Hi Tilo,
   At this point, I can't give much specific advice because I don't know 
enough about what you want. From your message, it seems like you are 
thinking of pursuing a career as a research mathematician by attending a 
grad school in math. Even within that, it depends on what area of math you 
are interested in (e.g., numerical analysis and topology would weight your 
programming experience/ability differently). It is hard to make general 
statements about grad school admissions, although anecdotally many in the 
US will place a large emphasis on test scores (e.g., GRE; if applicable), 
if there is someone you can work with there, and your letters of rec.

For SageMath, a GSoC project can involve doing research mathematics, which 
can include using the code written, advancements in order to write code to 
do computations, or to improve the speed of computations. A part of that is 
doing the reading to learn the corresponding subject area. You can see this 
in some of the projects (e.g., improving the combinatorial species 
project), but you are also free to propose your own. That being said, this 
is a coding-based program, so producing code will need to be a key 
component. Yet, depending on the project, it can result in a mathematical 
publication (which I can mentor such a project, not all of which are listed 
on the ideas page as they are a bit more math researchy).

For doing an REU, you are going to be working on a research question, which 
will also include building up your background knowledge. However, there is 
no guarantee of success or any tangible outputs, the rate depends largely 
on the subject area. Additionally, nearly all fields in math take over a 
year (oftentimes more) to publish a paper after submission, so you likely 
won't get that, but having a preprint on the arXiv will likely give you a 
major boost over other applicants. This is typically the output of doing an 
REU.

In short, I would need more information about what you want and what 
interest you. However, for both of these things, there is no guarantee you 
will be accepted, so you might consider applying for both. You can always 
withdraw/decline should the situation change. I am also happy to talk to 
you over Zoom and/or via direct email if you have any other questions.

Best,
Travis Scrimshaw

PS - Hope you are able to stay dry.

On Saturday, February 24, 2024 at 11:00:33 PM UTC+9 tilor...@gmail.com 
wrote:

> Hi SageMath community,
>
> I'm a junior at Pomona College (located in Claremont, California) and 
> participated 
> in GSoC with SymPy last year 
> <https://github.com/sympy/sympy/wiki/GSoC-2023-Report-Tilo-Reneau%E2%80%90Cardoso:-Improving-Relational-Assumptions-in-SymPy%E2%80%99s-New-Assumptions>.
>  
> I'm very interested in doing GSoC again, but one concern I have is that it 
> might not look that good when I apply to grad school (probably for computer 
> science but maybe for math or some related field). I haven't done any 
> research, so it seems like it might be a better use of my summer to 
> participate in an REU/undergraduate research opportunity. 
>
> I would love to hear your thoughts on the value of participating in GSoC 
> from an academic and professional standpoint, especially compared to 
> traditional research experiences. GSoC projects, particularly with SageMath 
> or SymPy, resonate with my interests more than most REUs I'm applying to. 
> However, I'm seeking advice on how such choices are perceived by graduate 
> admissions and how they might influence my career in the long run.
>
> Thank you in advance for your time and advice.
>
> Sincerely,
>
> Tilo Reneau-Cardoso
>

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