Biography on MacTutor: https://mathshistory.st-andrews.ac.uk/Biographies/Choquet-Bruhat/
Wikipedia: https://en.wikipedia.org/wiki/Yvonne_Choquet-Bruhat

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Hello, I've completed 2 years as a compsci major and will be starting my math major next semester. After some wandering about I feel fairly confident that I want to go down the pure math researcher / professor route (or at least try to). I heard research is pretty important for phd applications. In my country (Argentina) the best school combines the undergrad with a "masters" so its 6 years, which i feel like is enough time to get something going (the title is still bachelors though lol). So, how would I go about getting into research? I have some basic background from my cs studies, though I understand I might need a bit more to contribute. Just to get an idea, what would be steps I need to take to get started? Thanks

Currently reading a chapter on my topology textbook that concerns metric space geometry, in the section of the fixed point theorem, the author goes into Fredholm Integral equations and how the fixed point theorem relates to them. Considering this was my first time seeing anything under this name, I decided to search up some more on it, to which wikipedia told me that David Hilbert developed the abstraction of Hilbert Spaces in association with Fredholm's integral. Most of the information on the web is pretty specialized, since I am only an undergrad, I decided to ask here: What exactly is Fredholm Theory and why is the Fredholm Integral equation so important?

The 1920's translation is weirdly racist.

What are some fundamental mathematical formulas, theorems, and concepts that are particularly useful, especially those that can be backtracked or reversed (e.g., differentiation and integration)? I'm looking for a broad list across different areas of math.

I know this sounds little rubbish or waste of time, but these suggestions hold importance for me. All I can fill you with is, it's related to work and might be very impactful for my future.

So no matter how basic or childish or advanced theory/fundamentals/concept etc you got. Drop them in. I will try to absorb and use it. Thanks for the guidance and help.

Irrelevant information: [ university student in IT majors]

I'm an undergrad majoring in math, and I love learning math, but I feel like it's a very general interest in most of the topics I learn. How or when do people realize what field(s) they have the most interest in, or what they want to do?

What do you guys think? Have textbooks stood the test of time or are resources such as Khan Academy and Brilliant taking over?

Lets say you are studying an intoductory graduate level subject from a book. How in depth should you know the proofs? Most of the times it is not that hard to pick up the idea and, when needed, being able to reconstruct the proof from that. But in some cases, when the proof is quite long and technical it seems quite hard and time consuming to do that. This is why i asked myself that question.

Judging from what i saw during lectures it is quite often the case that even the lecturer has to chek their notes and it can happen that they get stuck (of course i am talking about the hardest proofs of the course). It seems to me that if someone were to ask them to recite the proof of some theorem not on the syllabus of their class it would be hard for them to do, assuming they already studied the proof. Just to make things more concrete: lets say someone is an algebraic geometer and is lecturing in an introductory course on algebraic topology (homotopy, fundamental group and covering spaces). Would they know the statement and proof of the excision theorem?

This is for things you can't easily practice, so things like definitions, properties etc.. same as in title. Let's say I've done the studying part, and I understand most of it. How do I make it stick?

I used to use anki for exams, but it doesn't feel right for maths. Making cards is tedious work, and with long proofs it also feels ineffective, and against what anki is usually about.

I think it can still work for definitions and the like, but I'm really not sure about proofs. It's just so much interconnected information to recall all at once. How do you recommend studying them effectively? Again, this is assuming I already understand everything, I just need a way to make sure I remember

Was interested about any examples of specific questions in mathematics, answered in the manner ,,a guy decides to solve it in his twenties, it takes him 40 years’’

I don’t just mean mathematicians working on a single topic throughout their whole life - but projects where the end goal was specifically stated at the beginning, and spending half of lifespan was expected by a person

How do people even get that kind of resolve?

It occured to me that there could be numbers with long decimal expansions which look transcendental but terminate eventually. I thought it would be interesting to explore this further and to try understand why or why not such numbers exist or are otherwise uncommon.

Hi everyone, if you are in the quant finance/ data science field and working. How long does it take you to learn a new subject by yourself?

I saw many posts on how someone should read some high level mathematics book to learn a new subject before the interview. I have a few questions as I am going through my first transition between the firms, and I would appreciate if you could share your experience (assuming high level of difficulty for all subjects):

1. How long does it take on average for you to learn a new subject (weeks/months)?
2. How do you self-study it?
3. Do you use any strategies to learn a new material while being employed?

Appreciate any input as I am trying to get back on self-learning. Thank you all!

I’m an undergraduate physics student interested in pursuing graduate school for mathematics and specializing in quantum information theory.

I was looking into the math aspects of QIT and wanted to prepare for grad school with taking relevant grad courses. Right now my plan is graduate coursework in Analysis (Measure theory), Functional analysis, Lie Algebras, Hilbert Spaces, and graduate quantum physics classes.

I’ve looked into operator QEC and other fields, what else should I focus on, and are there common resources for quantum info/QEC from a mathematical perspective?

Can someone please provide name of the competition or Olympiads for undergraduate engineering students in India?

It is 4 am i’m high and bored so let’s keep this short.

I’m an undergrad blah blah trying to carve my niche in mathematics. I received a lot of textbooks for christmas and it’s made me realize i really fly through algebra compared to analysis or anything else really. I’m studying Algebra Chapter 0 to prepare for a grad course on commutative algebra and the difference in difficulty between algebra and analysis for me is really not even close.

Real analysis courses were like actual hell from the actual bible for me but my modern algebra courses felt like water and I’ve been able to work through Aluffi’s book much faster than anything in another field so far.

So my question is: does the field you research in correspond much with what you’re good at.. Or is it purely interest based and what you can find a good advisor for.

I have 1.5 years before grad school so yeah i don’t even know that i’m going to go to graduate school yet but i really love algebra. Theorems like the fundamental theorem of ideals over number fields feel obvious well motivated and their lemmata seem logical to me. On the other hand I genuinely cannot comprehend some of the theorems in basic real analysis without a whole mining-truck full of effort and blood sweat tears. Naturally this means I find algebra more deep.. But should I??

Is this a common experience; Should it matter at all? Why do we choose to study a field with so many god damn introspections and pains? Is it for those 2 reasons that math is so gorgeous?????

Thanks, Undergrad under duress

Any recommendations for books on dynamical systems, perhaps with a section or perspective toward stochastic dynamics?

Edit: also aimed at mathematicians, and not engineers/scientists?

My building has 5 floors, each with two apartments (9 neighbors plus mine). There’s also an R button (for Rez-de-chaussée/ground floor).

My best assumption is that the ground floor is the most likely location for the cabin, since everyone uses it to reach the street. But what about the others ?

I am in the 6th grade and am interested in complex mathematical fields such as differential geometry and linear algebra (mostly the latter). Now that I have dived down this math rabbit hole, I am beginning to see some DECEPTIVELY simple titles for math fields. Here are some examples: Linear algebra (I thought this was just y=mx+c, and I was sorely mistaken), Analysis (the vaguest name I have ever seen for something that is so abstruse), Number theory (way more complex than I thought), and algebra means something completely different to me now (Lie, for example). Feel free to list other names, and please explain why they are so deceivingly easy.

I prefer physical textbooks to digital ones, and I can find older editions for very cheap.

The textbook I'm looking at is "Linear Algebra and its Applications" by David C Lay. For some reason the most recent two editions are both expensive, so I'd have to go with the third newest edition, published in 2011. Is there anything wrong with a book that old?

I'm not worried about the homework questions being different, I have other methods for getting those. I just need to know if it will be good for studying purposes.

Von Neumann was an incredibly talented individual with significant contributions to mathematics, physics, computer science, and economics, just to name a few. However, due to the modern day specializations, most individuals rarely break out of there own fields. Occasionally you get people who work on two fields, but I don't know of anyone who has anywhere near his breadth in modern day