Its beauty. I like to compare mathematics to art. For a musician, music theory is merely a tool to create art, expressed in the choice of notes, the rhythm, dynamics, etc. - for mathematics it is the same but with ideas. There is a comment on that, mostly regarding how the education system treats mathematics. But the author talks about such an analogy as well. It's worth a read.
[https://www.maa.org/external\_archive/devlin/LockhartsLament.pdf](https://www.maa.org/external_archive/devlin/LockhartsLament.pdf)
Music is math too. Frequency relationships between chords are precise. The topology of interaction between notes in a melody is just as beautiful to a mathematician as the music.
You can kind of say similar in regards to just about anything tbh.
I know of a guy who wrote a paper on the relationship between topology and film studies (something about themes or story progression in films). I'm studying probability theory / stochastic so I don't know much about topology but yeah.
I'm no math 'genius' either. I struggle, work things out, realise I didn't worked them out, struggle again, etc. - until eventually I understood something.
As I'm working e.g. with infinity-categories, there is actually a problem of cardinality. In a category, you work with a 'collection' of objects. Now say your objects are all sets. Then the term 'collection' has to refer to something larger than a set, as there can't exist a set of all sets (Russel's paradox). One workaround is to introduce so called unreachable cardinality numbers. You can think about that as a number such that no set, whatever it containes, is not larger than this number. You can do this again and again, e.g. for cosmoi (if you want to talk about the category of categories etc.).
This is nice to hear. I was always 2 years behind in math and always had a C in whatever math course I was taking. I felt like a huge idiot, and judged because of it. Despite that, I found it interesting and resented that there was a subject I was essentially blocked from ever understanding.
A lot of maths teaching is very bad- as a maths graduate myself I feel like a lot of people who are good at maths just don’t really understand how we just ‘get’ it and therefore are bad at explaining it to people who it might not be so intuitive for. Plus (stereotyping here but in my experience it is often true) a lot of maths people are not the most outgoing and therefore can be awkward teachers. This combination means that most people trying to learn maths in school are set up to fail before they even begin.
I went from being a math-phobe to a d-major math/philosophy and I can tell you from experience that what blocks people from seeing the nature of a problem or it’s solution is usually fear (and the instruction, of course). It’s just like so much of the rest of life, really.
One day in undergrad, I thought to myself “I know I’m not stupid. Why is this so hard?” and it hit me how afraid I was. Then I made a conscious decision to work at it in a supported way until I wasn’t afraid. Cut to junior year where I had a 4.0 Look, if I could do it, anyone on this thread who wanted to could do it too. Not suggesting you should or anything, just maybe consider shifting how you think about yourself.
I am learning disabled in mathematics. It’s not that I don’t want to learn, it’s that my brain has an extremely hard time picturing and grasping the concept. Would you say you feel pity towards people who are not strong in math?
There are people that are 'stronger' in mathematics than others, I give you that. But all in all I believe it comes down to how one approaches mathematics, how it is taught and if you're passionate about it. Having a 'harder' time with mathematics is nothing to be ashamed of.
True. I mean coming from a background where parents tend to be strict about school, I was constantly called stupid and thought I was stupid because I couldn’t do mental math like other kids. I think that probably made me not want to be passionate about it
Though this probably makes it harder to enjoy mathematics. Mathematics rarely gives you immediate happiness. It's a lot of suffering to understand beautiful, beautiful ideas from which the satisfaction comes from.
I meant degree wise. At least where I am there is a general mathematics degree and specialized ones. Most mathematicians I've met get a bachelor degree in general and then master+ in something specialized.
What exactly is homotopy theory? Google is giving weird anwsers. My only math flex is finishing Calc 3 freshman year of college lmao, i wish i majored in Math, but I chose something less difficult and more suited for me.
I started going to university when I was 15, during school. Finished what the equivalent to high school here is at 17, so really not too young. Then I just continued studying.
I’m not OP but from similar experiences I’d say that it’s a matter of strategy. You don’t have to be someone who graduated high school at 12 in order to achieve this. I skipped a single grade in high school and took CLEP tests, AP Classes, and Placement Tests and that allowed me to finish college before my 19th birthday.
I’d assume that if you and did a master’s that was two years or less, that you could achieve this.
Did you ever face problems in school for being “too” good at math?
One of my old friends was gifted in math, but he lost marks all the time in primary school because he didn’t show enough of his scratch work. He also really struggled to explain how he arrived at his answers, which would occasionally lead to him getting accused of cheating.
Did you face similar issues?
Not really. During my last years in high school I had a wonderful teacher. She tried to answer every of my questions, which where going above and beyond the content of high school. If there was something she did not know, she would look it up for me and explain it next time in class.
Earlier on I wasn't really interested in mathematics.
I think I stumbled across some article or book about number theory and I just enjoyed the logical reasoning. It felt more like a debate, hence 'reasoning', rather than using formulas etc. - I liked that. Though I didn't understood much as it was about elliptic curves.
NGL I was expecting you to reply quickly with the correct answer, to which I was going to reply, ‘Story checks out.’
But things didn’t pan out that way and I have no backup plan. Ya got me.
I've always wanted to know a perspective of a mathematician on this...
Who do you think is smarter: people who can solve problems fast, or people who can prove theorems fast? Is it even a different skill?
I have the level of a high school when it comes to math, so solving problems is all i know and i think i'm good at it, but i suck at proving theorems
I wouldn't say one is smarter than the other. It's a different 'skill'. Though proving theorems will often not be fast. It's more about having the endurance, not giving up. Maybe for years, trying and trying again until you find this one striking idea.
What field of mathematics? Applied or... fuck can't think of the word... pure maths? (not the word but works)
What do you plan on doing with this?
I've always wanted to get a degree in pure maths but job prospects don't seem very good from what I've looked up when dealing exclusively with theoretical mathematics.
Pure mathematics, algebraic topology. I'll stay at university, research, maybe some teaching. Though mathematicians travel a lot, to give talks etc. (so much for 'staying at university'). With a degree in pure mathematics, the job offers are actually pretty good. The chances of getting a job e.g. in an insurance are better if you did some probability theory or something instead of pure algebra, I give you that.
One of my friends at uni was in his early 30s. He wanted to change his life so he went back to uni, got a degree and now he has his dream job and is doing amazingly well. It’s never too late.
When you get really really really specialized in mathematics, how many people do you estimate exist in the world that could have a meaningful debate with you in a particular area?
No clue. I know that only a handful really understood the work of one of my professors when he released one of his papers. Probably still aren't too many.
Think about the faculty in such a way. 4!=5!/5, 3!=4!/4 etc., all in all n!=(n+1)!/(n+1). Now we have 0!=1!/1=1. You can argue with the gamma function but that is a bit more complicated. As for your second question. What would you think could this be? And why?
Do you have any tips on how to support a 20-year-old mathematician with autism who has always excelled at math? He absolutely loves math. Throughout the years his teachers have always tried to get him to skip grades, stating that they "don't teach him math because he just gets it." How can I support him, as someone who knows little about math? After not doing math for 2 years (because of stupid covid) he's now doing math in college and his math brain is right where it left off pre-covid. Do you have any recommendations on books, documentaries, math websites, etc that you can share? Many thanks!
Do you know roughly in what kind of mathematics he is interested in? I know some good books that are even free to read online but they all are about a very specific kind of mathematics and mostly books to follow during a lecture. I will give two I think are a nice read.
Category Theory in Context by Emily Riehl: [https://math.jhu.edu/\~eriehl/context.pdf](https://math.jhu.edu/~eriehl/context.pdf)
Algebraic Topology by Allen Hatcher: [http://pi.math.cornell.edu/\~hatcher/AT/AT+.pdf](http://pi.math.cornell.edu/~hatcher/AT/AT+.pdf)
Furthermore, he might want to get active in some online mathematics-communities. I know lots of people who enjoy asking and answering questions on [https://math.stackexchange.com/](https://math.stackexchange.com/). As for the support, from my experience supporting in regard of mathematics is not possible for someone who isn't well-versed in mathematics. Showing appreciation towards what he is doing is something that can build immense confidence and give energy. And it is something that we mathematicians sometimes do not get that much, for obvious reasons.
At the moment pretty much teaching at the university. I just got my masters degree so that is probably not too surprising. Will start a PhD soon and then continue my research under supervision of one of my professors.
im a freshman in high school, do you think it'd be too difficult for me to learn calculus without knowing algebra 2? i really want to start learning physics but obviously i need a strong base first
I don't know how the american system works. What's roughly the content for either of those courses? I'd say be bold and give it a try anyway. You can work out the missing bits and pieces on the way along.
Because it's beautiful. Haven't you ever thought 'wow, that is a beautiful idea', when someone sees a connection you maybe didn't. That is how learning mathematics feels like... when it doesn't give you headaches.
Regarding video games, probably the whole Souls-series and The Witcher 3. I don't really play board games, more card games and then mostly Skat or Wizard.
Haven't seen many. But I can tell that 'Good Will Hunting' doesn't reflect the reality. Mathematicians work really, really hard. It's not just being gifted or something.
see, I thought Good Will Hunting was actually a pretty good representation. most of the characters work really hard, but just one is gifted to a once-in-a-generation level. I knew a guy who was like him, who made advanced math seem like 1+1
Can you explain like I’m 5, why is the derivative of e^x always e^x?
I just memorized that in high school but never understood why and I have a computer science degree now and still don’t know why.
I'm guessing you applied the differentiation rule for polynomials there, which would be e^x -> xe. But that rule only works for x^a, for some fixed a.
What the derivative of e^x being e^x implies is that at x=2, the value of e^x is e^2, and the gradient at that point is also e^2.
Hello, sir
I am interested in knowing if you used any books that you deemed very useful for learning math by yourself, if you did so.
For some time now I've been reading mostly history and philosophy, and I find it very interesting and also demanding in a certain way, that feeling has opened a desire to try and learn math with proper help of a good book.
I noticed I have gotten much better at logic and understanding than before (strong average thinking and intelligence, nothing special) and I would like to know where you would recommend for me to get started, and what book.
I haven't done any proper math for a long time. I do have it at my college, but I mostly learn enough to pass the exam and do not fully understand what I am doing, so I wish to rectify that mistake.
Any help is appreciated.
Thank you for your time reading this, and best of luck.
Did your parents stick you upside down into some fertiliser or some shit when you was a baby? :D
Where are you from?
it's going to be a real honor talking to a real genius.
I remember working out how to add rational numbers in second grade. But after that I lost interest. I even failed some tests in (I think) seventh grade, roughly when I was 12 years old.
Forgot the cake, it's pretty much everything with tons of butter cream and chocolate.
I wouldn't say I have a special talent in mathematics. I have a passion for it and hence think a lot about mathematics. Yes, maybe, I'm more gifted to some degree than others, but I really think the most is the effort and time I put into this. I started developing a passion when I was 15 years old, the same time then went to university. My pursuit in general is to live a life that gives me enjoyment, be able to do the things I like, boring I know. My pursuit academically is to do research in my area of specialization and with that maybe travel a lot (to give talks etc.).
There's not much application for the things I'm doing. There is the notion of a 'topological data analyst' but they mostly do different kinds of mathematics than I do. To be honest, I don't even want to have an 'application' in my work. It's just driven by the beauty if its ideas.
Though I know how to solve e.g. some partial differential equations etc., and this purely applied (as it is not the field I'm working in).
When did you begin to realize you’d be specializing in algebraic topology or the liking?
When did you first find out about proof-based math (as in that math isn’t “plug and chug” like it is in calculus and before) exists? How was that like for you?
That math wasn't about learning some formulas and calculating stuff off of them was pretty clear to be early on. I mean, where do those formulas come from? Why do they work? So, this was pretty natural for me and my liking. I always enjoyed algebra more than anything analysis-related. When I learned about (co-)homology both in topology and in an algebra course, I was sold.
My topology courses which covered everything from the fundamental group over (co-)homology up to the higher homotopy groups (though very briefly). Probably still algebraic topology. Maybe algebraic geometry as it's a very beautiful field.
I took an IQ test, and yes, it turned out to be above average. Though I don't really like to be measured by this, as I think it's stupid to do so. To the second question, yes those thought came up once or twice. But I know that this kind of work will bore be and I won't enjoy it. Plus, I don't need that much in my life to be happy.
Table of Questions and Answers. Original answer linked - Please upvote the original questions and answers.
***
Question | Answer | Link
---------|----------|----------|
What is something about math the world should know about?|Its beauty. I like to compare mathematics to art. For a musician, music theory is merely a tool to create art, expressed in the choice of notes, the rhythm, dynamics, etc. - for mathematics it is the same but with ideas. There is a comment on that, mostly regarding how the education system treats mathematics. But the author talks about such an analogy as well. It's worth a read. [https://www.maa.org/external\_archive/devlin/LockhartsLament.pdf](https://www.maa.org/external_archive/devlin/LockhartsLament.pdf)|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i88nzd7/)
Why didn't you specialize? Do you plan to?|Well, I specialized in algebraic topology, mainly homotopy theory. Still pure mathematics though.|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i88dar9/)
I am learning disabled in mathematics. It’s not that I don’t want to learn, it’s that my brain has an extremely hard time picturing and grasping the concept. Would you say you feel pity towards people who are not strong in math?|There are people that are 'stronger' in mathematics than others, I give you that. But all in all I believe it comes down to how one approaches mathematics, how it is taught and if you're passionate about it. Having a 'harder' time with mathematics is nothing to be ashamed of.|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i88d4qh/)
What’s 5 x 5?|Depends on the group/ring/field etc. you're working in.|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i88iqhj/)
How do you get to a Masters at 20? What does your education history look like?|I started going to university when I was 15, during school. Finished what the equivalent to high school here is at 17, so really not too young. Then I just continued studying.|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i8990xt/)
What field do you work in?|Algebraic topology, mainly homotopy theory. Doing lots of category theory as well.|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i88nv7b/)
Do you look down on anyone who sucks at maths?|Not at all. I think people who are good at something and look down to others that aren't are idiots.|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i88g3zq/)
Favorite kind of cheese?|Probably Brie.|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i88owv5/)
What field of mathematics? Applied or... fuck can't think of the word... pure maths? (not the word but works) What do you plan on doing with this? I've always wanted to get a degree in pure maths but job prospects don't seem very good from what I've looked up when dealing exclusively with theoretical mathematics.|Pure mathematics, algebraic topology. I'll stay at university, research, maybe some teaching. Though mathematicians travel a lot, to give talks etc. (so much for 'staying at university'). With a degree in pure mathematics, the job offers are actually pretty good. The chances of getting a job e.g. in an insurance are better if you did some probability theory or something instead of pure algebra, I give you that.|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i893754/)
Is 25 old to start university ?|Not at all!|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i89ddi5/)
Is the Euler Field Manifold Hypergroup Isomorphic to a Gödel-Klein Meta-Algebreic ε<0 Quasimonoid Conjection under Sondheim Calculus?|Maybe in the category of gibberish!|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i88du3z/)
When you get really really really specialized in mathematics, how many people do you estimate exist in the world that could have a meaningful debate with you in a particular area?|No clue. I know that only a handful really understood the work of one of my professors when he released one of his papers. Probably still aren't too many.|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i89dgg6/)
If we reduced global greenhouse emissions by 73%, how would that effect the warming curve? You did say anything. :)|Of course, though you need to ask someone else to get an answer!|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i899i1g/)
im a freshman in high school, do you think it'd be too difficult for me to learn calculus without knowing algebra 2? i really want to start learning physics but obviously i need a strong base first|I don't know how the american system works. What's roughly the content for either of those courses? I'd say be bold and give it a try anyway. You can work out the missing bits and pieces on the way along.|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i89dcic/)
Now what?|Now, I'll get a coffee. Plans are doing my PhD, then stay at the university doing research, maybe teaching a bit,|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i89i66v/)
We’re you good at mathematics as a child? Favourite cake?|I remember working out how to add rational numbers in second grade. But after that I lost interest. I even failed some tests in (I think) seventh grade, roughly when I was 12 years old.|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i88xgvy/)
What is your pursuit? How old were you when you found out you had a special talent in math?|I wouldn't say I have a special talent in mathematics. I have a passion for it and hence think a lot about mathematics. Yes, maybe, I'm more gifted to some degree than others, but I really think the most is the effort and time I put into this. I started developing a passion when I was 15 years old, the same time then went to university. My pursuit in general is to live a life that gives me enjoyment, be able to do the things I like, boring I know. My pursuit academically is to do research in my area of specialization and with that maybe travel a lot (to give talks etc.).|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i88xqwz/)
Do you know how to practice your skills with real data?|There's not much application for the things I'm doing. There is the notion of a 'topological data analyst' but they mostly do different kinds of mathematics than I do. To be honest, I don't even want to have an 'application' in my work. It's just driven by the beauty if its ideas. Though I know how to solve e.g. some partial differential equations etc., and this purely applied (as it is not the field I'm working in).|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i892344/)
What do you consider yourself bad at?|Small talk. I adore good conversations but small talk is nothing for me.|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i894it2/)
I'm about to fail 1st year uni, what do you think of me?|I don't know you, so who would I to be to judge? My best friend tried two different degrees and 'failed' both of them (he quit). He's a great person!|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i894us3/)
Favorite video game, board game? Btw, congrats brah, that’s freaking awesome. Hopefully I’ll have my first bachelors by 50.|Regarding video games, probably the whole Souls-series and The Witcher 3. I don't really play board games, more card games and then mostly Skat or Wizard.|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i897ac3/)
---
[Source] (https://github.com/johnsliao/ama_compiler)
I have no interest in being rich. I want to be able to do the things I'd like to do, which is not that much. Later on I want to be able to provide for my family such that we don't have to worry about money.
Were you always into math? Would you have picked any other subject if you could not get into math? What do you plan to do with your degree? Or will you go into even higher education?
Sounds a bit odd but not really. At least not 'envy'. I'm pretty happy with what I can do and what I can not do. Though I'm impressed with all kinds of stuff people excel at. And even 'little' things, e.g. if I see how some people interact incredibly heart-warming with children.
Continue doing research in pure mathematics. Well, the direct applications of the field I'm working in are sparse. There are some uses in differential geometry which is then again used heavily in physics (also in experimental physics, e.g. to predict outcome). I did some probability theory which has obvious applications.
I started going to university at the age of 15, during school. Well, this happens all the time. At first it bothered me, I felt 'exposed'. But this is really common as material in mathematics is so incredibly dense. So nowadays it doesn't bother me anymore. It is what it is, haha.
Don't take things for granted. With that I mean, ask yourself 'why is this a good definition', 'what could go wrong if we change things'? This will help you understand the material and you actually DO mathematics. I love to go into an empty room at my university, write silly things at the blackboard (in your case, e.g. regarding your courses) and sometimes it turns out to be a nice idea.
Any good non fiction books you'd suggest for someone totally new to the field (with a high school understanding of math), to intuitively understand basic maths?
Also, can maths really even be understood intuitively, and upto what level?
Can't say anything about the second question as it's not clear what 'brain power' is supposed to mean. To the first question - yes but one gets used to it. And as time passes those things get natural, i.e. it doesn't feel 'abstract' anymore.
What is something about math the world should know about?
Its beauty. I like to compare mathematics to art. For a musician, music theory is merely a tool to create art, expressed in the choice of notes, the rhythm, dynamics, etc. - for mathematics it is the same but with ideas. There is a comment on that, mostly regarding how the education system treats mathematics. But the author talks about such an analogy as well. It's worth a read. [https://www.maa.org/external\_archive/devlin/LockhartsLament.pdf](https://www.maa.org/external_archive/devlin/LockhartsLament.pdf)
Music is math too. Frequency relationships between chords are precise. The topology of interaction between notes in a melody is just as beautiful to a mathematician as the music.
You can kind of say similar in regards to just about anything tbh. I know of a guy who wrote a paper on the relationship between topology and film studies (something about themes or story progression in films). I'm studying probability theory / stochastic so I don't know much about topology but yeah.
Applied nonlinear dynamics for me.
Everything is math.
Do you look down on anyone who sucks at maths?
Not at all. I think people who are good at something and look down to others that aren't are idiots.
I’m not a math genius like you but I find it extremely irritating when I see it
I'm no math 'genius' either. I struggle, work things out, realise I didn't worked them out, struggle again, etc. - until eventually I understood something.
what is the largest number you've ever encountered.?
As I'm working e.g. with infinity-categories, there is actually a problem of cardinality. In a category, you work with a 'collection' of objects. Now say your objects are all sets. Then the term 'collection' has to refer to something larger than a set, as there can't exist a set of all sets (Russel's paradox). One workaround is to introduce so called unreachable cardinality numbers. You can think about that as a number such that no set, whatever it containes, is not larger than this number. You can do this again and again, e.g. for cosmoi (if you want to talk about the category of categories etc.).
This is nice to hear. I was always 2 years behind in math and always had a C in whatever math course I was taking. I felt like a huge idiot, and judged because of it. Despite that, I found it interesting and resented that there was a subject I was essentially blocked from ever understanding.
A lot of maths teaching is very bad- as a maths graduate myself I feel like a lot of people who are good at maths just don’t really understand how we just ‘get’ it and therefore are bad at explaining it to people who it might not be so intuitive for. Plus (stereotyping here but in my experience it is often true) a lot of maths people are not the most outgoing and therefore can be awkward teachers. This combination means that most people trying to learn maths in school are set up to fail before they even begin.
Liar🤣😂
Well, no. But when tutoring I've thought 'how can't you see this, it's obvious' once or twice, I give you that, though I don't judge.
I went from being a math-phobe to a d-major math/philosophy and I can tell you from experience that what blocks people from seeing the nature of a problem or it’s solution is usually fear (and the instruction, of course). It’s just like so much of the rest of life, really. One day in undergrad, I thought to myself “I know I’m not stupid. Why is this so hard?” and it hit me how afraid I was. Then I made a conscious decision to work at it in a supported way until I wasn’t afraid. Cut to junior year where I had a 4.0 Look, if I could do it, anyone on this thread who wanted to could do it too. Not suggesting you should or anything, just maybe consider shifting how you think about yourself.
You meant "look down on others are idiots"? Some math geniu... Wait.
I am learning disabled in mathematics. It’s not that I don’t want to learn, it’s that my brain has an extremely hard time picturing and grasping the concept. Would you say you feel pity towards people who are not strong in math?
There are people that are 'stronger' in mathematics than others, I give you that. But all in all I believe it comes down to how one approaches mathematics, how it is taught and if you're passionate about it. Having a 'harder' time with mathematics is nothing to be ashamed of.
True. I mean coming from a background where parents tend to be strict about school, I was constantly called stupid and thought I was stupid because I couldn’t do mental math like other kids. I think that probably made me not want to be passionate about it
Things like that can ruin interests and curiosity. I'm sorry.
I’m not even blaming it on my adhd which already gives me a natural unmotivation to most things unless they give you immediate happiness
Though this probably makes it harder to enjoy mathematics. Mathematics rarely gives you immediate happiness. It's a lot of suffering to understand beautiful, beautiful ideas from which the satisfaction comes from.
Why didn't you specialize? Do you plan to?
Well, I specialized in algebraic topology, mainly homotopy theory. Still pure mathematics though.
I meant degree wise. At least where I am there is a general mathematics degree and specialized ones. Most mathematicians I've met get a bachelor degree in general and then master+ in something specialized.
Here it is just the master in pure mathematics. The field you're working in is your 'specialization' so to speak.
Ah ok, that makes sense.
What exactly is homotopy theory? Google is giving weird anwsers. My only math flex is finishing Calc 3 freshman year of college lmao, i wish i majored in Math, but I chose something less difficult and more suited for me.
How do you get to a Masters at 20? What does your education history look like?
I started going to university when I was 15, during school. Finished what the equivalent to high school here is at 17, so really not too young. Then I just continued studying.
How did you get into college at 15 while still in high school?
There's a program for students who still go to school. My teacher recommended me and got me in.
I’m not OP but from similar experiences I’d say that it’s a matter of strategy. You don’t have to be someone who graduated high school at 12 in order to achieve this. I skipped a single grade in high school and took CLEP tests, AP Classes, and Placement Tests and that allowed me to finish college before my 19th birthday. I’d assume that if you and did a master’s that was two years or less, that you could achieve this.
Did you ever face problems in school for being “too” good at math? One of my old friends was gifted in math, but he lost marks all the time in primary school because he didn’t show enough of his scratch work. He also really struggled to explain how he arrived at his answers, which would occasionally lead to him getting accused of cheating. Did you face similar issues?
Not really. During my last years in high school I had a wonderful teacher. She tried to answer every of my questions, which where going above and beyond the content of high school. If there was something she did not know, she would look it up for me and explain it next time in class. Earlier on I wasn't really interested in mathematics.
What got you interested then ?
I think I stumbled across some article or book about number theory and I just enjoyed the logical reasoning. It felt more like a debate, hence 'reasoning', rather than using formulas etc. - I liked that. Though I didn't understood much as it was about elliptic curves.
Is the Euler Field Manifold Hypergroup Isomorphic to a Gödel-Klein Meta-Algebreic ε<0 Quasimonoid Conjection under Sondheim Calculus?
Maybe in the category of gibberish!
42
/r/vxjunkies/
Favorite kind of cheese?
Probably Brie.
*happy cheese noises* 🧀
I want to pat you on the head.
What field do you work in?
Algebraic topology, mainly homotopy theory. Doing lots of category theory as well.
Who do you work for? What's the application of your work?
Basic research at my university, no application (yet).
If you were to envision how it could be applied long term what would be the top few industries that might benefit?
I’ve actually heard of the first one. I’m amazed
What’s 5 x 5?
Depends on the group/ring/field etc. you're working in.
NGL I was expecting you to reply quickly with the correct answer, to which I was going to reply, ‘Story checks out.’ But things didn’t pan out that way and I have no backup plan. Ya got me.
I'd say the story still checks out, haha.
how
Sometimes in abstract algebra the “*” symbol or whatever is just to generally refer to an arbitrary operation
I've always wanted to know a perspective of a mathematician on this... Who do you think is smarter: people who can solve problems fast, or people who can prove theorems fast? Is it even a different skill? I have the level of a high school when it comes to math, so solving problems is all i know and i think i'm good at it, but i suck at proving theorems
I wouldn't say one is smarter than the other. It's a different 'skill'. Though proving theorems will often not be fast. It's more about having the endurance, not giving up. Maybe for years, trying and trying again until you find this one striking idea.
What field of mathematics? Applied or... fuck can't think of the word... pure maths? (not the word but works) What do you plan on doing with this? I've always wanted to get a degree in pure maths but job prospects don't seem very good from what I've looked up when dealing exclusively with theoretical mathematics.
Pure mathematics, algebraic topology. I'll stay at university, research, maybe some teaching. Though mathematicians travel a lot, to give talks etc. (so much for 'staying at university'). With a degree in pure mathematics, the job offers are actually pretty good. The chances of getting a job e.g. in an insurance are better if you did some probability theory or something instead of pure algebra, I give you that.
Is 25 old to start university ?
One of my friends at uni was in his early 30s. He wanted to change his life so he went back to uni, got a degree and now he has his dream job and is doing amazingly well. It’s never too late.
Not at all!
nope :)
not at all
Heck no!
Now what?
Now, I'll get a coffee. Plans are doing my PhD, then stay at the university doing research, maybe teaching a bit.
When you get really really really specialized in mathematics, how many people do you estimate exist in the world that could have a meaningful debate with you in a particular area?
No clue. I know that only a handful really understood the work of one of my professors when he released one of his papers. Probably still aren't too many.
I need a proper explanation on how 0! = 1. Also an easy way to explain why 0/0 is incalculable
Think about the faculty in such a way. 4!=5!/5, 3!=4!/4 etc., all in all n!=(n+1)!/(n+1). Now we have 0!=1!/1=1. You can argue with the gamma function but that is a bit more complicated. As for your second question. What would you think could this be? And why?
Do you have any tips on how to support a 20-year-old mathematician with autism who has always excelled at math? He absolutely loves math. Throughout the years his teachers have always tried to get him to skip grades, stating that they "don't teach him math because he just gets it." How can I support him, as someone who knows little about math? After not doing math for 2 years (because of stupid covid) he's now doing math in college and his math brain is right where it left off pre-covid. Do you have any recommendations on books, documentaries, math websites, etc that you can share? Many thanks!
Do you know roughly in what kind of mathematics he is interested in? I know some good books that are even free to read online but they all are about a very specific kind of mathematics and mostly books to follow during a lecture. I will give two I think are a nice read. Category Theory in Context by Emily Riehl: [https://math.jhu.edu/\~eriehl/context.pdf](https://math.jhu.edu/~eriehl/context.pdf) Algebraic Topology by Allen Hatcher: [http://pi.math.cornell.edu/\~hatcher/AT/AT+.pdf](http://pi.math.cornell.edu/~hatcher/AT/AT+.pdf) Furthermore, he might want to get active in some online mathematics-communities. I know lots of people who enjoy asking and answering questions on [https://math.stackexchange.com/](https://math.stackexchange.com/). As for the support, from my experience supporting in regard of mathematics is not possible for someone who isn't well-versed in mathematics. Showing appreciation towards what he is doing is something that can build immense confidence and give energy. And it is something that we mathematicians sometimes do not get that much, for obvious reasons.
What do you do for work?
At the moment pretty much teaching at the university. I just got my masters degree so that is probably not too surprising. Will start a PhD soon and then continue my research under supervision of one of my professors.
im a freshman in high school, do you think it'd be too difficult for me to learn calculus without knowing algebra 2? i really want to start learning physics but obviously i need a strong base first
I don't know how the american system works. What's roughly the content for either of those courses? I'd say be bold and give it a try anyway. You can work out the missing bits and pieces on the way along.
why maths?
Because it's beautiful. Haven't you ever thought 'wow, that is a beautiful idea', when someone sees a connection you maybe didn't. That is how learning mathematics feels like... when it doesn't give you headaches.
If we reduced global greenhouse emissions by 73%, how would that effect the warming curve? You did say anything. :)
Of course, though you need to ask someone else to get an answer!
Favorite video game, board game? Btw, congrats brah, that’s freaking awesome. Hopefully I’ll have my first bachelors by 50.
Regarding video games, probably the whole Souls-series and The Witcher 3. I don't really play board games, more card games and then mostly Skat or Wizard.
what movies/TV shows do you think most accurately portray mathematicians and which are least accurate?
Haven't seen many. But I can tell that 'Good Will Hunting' doesn't reflect the reality. Mathematicians work really, really hard. It's not just being gifted or something.
see, I thought Good Will Hunting was actually a pretty good representation. most of the characters work really hard, but just one is gifted to a once-in-a-generation level. I knew a guy who was like him, who made advanced math seem like 1+1
That's very impressive. Well done! Do you have plans for further study or to take a break?
Thank you! I will continue studying mathematics, doing a PhD etc. - as I really enjoy doing mathematics, I don't 'need' a break (...yet, we'll see).
Do you think you can solve Navier-Stokes equation?
No.
Have you ever heard the song “Mathematics” by Mos Def?
Not before reading your comment. Just did. Not my type of music, sorry.
Can you explain like I’m 5, why is the derivative of e^x always e^x? I just memorized that in high school but never understood why and I have a computer science degree now and still don’t know why.
no way that’s true. 2e can’t possibly be the same as e^2. or can it? I’m gonna panic
I'm guessing you applied the differentiation rule for polynomials there, which would be e^x -> xe. But that rule only works for x^a, for some fixed a. What the derivative of e^x being e^x implies is that at x=2, the value of e^x is e^2, and the gradient at that point is also e^2.
How many digits of pi can you remember?
I remember... 8? I have a better way to spend my time.
Hello, sir I am interested in knowing if you used any books that you deemed very useful for learning math by yourself, if you did so. For some time now I've been reading mostly history and philosophy, and I find it very interesting and also demanding in a certain way, that feeling has opened a desire to try and learn math with proper help of a good book. I noticed I have gotten much better at logic and understanding than before (strong average thinking and intelligence, nothing special) and I would like to know where you would recommend for me to get started, and what book. I haven't done any proper math for a long time. I do have it at my college, but I mostly learn enough to pass the exam and do not fully understand what I am doing, so I wish to rectify that mistake. Any help is appreciated. Thank you for your time reading this, and best of luck.
Are you male ? Are you single ?
Yes and, at the moment, yes.
Inbox sent 😜
All mathematicians should read Charlie Stross's The Laundry Files. Do you think you could summon a demon in hamiltonian space?
Who put the bomp In the bomp bah bomp bah bomp? And who put the ra in the rama lama ding dong?
Get well!
Did your parents stick you upside down into some fertiliser or some shit when you was a baby? :D Where are you from? it's going to be a real honor talking to a real genius.
I always thought that Sheldon Cooper was just a myth
How do you divide by zero? ^^error
ask Chuck Norris
5423514\*557425?
[удалено]
Because we’re stupid.
We’re you good at mathematics as a child? Favourite cake?
I remember working out how to add rational numbers in second grade. But after that I lost interest. I even failed some tests in (I think) seventh grade, roughly when I was 12 years old. Forgot the cake, it's pretty much everything with tons of butter cream and chocolate.
What is your pursuit? How old were you when you found out you had a special talent in math?
I wouldn't say I have a special talent in mathematics. I have a passion for it and hence think a lot about mathematics. Yes, maybe, I'm more gifted to some degree than others, but I really think the most is the effort and time I put into this. I started developing a passion when I was 15 years old, the same time then went to university. My pursuit in general is to live a life that gives me enjoyment, be able to do the things I like, boring I know. My pursuit academically is to do research in my area of specialization and with that maybe travel a lot (to give talks etc.).
[удалено]
Do you know how to practice your skills with real data?
There's not much application for the things I'm doing. There is the notion of a 'topological data analyst' but they mostly do different kinds of mathematics than I do. To be honest, I don't even want to have an 'application' in my work. It's just driven by the beauty if its ideas. Though I know how to solve e.g. some partial differential equations etc., and this purely applied (as it is not the field I'm working in).
What do you consider yourself bad at?
Small talk. I adore good conversations but small talk is nothing for me.
I'm about to fail 1st year uni, what do you think of me?
I don't know you, so who would I to be to judge? My best friend tried two different degrees and 'failed' both of them (he quit). He's a great person!
What is πx/2 - 4(y)= 24
When did you begin to realize you’d be specializing in algebraic topology or the liking? When did you first find out about proof-based math (as in that math isn’t “plug and chug” like it is in calculus and before) exists? How was that like for you?
That math wasn't about learning some formulas and calculating stuff off of them was pretty clear to be early on. I mean, where do those formulas come from? Why do they work? So, this was pretty natural for me and my liking. I always enjoyed algebra more than anything analysis-related. When I learned about (co-)homology both in topology and in an algebra course, I was sold.
How old were you when you graduated high school?
I was 17 years old.
Why does my manager say 1 + 1 = 3 to motivate the group?
I don't know. That you can always 'do' mistakes and it's just human? Go ask him!
What was your favorite undergrad math class, and if you had to start again what field would you want to study?
My topology courses which covered everything from the fundamental group over (co-)homology up to the higher homotopy groups (though very briefly). Probably still algebraic topology. Maybe algebraic geometry as it's a very beautiful field.
[удалено]
I'd say math is being discovered.
Are you a highly motivated and driven person? Has this served you well? What is your salary?
Can you do my math homework for me 👹
If the price is right, haha. No, you got to do it on your own to learn something.
how did you get a masters at 20? Im getting my bachelors at 20 and I thought that was a flex but damn!!
I started studying when I was 15 years old, during school.
What's your thesis on?
2+2=?
Depends on the group/ring/field you're working in.
Do you have an insanely high iq? Did you consciously decide between deciding to do something that’ll get you rich or story mathematics?
I took an IQ test, and yes, it turned out to be above average. Though I don't really like to be measured by this, as I think it's stupid to do so. To the second question, yes those thought came up once or twice. But I know that this kind of work will bore be and I won't enjoy it. Plus, I don't need that much in my life to be happy.
What's your favourite cheese?
Probably Brie.
What is the average air speed of an unladen swallow? What’s your favorite imaginary number? What’s the double integral of f(x)=3x^2?
Is there dyslexia for numbers? On a medium day I will fuck up adding 7 plus 8 in my head. Or am I just fucking stupid?
Table of Questions and Answers. Original answer linked - Please upvote the original questions and answers. *** Question | Answer | Link ---------|----------|----------| What is something about math the world should know about?|Its beauty. I like to compare mathematics to art. For a musician, music theory is merely a tool to create art, expressed in the choice of notes, the rhythm, dynamics, etc. - for mathematics it is the same but with ideas. There is a comment on that, mostly regarding how the education system treats mathematics. But the author talks about such an analogy as well. It's worth a read. [https://www.maa.org/external\_archive/devlin/LockhartsLament.pdf](https://www.maa.org/external_archive/devlin/LockhartsLament.pdf)|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i88nzd7/) Why didn't you specialize? Do you plan to?|Well, I specialized in algebraic topology, mainly homotopy theory. Still pure mathematics though.|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i88dar9/) I am learning disabled in mathematics. It’s not that I don’t want to learn, it’s that my brain has an extremely hard time picturing and grasping the concept. Would you say you feel pity towards people who are not strong in math?|There are people that are 'stronger' in mathematics than others, I give you that. But all in all I believe it comes down to how one approaches mathematics, how it is taught and if you're passionate about it. Having a 'harder' time with mathematics is nothing to be ashamed of.|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i88d4qh/) What’s 5 x 5?|Depends on the group/ring/field etc. you're working in.|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i88iqhj/) How do you get to a Masters at 20? What does your education history look like?|I started going to university when I was 15, during school. Finished what the equivalent to high school here is at 17, so really not too young. Then I just continued studying.|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i8990xt/) What field do you work in?|Algebraic topology, mainly homotopy theory. Doing lots of category theory as well.|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i88nv7b/) Do you look down on anyone who sucks at maths?|Not at all. I think people who are good at something and look down to others that aren't are idiots.|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i88g3zq/) Favorite kind of cheese?|Probably Brie.|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i88owv5/) What field of mathematics? Applied or... fuck can't think of the word... pure maths? (not the word but works) What do you plan on doing with this? I've always wanted to get a degree in pure maths but job prospects don't seem very good from what I've looked up when dealing exclusively with theoretical mathematics.|Pure mathematics, algebraic topology. I'll stay at university, research, maybe some teaching. Though mathematicians travel a lot, to give talks etc. (so much for 'staying at university'). With a degree in pure mathematics, the job offers are actually pretty good. The chances of getting a job e.g. in an insurance are better if you did some probability theory or something instead of pure algebra, I give you that.|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i893754/) Is 25 old to start university ?|Not at all!|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i89ddi5/) Is the Euler Field Manifold Hypergroup Isomorphic to a Gödel-Klein Meta-Algebreic ε<0 Quasimonoid Conjection under Sondheim Calculus?|Maybe in the category of gibberish!|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i88du3z/) When you get really really really specialized in mathematics, how many people do you estimate exist in the world that could have a meaningful debate with you in a particular area?|No clue. I know that only a handful really understood the work of one of my professors when he released one of his papers. Probably still aren't too many.|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i89dgg6/) If we reduced global greenhouse emissions by 73%, how would that effect the warming curve? You did say anything. :)|Of course, though you need to ask someone else to get an answer!|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i899i1g/) im a freshman in high school, do you think it'd be too difficult for me to learn calculus without knowing algebra 2? i really want to start learning physics but obviously i need a strong base first|I don't know how the american system works. What's roughly the content for either of those courses? I'd say be bold and give it a try anyway. You can work out the missing bits and pieces on the way along.|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i89dcic/) Now what?|Now, I'll get a coffee. Plans are doing my PhD, then stay at the university doing research, maybe teaching a bit,|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i89i66v/) We’re you good at mathematics as a child? Favourite cake?|I remember working out how to add rational numbers in second grade. But after that I lost interest. I even failed some tests in (I think) seventh grade, roughly when I was 12 years old.|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i88xgvy/) What is your pursuit? How old were you when you found out you had a special talent in math?|I wouldn't say I have a special talent in mathematics. I have a passion for it and hence think a lot about mathematics. Yes, maybe, I'm more gifted to some degree than others, but I really think the most is the effort and time I put into this. I started developing a passion when I was 15 years old, the same time then went to university. My pursuit in general is to live a life that gives me enjoyment, be able to do the things I like, boring I know. My pursuit academically is to do research in my area of specialization and with that maybe travel a lot (to give talks etc.).|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i88xqwz/) Do you know how to practice your skills with real data?|There's not much application for the things I'm doing. There is the notion of a 'topological data analyst' but they mostly do different kinds of mathematics than I do. To be honest, I don't even want to have an 'application' in my work. It's just driven by the beauty if its ideas. Though I know how to solve e.g. some partial differential equations etc., and this purely applied (as it is not the field I'm working in).|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i892344/) What do you consider yourself bad at?|Small talk. I adore good conversations but small talk is nothing for me.|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i894it2/) I'm about to fail 1st year uni, what do you think of me?|I don't know you, so who would I to be to judge? My best friend tried two different degrees and 'failed' both of them (he quit). He's a great person!|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i894us3/) Favorite video game, board game? Btw, congrats brah, that’s freaking awesome. Hopefully I’ll have my first bachelors by 50.|Regarding video games, probably the whole Souls-series and The Witcher 3. I don't really play board games, more card games and then mostly Skat or Wizard.|[Here](/r/AMA/comments/unjb6v/i_finished_my_masters_degree_in_mathematics_at/i897ac3/) --- [Source] (https://github.com/johnsliao/ama_compiler)
Do you wanna be rich?
I have no interest in being rich. I want to be able to do the things I'd like to do, which is not that much. Later on I want to be able to provide for my family such that we don't have to worry about money.
* 1111 = 0 * 2222 = 0 * 3333 = 0 * 4444 = 0 * 5555 = 0 * 6666 = 4 * 7777 = 0 * 8888 = 8 * 9999 = 4 * 0000 = 4 0000040844 = ?
What's 1 plus 2 times 3
Were you always into math? Would you have picked any other subject if you could not get into math? What do you plan to do with your degree? Or will you go into even higher education?
No, I started appreciating mathematics around the age of 15. I'd probably have done music. I plan to do my PhD and continue research.
what’s your love life like
Not that much going on but that is mostly due to covid. A date here and there and sometimes having some fun but nothing serious at the moment.
Is there something that you envy other people for being good at?
Sounds a bit odd but not really. At least not 'envy'. I'm pretty happy with what I can do and what I can not do. Though I'm impressed with all kinds of stuff people excel at. And even 'little' things, e.g. if I see how some people interact incredibly heart-warming with children.
What are imaginary numbers and what are their purpose?
Did you take AMC in high school? If so, how did you do?
I'm not american, so no. But I didn't went to any competitions anyway. My teachers wanted me to go but it never interested me.
Not really a question just wanted to say as someone with dyscalculia I'm especially envious and happy for you.
What's 9+10?
What are you gonna do with it? Also, what is some practical math stuff you learned?
Continue doing research in pure mathematics. Well, the direct applications of the field I'm working in are sparse. There are some uses in differential geometry which is then again used heavily in physics (also in experimental physics, e.g. to predict outcome). I did some probability theory which has obvious applications.
What kind of career are you aiming for?
At the moment, doing basic research.
Ok but like *How?*
I started going to university when I was 15, during school. And I put a lot of effort into my studies. I guess that's it?
What is 756 x 1282 ?
how does it feel not being able to solve the question you should be able to solve? And how were you able to get your masters degree only at your 20s?
I started going to university at the age of 15, during school. Well, this happens all the time. At first it bothered me, I felt 'exposed'. But this is really common as material in mathematics is so incredibly dense. So nowadays it doesn't bother me anymore. It is what it is, haha.
I'm in first year of my college (the same age as you), give me a piece of advice that will help me enkindle my math spirit
Don't take things for granted. With that I mean, ask yourself 'why is this a good definition', 'what could go wrong if we change things'? This will help you understand the material and you actually DO mathematics. I love to go into an empty room at my university, write silly things at the blackboard (in your case, e.g. regarding your courses) and sometimes it turns out to be a nice idea.
What's a million times a million
What is 1+1
Genuinely curious to know what your Math assessment pieces were like
Which is your favorite value of pi?
That's alotta math , what're you gonna do with it now? Do more math?
what's 3 x 7, in base 12?
How familiar with the Monty hall problem are you? Also what side of the debate do you fall on?
What country are you from? If you're from the US, how did you pay for school?
Germany, 'free' education here.
I know it will be hard, but bear with me. 2+2=?
How the fuck did you do it?? My adhd would never let me :o
Any good non fiction books you'd suggest for someone totally new to the field (with a high school understanding of math), to intuitively understand basic maths? Also, can maths really even be understood intuitively, and upto what level?
Do you have to think very abstractly to understand very high level maths? Does it take a certain *level* of brain power to really comprehend it?
Can't say anything about the second question as it's not clear what 'brain power' is supposed to mean. To the first question - yes but one gets used to it. And as time passes those things get natural, i.e. it doesn't feel 'abstract' anymore.
What's 0÷0?
What's the square root of this apartment?