Does this kind of advice apply to all research or specifically mathematics?
[deleted]
How to be successful as a research mathematician? Follow your gut
31–40 of 69 posts
Re: How to be successful as a research mathematician? Follow your gut
#32That's not very actionable advice. I've found this article [0] from Terence Tao very insightful: [A]ctual solutions to a major problem tend to be arrived at by a process more like the following (often involving several mathematicians over a period of years or decades, with many of the intermediate steps described here being significant publishable papers in their own right): 1. Isolate a toy model case x of major pro…
That's about how to solve problems, but to do research you need to find good problems, and that turns out to be more important, imo. How do you pick "major problem X" anyway? This strategy from Tao just leads to incremental results...
Re: How to be successful as a research mathematician? Follow your gut
#33That's not very actionable advice. I've found this article [0] from Terence Tao very insightful: [A]ctual solutions to a major problem tend to be arrived at by a process more like the following (often involving several mathematicians over a period of years or decades, with many of the intermediate steps described here being significant publishable papers in their own right): 1. Isolate a toy model case x of major pro…
This is a great way to go about implementing features that deal with complex situations in NP-Complete problems, where you know a subset is trivially solvable, you build patterns / approaches for said problem, and for the remaining cases, just use approximate solutions.
Re: How to be successful as a research mathematician? Follow your gut
#34That's not very actionable advice. I've found this article [0] from Terence Tao very insightful: [A]ctual solutions to a major problem tend to be arrived at by a process more like the following (often involving several mathematicians over a period of years or decades, with many of the intermediate steps described here being significant publishable papers in their own right): 1. Isolate a toy model case x of major pro…
That's about how to solve problems, but to do research you need to find good problems, and that turns out to be more important, imo. How do you pick "major problem X" anyway? This strategy from Tao just leads to incremental results...
1. If Tao (a Fields medalist) is telling you a process to follow, a dismissal of "just leads to incremental results" requires more evidence than just a bald claim. IMO, he's giving away his working process for free.
2. If "all" you want is tenure at a research 1 institution in the us, there's a lot to be said for this process. Another ingredient is "pick an area where other people will be interested in the results."
PS I don't know what to make of your username, but perhaps you have more to say about picking a problem... in which case I'm sure many of us would love to hear it.
Re: How to be successful as a research mathematician? Follow your gut
#35That's not very actionable advice. I've found this article [0] from Terence Tao very insightful: [A]ctual solutions to a major problem tend to be arrived at by a process more like the following (often involving several mathematicians over a period of years or decades, with many of the intermediate steps described here being significant publishable papers in their own right): 1. Isolate a toy model case x of major pro…
Overheard at the watercooler: The only way a CS guy knows how to prove an algorithm works/does not work is to find counterexamples.
My real analysis instructor drily pointed out “You really like proof by contradiction huh” and my defense was that my main life skill is spotting why plausible-seeming things don’t work correctly
Re: How to be successful as a research mathematician? Follow your gut
#36That's not very actionable advice. I've found this article [0] from Terence Tao very insightful: [A]ctual solutions to a major problem tend to be arrived at by a process more like the following (often involving several mathematicians over a period of years or decades, with many of the intermediate steps described here being significant publishable papers in their own right): 1. Isolate a toy model case x of major pro…
Tao’s advice is characteristically excellent but I think Eugenia Cheng’s advice (not just the article title but as a whole) is actionable, just not so much for someone who is ready for specific advice like Tao’s. Her message seems to be targeted towards those who are just getting started and who may not otherwise have been interested in studying math.
Re: How to be successful as a research mathematician? Follow your gut
#37I appreciated Eugenia Cheng's youtube lectures on category theory and I know interviews aren't the best format for sustained exposition, but the remark about mathematical rigor being a European colonialist thing seemed pretty forced. If anything, it underestimates the strangeness of the history of math in an effort to cram it into a simple frame: "Europeans bad".
There was something distinctive about work in foundations of math in the late 19th / early 20th centuries, work which came out of European cultures (or more accurately Latin Christendom). Plausibly, this work was centuries in the making, the culmination of a trend towards increasingly analytic and systematizing modes of thought that begins with the recovery of Greek philosophy in the middle ages.
But, ok, even if you don't buy that, how do you get from the Congo Free State to Frege, Hilbert and Goedel? It's a radical claim that would be utterly fascinating if it were true. But Chang just kind of tosses it off at the end and asks us to accept it as an unremarkable truism.
Re: How to be successful as a research mathematician? Follow your gut
#38Being a successful research mathematician, although I am not one, sounds nowadays like more about figuring out the market for your skills among multitudes of opaque research projects so I imagine following your gut you might just get into a good post if you're lucky.
We are truly in a time where there are plenty of (bad, unsubstantial) ideas out there, i reckon it takes a good instinct to be a good mathematician (or any other thing that does not rely on public opinion).
Re: How to be successful as a research mathematician? Follow your gut
#39Earlier quoted context omitted.
Polya‘s „How to solve it“ might also be worth a look. Summary: https://www.math.utah.edu/~alfeld/math/polya.html
I loved this book and respect the author but to be honest, for anyone that doesn't already know, it is geared towards highschool level mathematics. Still a great book though.
I read this book while I was studying mathematics as an undergraduate. I found the information in it to be very helpful. The math is lower level, but the problem solving techniques that the author presents generalize very nicely to upper level mathematics. I’m not sure that I’d say that it’s geared toward high school students. I think that it’s geared toward beginner math students.
Re: How to be successful as a research mathematician? Follow your gut
#40About as useful as Feynman's algorithm for solving problems: 1. Write down the problem. 2. Think very hard. 3. Write down the solution.
somewhere between steps 1-3: be as smart as him