I'm hoping I could do with some advice. It's not that long, but I've broken it into bullet points to be as concise as possible, which may make it seem pretty lengthy:
Background:
-Maths BSc student in my penultimate year. My course is equivalent to the Masters in Arts in Mathematics at my university.
-Grades aren't bad, but they're not great. I've a Second Class Honours Grade One (for people in America, that'd be between a 3.08 and a 3.68 GPA, and a First Class Honours Grade One would be over a 3.69). I have the second best GPA in my course in my year (of 18).
-I'm interested in a PhD in Maths but not certain.
Situation:
-I've been offered a Summer Maths Research project. It's one of the only research projects in the country in Maths, and has less than five positions, open to applicants from any university. It's for half the summer and not particularly well-paid. It's in a topic (Abstract Algebra) I'm quite interested in and the supervisor I've had before but don't know particularly well.
-I've interviewed for, and may be offered, an analytics position in a technology and consulting company. It's fully-paid and is for the entire summer. The position requires coding and statistical experience, both of which I have, but I do not have a huge amount of coding experience in projects. It would, I believe, be focusing particularly on machine learning which I think would be very cool. The company is an extremely large business, and could be good for getting into larger firms (particularly one of the Big Four) in the future.
My list of positives for each:
Summer Maths Research Project:
Positives and Negatives:
+I've an interest in a PhD, and this would be very good to have. It might mitigate my okay grades.
+It's paid, even if not particularly well.
+It's one of the only (if not the only) undergraduate research projects in the entire country.
+I could get an academic reference if it goes very well (uncertain).
+I'd learn a lot.
+I'm interested in the topic.
+It's at a very convenient location extremely near my house.
+It'd look good on my CV.
+I'm guaranteed this position.
+It'd be something I could take home with me and focus on for hours, which is something I would enjoy.
-I'm not very familiar with the supervisor.
-If I was to do this, and eventually do a PhD, I'd earn considerably less money in ten years time than in industry.
-There's much less job security if I were to do this and go on to academia.
-There'd be a lot of pressure to get results in the period we have.
-I don't know if I'd get funding for a PhD with my grades.
Company
Positives/Negatives
+It's paid well, better than the Maths internship but not as much as a job I've previously had over summer.
+Excellent on my CV (in conjunction with what experience I already have).
+Most interns get offered a job for after they complete their degree, providing security that I'd have my job once I finish my BSc (was planning to do a Masters)
+If I was to do this, it'd be much easier to leverage my way into a well-paying job in one of The Big Four and make considerably more money in ten years time than if I was in academia.
+Much higher job security taking this as it'd be easier to get into positions which this on my CV.
+Much more pressure, I've heard it's an intense internship program.
+I'd learn a lot, particularly relating to coding which I enjoy, but have not done very expansive projects.
+I'm interested in Machine Learning.
+If I do well and stick with the position after college, I may be able to leverage myself into a company willing to pay for a Masters.
+Much better for networking, it works with a lot of companies in the Fortune 500.
+Probably better if I wanted to work in Google or Facebook.
-I'd need to do a lot of preparation to bring my coding up to scratch.
-I've done a lot of statistics, but I don't necessarily enjoy it.
-The more corporate culture is not necessarily what I'd prefer to academia I think.
-It's a much further commute.
-I'd need to travel much more which is not something I'd necessarily enjoy (and I don't have a car).
-Would be unlikely to ever get the opportunity to complete further study in mathematics if I did this and went into industry.
-Not necessarily something I'd enjoy (neither is the Maths Project, to be fair, but I'm more uncertain as to how well I'd like it).
-It'd be more expensive (wearing suits would be expected and I'd need to buy some, cost of travel would go from 0 to 40 euro a week minimum, cost of lunch, social events with colleagues which are expected, travelling to other locations, etc.)
-Longer hours actually in work and taking much longer to get to work and from work.
-Not even guaranteed to be offered this, it's still up in the air.
Question:
Which would people recommend if I was offered the latter too? I'm going to speak to one of the university professors I really like if I hear back from the company (as I don't know yet if I'll even be offered both) asking for advice, but I'd like to hear from as many people as possible pre-emptively, so I know roughly what to do as soon as I am either offered (or declined from) the company's internship.
At the moment, one sets me up somewhat for a PhD and academia, while the other sets me up much better to go into industry, and I don't know what I really want to do.
EDIT: I accepted the maths one