Isn't the last one the Fourier series, not the transform? The transform transforms a function from the time domain to the frequency domain, and it's pretty tough to wrap your head around intuitively. I guess, if you're looking at a periodic signal, using the FS to find the FT is relevant.


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## Nightmaker81

Yomiel said:


> Isn't the last one the Fourier series, not the transform? The transform transforms a function from the time domain to the frequency domain, and it's pretty tough to wrap your head around intuitively. I guess, if you're looking at a periodic signal, using the FS to find the FT is relevant.



Yeah good call dude! I ended up mixing them up


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## Psychophant

Nightmaker81 said:


> Yeah good call dude! I ended up mixing them up


Lol, this was like.. all I did last term since it was used for both partial differential equations and signal processing.


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## BroNerd

What do you think is the most interesting currently unproved theorem in mathematics?


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## yet another intj

Are we still doomed to use an irrational number while messing with circles/spheres?

I know this one is an engineering problem but is there any practical problems caused by unknown digits of pi in calculations?


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## SalvinaZerelda

Do you like the idea of sacred geometry?


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## Nightmaker81

Rune said:


> Do you like the idea of sacred geometry?



I know this isn't my thread but this is a fascinating subject for me. It's really interesting how math works in nature and the real world to us humans. Things that work look aesthetically appeasing. 

Take a fighter jet. It looks fucking cool, but at the same time aerodynamically the design is at its best. 

Plants also have this thing where they have this insane perfect geometry, but it's for a purpose: 
http://www.wherecoolthingshappen.co...rfect-Geometric-Patterns-In-Nature-wcth15.jpg

Sacred geometry I always felt had a purpose. Since it was for religious purpose it worked to get people towards the religion and showed that humans and the entire world have some kind of affinity towards geometrical symmetry which I find really interesting


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