u/scripto_entity_1010

Ever since I graduated and am now an upcoming freshman, there has been many challenges that I faced which made me question my abilities and self-worth. I see people who are way better than me and I couldn't keep up on the pace that I hoped to achieve. I thought that maybe I could change my habits by reading books and going to the gym. Yet, whenever I try to pursue my passion in math and programming I am reminded of how "little" I am compared to others and I feel frustrated sometimes. Although there are moments when I feel this "motivation" there are also times when I feel down and have that sense that I am so behind. I don't want to be a victim of the highs and lows that I achieve. I want to be consistent at it. I want to be better than giving into the extreme positives and negatives and have a more robust mindset as early as now to help my family as well once I graduate. I can tell that this way of thinking that I have will not get me anywhere. What has helped you so far when it comes to dealing with this kind of personal issue?

I've started learning about Data Structures and Algorithms as an upcoming freshman and it reminded me of one of the seven millennium prize problems which is concerned about algorithms in computers also known as P = NP. What progress in math research has been made so far in solving this? And as mathematicians or computer scientists do you think it will ever be solved at all? Given the complexity of this problem. If it has been solved, or cannot be solved, what will this mean for the math and computer science community?

I'm an upcoming undergraduate as well as someone considering further studies and I would like to hear from you people who have went through further studies about what set of beliefs / practices has helped you excel in your respective field. As early as now, I've already been trying to get myself used to the "studying" mindset for me to remain steadfast regardless of the struggles I go through in college. I'm sure that there are many of you, reading this post, has a story and lesson to offer to someone like me who has dreams of one day excelling in their studies. What would you say?

I've been reading through Roger Penrose's Road to Reality and stopped at the Calculus part, and I'm starting to see now how math plays a substantial role in physics. As someone who has been exposed to the field some time and have been enlightened by how some higher mathematics, such as hyperbolic geometry and complex analysis (though there were parts where I got confused, at least I have an idea how it is applied in particle physics) plays a role in understanding physics. As students of physics and professionals in the field what do you think of his book and what other good books would you recommend to me as someone who aspires to one day take part in research related to physics / math just to have more enrichment in understanding?

Since I've been having an interest in mathematical / theoretical physics what are some books that I can read to introduce myself to how physicists and mathematicians do their work? You can set aside Roger Penrose's Road to Reality, I've already read a few pages of it, and I just want to know what else I can read for me to have a better idea.

This has been of a concern for me some time. I would really want to know how to deal with the feeling of "being overloaded by information" and how I can efficiently absorb what I need or want to read. To professional academics what advice would you give to someone who would wish to combat this kind of issue related to reading?

As someone who not only is considering going to mathematics but physics for further studies what is the distinction between mathematical and theoretical physics. They sound like something that looks so similar, as they involve making use of mathematics for making theories in physics. As experience physicists / mathematicians can someone clarify to me what is the difference between the two?

Aside from aspiring to get a PhD in mathematics, I too would want to get into theoretical physics. Although I'm more of a math person I currently lack the humility to try to explore physics, particularly theoretical physics as I tend to get discouraged because of past failures and mistakes at school. How is it that you guys dealt with doubt and uncertainty as theoretical physicists? I wouldn't want to just hold on to mathematics, I also want to explore theoretical physics and yet I'm held back by my own failures and setbacks. All I see are just "geniuses" and "prodigies" who got into theoretical physics. I just want to make myself enlightened to how you guys went on to becoming who you are and what mindset I should instill on myself as someone who dreams of one day excelling at math and theoretical physics. Thanks!

I've heard of the craze in AI and mathematics, especially how it can affect the way mathematicians do things. And as a person who aspires to one day earn a PhD in mathematics and work on research, what can I do best as of now to make sure that this is really for me? I sometimes am hesitant as I've heard from many, I know that I wouldn't be able to excel that much in academe, especially now that AI is dominating the industry and it has been able to do math research (I've seen Tim Gowers' post on it). From my perspective, it's very political, and I wouldn't want to be in that mess and end up feeling as if I've wasted my time doing mathematics.

The person talking here by the way is an upcoming freshman who is already considering a PhD as early as now. I've already been considering getting one as I had good teachers and have been exploring higher mathematics and realized that maybe this is the right path for me. I really loved the richness in concepts and how it can be applied to other fields of studies, but the thing is the AI trend is also making me rethink if I should just end up going for corporate.

What are your thoughts on the situation, and what do you think is best for young people like me who would want to do math research in an age where because of AI it can be a challenge?

The quote above is a reddit comment I've received months ago when I was asking about how I should tackle mathematics, particularly how I can maintain that "fun" in learning. So why is it that a lot of math, really, has nothing to do with numbers? It sometimes confuses me because I remember when Gauss said that number theory is the queen of mathematics. Can anyone clarify this to me? I just want to get a better idea on how I can view math before I start the semester. I'm an upcoming freshman in a top university in my country and would love to gain some insights about what outlook I should get in learning about mathematics as early as now to have a better idea. I've also been exploring some higher mathematics such as topology and complex analysis as well as have been solving some Olympiads with some freshies I've met online, but I still want to get some tips / advice from professionals.

I've been having an interest in learning higher mathematics. Do you guys know any free online e books that I can read in my free time to enrich my understanding at Linear Algebra, Topology, and Complex Analysis? It's something that I won't really take seriously, just for me to enlighten myself to what other branches of mathematics.

Thank you!

I've been intrigued by how people solve IMO problems and the success that follows from their math journey afterwards. To all of you who have participated / received medals in the competition what got you into math? I would really love to hear from people like you as a math enthusiast and aspiring math competitor in college and as well as your advice to people like me who would love to excel and stay passionate in the subject. Thanks!

I've been having an interest in mathematics out of necessity (for college) and passion at the same time. So I've also been wondering, to those of you professional mathematicians who have been in the field for some time, what got you guys into math? Being that most of the time math gets frustrating and boring just to understand a concept, what keeps you guys motivated and what else can you say about your journey so far and the lessons you've learned?

I've been having an interest in math research particularly how mathematicians solve difficult problems as well as their contributions to various fields to expand our understanding on modern mathematics. And so, this made me consider that maybe this kind of career is suitable for me as mathematics I believe has been my most proficient subject so far throughout my high school life. To those experienced people out there how long would it take to become one and what would be some challenges and advice that you would give to young people like me who shows interest in this kind of undertaking?