Tell you what. I’ll do my best to answer this question.

As someone neck deep in both philosophy of physics and mathematics and your standard epistemology and metaphysics, both continental and analytical thinkers, here’s what I think about this.

The difference between a mathematician and a physicist are likely two things. They may not be aware of these things on their own, but I believe they are true none the less.

• 1. Their metaphysics are different. Physicists tend to be actualists, where as mathematicians tend to be possibilists. This has to do with how one interprets equally formed sentences such as “it’s possible that aliens exist.” An actualist tends to base the truth of this statement as contingent on whether or not aliens actually do exist in the world. A possibilist, however, interprets such sentences differently. Rather than simply consider how things are in this world, they’ll also start considering hypothetical worlds different than ours in order to conceive of one where aliens could exist. But here’s the crucial difference. After doing that, they will further claim that in fact the statement ‘Aliens exist’ is true if and only if at least one suitable possible world exists. Because they possibly exist in some other world. Therefore, truths of statements for them depend only on the possibility of statements being true in at least one possible world. Hence the phrase possibilist. You can read more about the Three Types of Possibilism.

Here’s the connection to mathematics. When a mathematician claims that there is an uncountably infinite number of points between the path of a fly as it travels through the air — often an ‘applied’ question in an intro calculus class, they don’t actually mean this was true in the actual world. They mean it’s true in one possible world, namely ‘the world of mathematics’ which doesn’t depend on the way the world actually is at all, really. That’s how mathematicians think in the majority of cases.

Most physicists balk at these types of arguments because science is an empirical study, not a hypothetical one. Science concerns itself with what is actually true of reality, here and now. There are a wide spectrum of complex and nuanced atypical actualist positions, such as those adopted by Edward Zalta, Penelope Maddy, and Willard Quine for which you can read Actualism (Stanford Encyclopedia of Philosophy). But the typical actualist is someone like Arthur Prior. You can read about him there as well.

• 2. Their epistemology is different. Mathematicians tend to believe that proof = knowledge. This builds on the possibilist metaphysic operating in the background. The word people often ascribe to possibilist’s notion of ‘knowledge’ is called rationalism. Often contrasted with empiricism or nominalism. Though there are subtle nuances here as well, like with naturalism — which lands in one of the intermediary actualist positions above. There’s also people like Godel, one of the odd in between possibilists. He argues there are truths which cannot be proven inside a logical system; and then proves his argument to be true for arithmetic. He stops there, but his point was made.

So, mathematicians tend to trust proof in hypothetical situations above any sort of empirical evidence. Usually, empirical evidence is irrelevant to mathematics which is why mathematicians are completely unfazed by the strict actualist argument put forth by a group of odd-ball actualist mathematicians called ‘ultra-finitists.’ These people argue the set of natural numbers do not exist, because there’s a certain largest number of physical things in the actual universe, and postulating any sort of hypothetical entity beyond that number, or less than the smallest number of things in the universe, is silly. Their epistemology does not reflect that of the field. And they are ostracized from the community quite harshly. Normand Wildberger is the textbook example of this.

For physics, just because something is proven in a theory it has nothing to do with whether we have knowledge of something’s truth in the actual world. This is the whole point of the notion empirical confirmation via experiment. For Physics, then, experimental confirmation = knowledge, not theoretical proof. Rather, they say a theory predicts things contingent on whether or not they can be empirically confirmed via experiment. Not until then do physicists claim to have knowledge. This is the difference between actualism and possibilism.

Ultimately, I see the ‘end-game’ of strict actualism to be the embodiment of Derrida’s Decontructionism. If you want to learn more about this, you can read about it here: Jacques Derrida (Stanford Encyclopedia of Philosophy). For a couple more slants, click here and here. For instance, I think Derrida’s intuition that ‘essences’ are found inside of, or within, appearances is exactly right. And so it follows that any insistence that essences precede appearances is circular. That’s the crux for which I nail Platonism to obvlion. Especially given that all semantic mathematical intuition is inherently visual.

The point is, where do your natural intuitions fall on the spectrum? This should be your deciding factor, because it will be the difference of whether or not you will be dancing in harmony with your professors, colleagues and advisors for the rest of your career, or whether or not you will be constantly butting heads, rustling feathers and creating discomfort, feelings of being stupid and wrong all the time. Leading to few friendships and to becoming the hated one in the community.

(The other point is, never ask a mathematician about facts about the actual world. They’ll get confused. :P).

Choose wisely.

I was pretty much in exactly this situation when I was finishing college. I was a physics/math double major, I knew that I wanted to go to grad school, but I couldn't decide whether to get a degree in physics (I probably would have gone into particle physics) or to go for the math PhD.

This problem more or less resolved itself when I asked to meet with my two favorite physics professors to discuss grad school options. The meeting went something like this:

Professor #1: So, tell me, when you are doing physics, are you more interested in how it describes the real world, or are you more interested in the mathematics that it involves.

Me: Hmmm... well, probably I'm more excited about the math.

Professor #2: Okay, then I guess we are done here.

Needless to say, I was very dissatisfied by this answer. But, I've come to understand that it was really the only thing they could have possibly said.

At the time, I was telling myself that I would try to go into a field that was a little more "practical," which was probably the biggest reason why I was considering physics over mathematics. But, really, I was just kidding myself, because there's no difference between the salaries of a theoretical mathematician and a theoretical physicist, which was certainly where I was heading.

So, basically, if getting a decently-paying job out of college is a top priority, leave theory behind, pick up some applied math skills and some programming skills, get a job in industry, and live happily ever after.

If not, then do whatever seems to be the most enjoyable. To quote Professor #1 (I think it was him), "If you really love what you are working on before grad school, there is a chance that you will still like it after grad school." Do what you love, and don't worry too much. It might be a bit of a pain, but you can always switch disciplines. Plenty of people have gone from math to physics, from physics to math, and all other possible permutations. You'll be fine.

You are in the same boat as most of the people that ultimately end up as physicists (if not almost all). Math is just not a naturally intuitive thing for the human brain and most of us (even the ones that ended up being good at math) had to work at it. Depending on your level, you may not even be studying “math” the way it is used in physics.

The question to ask yourself, however, is whether you feel that way because your interest isn’t strong enough to impel you to work on it. If so, then I agree that physics may not be for you. If you do work at it, and are just concerned with how much effort it takes, then have no fear - you are just a human being.

In short, do it if you really want to.

A physicist runs 100 trials of an experiment, sees the same result 100 times, and concludes that the same result will always occur.

A mathematician runs 100 trials of an experiment, sees the same result 100 times, devises a theorem, and proves it to be true for all cases, just in case that 101st trial would have had a different outcome. Or, even better, the mathematician proves the theorem to be false for certain cases… they just haven't been observed yet.

Physicists conclude.

Mathematicians prove.

If it drives you nuts not knowing whether a conclusion is 100% always true in all possible cases forever, mathematics is the place for you.

Either way, you finish your experiment just in time to get back to grading exams.

I don’t know what you mean by physical engineering. There are lots of kinds of engineering. Here:

(from xkcd.com)

Engineers are usually hanging out with the physicists in the above “figure”, though as a chemical and biomedical engineer, I meld it all. My math skills aren’t to be scoffed at either. It depends on what you want to DO. Do you want to make something, or discover something? Do you want to be a teacher and fight for funding, or work for a company and prioritize the bottom line? It’s a good question, but one that will mean nothing without a good education.

Don’t think of it as a choice between subjects. Continue learning about everything you love no matter what degree you pursue. For example, you could study quantum computation or Markov chain analysis of models from statistical mechanics in any of the three degree programs. If the problem isn’t how you’ll define yourself as a researcher, but merely what degree program to pursue, think about it the same way you will when choosing which department to go to. Which department has the people you want to work with? Which department has the best quality of life for its students? Which department has the most success at placing its students in good positions after graduate school?

Pure math or theoretical physics.

These are both “genius” level fields, where normal students tend to struggle.

Between the two, pure math is probably more difficult, simply due to the broad nature of mathematical structures.

Physicists care about specific cases which tends to make things a little nicer, whereas mathematicians tend to care about generalized reasoning (which can be immensely complicated).

A good quote from famous Physicist Dick Feynman sums it up well:

“If you say "I have a three-dimensional space" [...] and you ask mathematicians about theorems then they say "now look, if you had a space of n dimensions" then here are the theorems". "Yeah, well I only want the case of three dimensions..." "Well, then substitute n = 3!". It turns out that very many of the complicated theorems they have are much simpler because they happen to be special cases. The physicist is always interested in the special case. He's never interested in the general case. He's talking about SOMETHING.”

It doesn’t matter. Really: it does not matter.

My undergraduate degrees were electrical engineering, CS, applied math, and art. Things kind of centered around and supported CS, but when I got to the phase of doing research — original research — It was a wide frontier.

One of the most useful things about a PhD program is not the terminal knowledge that you receive from having done the research, it is the fact that you actually *learn how to do research*. And in nearly all cases of which I’m aware, your undergraduate education is only a framework upon which you can pin various things that you encounter in your journey.

As you step into a new area, and discover that you are missing key knowledge that would advance your cause, well you don’t sit around bemoaning the fact that you don’t have the knowledge… you fucking go get it. You take a seminar. You can get a tutorial session with an expert. You read the book and do the problem sets…

So as far as your degree path as an undergraduate goes… The thing that you can do that is most valuable for your future self is take courses where you have to learn completely alien stuff that really challenges you. The risk of that is OMG your GPA might suffer… The reality is that in a short time following, you will blow past of those in your grad school cohort who had perfect GPAs but never learned how to really learn stuff they didn’t know.

Good luck!

Order the following questions by what interests you the most.

1. Your website slowed to a crawl when the traffic went from thousands of hits to tens of thousands. Is it just your bandwidth, or is there some glitch in your server script algorithms, or is there perhaps some unrelated system error?
2. If you start at (0,0) and randomly choose to move north, south, east, or west, then how far away from (0,0) would I expect to be after n such random moves, as a function of n?
3. Why does your worst case O(n^2) sorting algorithm outperform my O(n log n) on some particular data?
4. Is the set of all computer programs a countable set?
5. What are the chances in Texas Hold-Em that you will make a flush if you have two hearts in your hand, and the 3-card flop also has two hearts?
6. Prove for integers a, b, and c, that the quantity a^(b/c) is either irrational or an integer.
7. Is there an algorithm to solve any system of linear equations?
8. Prove that in a graph with 6 nodes, there are either three mutual friends or three mutual strangers.
9. What is the best way to sell furniture on the web?
10. How can I send information securely over a wide open communication channel?

Depending on the order, I can advise you on math, cs, or both.

There’s really no “run of the mill” developer job. But most software developers don’t use a great deal of math in their day-to-day work.

I have a BS in Software Engineering. I graduated Magna Cum Laude. I was required to take Calculus 1 and 2. That’s some hard stuff. That was almost 30 years ago.

I haven’t used any of it since.

This is Veronica. Veronica is a software engineer. Veronica sucks at math, but she’s an awesome engineer. She’s so good, she can play Skyrim while working and her employers don’t even care (image credit)

How much math does a software engineer need then? It depends on the roles they fill. Someone writing a 3D renderer is going to need linear algebra and some other mathy goodness. A developer just hooking up a line-of-business application won’t.

In general, more math is better, but a great deal of software development is more focused on logic and design patterns than “math”.

If there’s a bug that needs to be fixed or a feature to be added, chances are I may use some math to solve it, but chances are even better that it’s arithmetic that I learned in sixth grade, not calculus or trigonometry. And any design patterns I use probably aren’t closely related to math at all, with the exception of their Big O (but those are more closely linked to algorithms, not design patterns).

But if I was building the next great 3D renderer, ya I’d need math. As I said, lots of linear algebra and other stuff. A physics simulator? Ya, I’ll need some hefty math! A video game like Among Us? Hardly any math at all.

So it really depends on the type of software engineering role you want to fill. Some require lots of math. Some require little. If you don’t love math, you can still be a good software engineer.

Why do CS degrees require so much math then?

Three reasons:

One

Ignorance. People from the outside see software engineering as something they don’t understand; a very nerdy thing. Nerdy people are good at math. So, software engineering must require a lot of math.

Two

Back in the days of assembly, software engineering was very math-heavy. You were doing math with every operation you carried out. Nearly every line of assembly involved some math. So you needed a lot of math to do the work.

While those days haven’t completely disappeared, most software engineers won’t work in assembly. Even though I was a game programmer, I never used assembly. The transition from assembly to C and C++ happened in the early 1990s and it hasn’t gone back. I doubt it will: today’s compilers are better at optimizing code than squishy human brains.

Three

Exposure. The thinking goes, the more you’re exposed to, the more solutions you see. So they make you take these heavy-math classes to see if you like them. If so, maybe you’ll take a more math-oriented programming role afterwards.

So, you won’t necessarily need a lot of math if you study Computer Science (or Software Engineering). The math classes are just a relic of old thinking and unfamiliarity. Right now, they’re just a necessary hurdle. So take them, pass them, but don’t worry if you hate them. There’s a more than an even chance you can find a software engineering role that doesn’t require tons of math.

I would imagine physics would be top of the list.

People in business know that physics training requires data analysis, computers, and applied math.

It’s the whole package.

I know lots of them in industry and engineering, medicinal tech and gene research, simulators for aerospace and nuclear power plants, of course robotics and AI.

More than one ended up in brokerage houses crunching numbers. One was leading fiber optics research at Bell. One is doing weather forecasting, winds and explosive storm prediction. One watches lightening. More than one is doing music and performance art.

You name it, a physics guy can learn it, do it, and experiment with it.

Me, I’m more of a math guy, I just teach these physics yahoos.

Yes. Math. It’s a field all on its own.

How much math you need in physics or computer science depends strongly on your specialization. For example, I was an experimentalist in solid-state physics. I needed calculus and differential equations at times, but my math skills didn’t have to be nearly as sophisticated as a theorist in elementary particle physics. I made a career shift to software engineering where the required math skills were not nearly as intense, but I still needed to be able to do the basics like algebra and geometry. That’s not to say programmers don’t ever need mad math skills. They often do. It all depends on what you want to do.

If you are doing it to prove you are smart or to prove to someone (your parents, friends, or yourself) that you can do it, then it is a big mistake. If you think you might be the best person you know in the field, then it is for you. (But only marginally). You may be the best person that you know in your entire state in your age group, but that doesn’t mean you are good enough. Physics and math are absolutes, not relative. There is little intellectual or market value for second or third tier physicists. This means if you discover that you are not top tier, you are best off to get out ASAP and get into software or a startup. You may hear stories from some physicist who claims they used their physics background to help them in their software job etc but it’s more likely them self-justifying their life choices. It’s more likely they would have been better off had they studied a field more directly related to what they are now doing.

All of these majors require excellent math skills. If you want to succeed at any of these majors, be sure your math skills are up to the challenge - and expect to be challenged by the math required in any of these majors, no matter how good you are at high school math.

If you don’t know very much about some or all of these majors (and the careers they can lead to), you might consider spending your first year in college as an EE major but be prepared to change majors as you learn more about the subjects. Also talk to junior and senior students (and grad students if you can find any) in each major to find out more about what they are like academically. Professors can also be helpful as they will know more about careers after graduation (but be respectful of their time, of course).

Why EE? Simply because its usually the most difficult schedule in terms of required classes, particularly with regard to prerequisites. So its harder to switch to EE than to any of the others.

Once you have more information, decide which major you want to complete based on your interest in the subject.

You’ll be spending 20 to 40 years of your working life (perhaps less if you go into management) working in that field. Don’t pick a field that you don’t enjoy working in just for the money.

A2A: “How do I choose between majoring in electrical engineering, computer science, math, and physics?”

Many people are not mathematically oriented or gifted. Further complicating the picture, excellent teaching of math appears to be the exception rather the rule (Apologies to former colleagues who were excellent instructors). Many students are turned off by math and anything to do with it. Many become actively math phobic. There are also growing tendencies in our society to regard math, the sciences, and high technology as something for “nerds.” eggheads, and a select few. This is greatly contributing to the small numbers of American Students majoring in the sciences and medicine. In other cutlures—India, China, etc., science and math are greatly valued. This partially answers why so many doctors are of foreign extraction. Too many students want something that is fun, easy, not requiring years of study, and that pays well. Many areas in science, economics, and IT pay very well—-but are not easy subjects, require some major time committed to their study, and are not always “fun.” Finally, not everyone is computer compatible. Some people simply do not have minds that work well with computers.

Do you like chocolate or strawberry ice cream? Because what you are asking is more like different flavors of the same for rather than different foods. There is an overlap between the two majors and both majors require graduate school. Your end game determines your choice.

Quora User gives his opinion; however, when you look at choosing one subject over another in a future job market, you will find both majors have limited entry level jobs. To be employable, you will need to have some computational aspect as was suggested earlier.

Choosing a major is not making a lifetime commitment but an immediate decision based on your current situations. The most important is which major leads to graduating in the quickest. Most students have enough electives to major in and minor (or double major) in the other, so my best advice at this point of your life is to choose the one you like the best.

If you do decide to major in mathematics, understand that it is a game that everyone looses at some point in time.

If you like math more that stats, choose CS+math.

If you like stats more than math, choose CS+stats.

The different majors will provide you with different knowledge and skills and experience, but there is no sense in which one is better than the other. Both options are good preparation for CS research—after all, it’s all the same core CS classes—just different types of CS research.

CS+math is slightly better preparation for research in theoretical CS, graphics, robotics, scientific computing, and some parts of machine learning.

CS+stats is slightly better preparation for research in data science, different parts of machine learning, and more experimental areas.

But these are not hard and fast rules. For example, majoring in stats+CS doesn’t mean you can’t do robotics research; it just means you may have to pick up more math through electives or self-study. Studying math doesn’t prevent you from learning statistics or vice versa.

But by far the most important preparation for CS research is CS research. If you’re a student at Illinois, sign up for the PURE program as a freshman. Join ACM and find people to work with on independent projects. Talk withou your instructors and TAs in office hours, not just about course materials, but about research opportunities—maybe as a paid researcher, maybe for independent study or senior thesis credit, maybe just to get a nice problem to chew on. Once you get through the core curriculum, take graduate-level and special-topics classes, especially classes that involve a significant semester project. No matter what you major in, opportunities for research aren’t going to fall in your lap; you have to hunt them down.

“How do I choose between majoring in electrical engineering, computer science, math, and physics?”

All of those fields are meritocratic and competitive, and require actual, rare talents. So the biggest question would be: do you have what it takes to succeed?

You can generally tell if you have talent for these fields: you find your courses easy and fun, and can’t understand why your classmates complain and struggle. (Not just, you work harder than them so you succeed more: rather, you don’t work nearly as hard as them and yet you succeed more.)

Assuming you could succeed in more than one, CS and EE have the best job prospects.

Math and Physics are fundamental, but don’t actually have a lot of job openings at the BS level. You would need to craft a winning resume: lots of experiential learning, a compelling story about how you can use your Math/Physics skills to solve problems and add value for your prospective employers. For example: double-major in Finance and become a Wall Street quant. That sort of thing.

Of course, there is always graduate school……

As Izzy Cahn mentioned, lots of us students are intellectually-driven, keen to learn, and frankly, all over the place. From what I’ve noticed, the students who succeed most in college and in the real world are those who pick a major and stick with it. Moreover, if you desire to get ahead in pretty much any of the above fields except for maybe computer science, you’d be advised to go onto graduate school upon getting your bachelor’s degree. You’ll sound smart but confusing to employers if you get all of the above degrees. I strongly recommend you pick one, or at most, two. They all involve math but are otherwise not one and the same fields of study.

You don't get hired because of your A Levels, at least not in the UK. No employer would look at your CV or resume and would guarantee you a job just because you did Maths at A Level. Thinking this way is pure delusion and entitlement.

You get hired because of what you can bring to the employer and what value you can add to the organisation. If all you can bring is a bunch of qualifications, you’d be rejected.

In the UK at least, you can go into 600+ different roles with A Levels in any subjects. Due to the impracticality, as well as the tone of the question, I won't entertain this part of the question.

What degrees you can go into with your A Levels though (at least in the UK):

• Maths and statistics
• Economics and MORSE (not because of Economics A Level though, more so the Maths A Level)
• Physics
• Most branches of engineering except for chemical engineering and bioengineering
• Computer science and software engineering
• Biological mathematics (and quantitative bioinformatics undergrad degrees outside of the UK, if they exist)
• Data science, business analytics, data analytics
• A number of life science degrees that ask for 2 “sciences” e.g. environmental science
• A number of healthcare related degrees that ask for 2 “sciences” e.g. radiography, optometry
• Geophysics, earth science, and geology
• Degrees that ask for 3 A Levels in any subjects, including business, law, nursing, architecture, archaeology, anthropology, politics, philosophy, theology

Note: economics is not a required subject at A Level for any degree, not even economics. If you study the subject, make sure you get a high grade to meet entry requirements.

Again, you don't get hired because of your degree. Thinking this means you are still delusional and entitled. You get hired because of what you bring to the table.

Whilst it's true that you require specific degrees in order to enter specific industries (e.g. medicine to become a doctor, architecture to become an architect, etc.), the vast majority of jobs don't require specific degrees or specific qualifications at all. Flaunting your degree in these scenarios will likely get you kicked out of the interview.

Where they do require specific degrees, they tend to be required for regulatory purposes and this would require specific accreditation from specific professional bodies. If the degree isn't accredited by the appropriate body, it's likely not going to help with your job application.

If you don't know what you need to get into specific roles, it's probably a better place to start your research as opposed to thinking what you can do with your current qualifications and then decide whether it's worthless or not.

Do note, professional requirements and accreditation will vary from degree to degree, university to university, and country to country. What's valid in one country might not be valid in the next. So on an international platform, you might want to be ultra specific about what you are looking for and in which country you are based in. Otherwise, you can get the wrong advice for your situation.

QUESTION:

I am currently 14 years old. Over the last year I’ve developed a rather serious interest in mathematics. I decided to joined a course for math enrichment, I stay up late learning math and working on proofs for my own theorems as well as things I read online. I have decided that money is of no importance to me, and I’m considering to pursue a PhD in mathematics or physics. However I have some questions and concerns:

1. I am not particularly gifted in mathematics. Everything that I’ve achieved, was a result of hard work and perseverance. Although I don’t believe in IQ as a system, I have a relatively high IQ (130 - 140). I would say that I am more naturally gifted at public speaking and writing than I am in maths and sciences. However, I don’t have a lot of interest for either of those things.

2. I am not a quick learner and thinker. I have never performed well on contest math and am generally slow, yet accurate and over-analytical. Also information stays in my head for a very long time.

Considering all this information, would you say that a career in mathematics or physics is right for me? Thank you for taking your time to read this question :)

I will simply answer you with one quote from J.M. Keynes:

“The master-economist must possess a rare combination of gifts .... He must be mathematician, historian, statesman, philosopher—in some degree. He must understand symbols and speak in words. He must contemplate the particular, in terms of the general, and touch abstract and concrete in the same flight of thought. He must study the present in the light of the past for the purposes of the future. No part of man's nature or his institutions must be entirely outside his regard. He must be purposeful and disinterested in a simultaneous mood, as aloof and incorruptible as an artist, yet sometimes as near to earth as a politician.”

Math is often a small part in economic research (aside from specific math heavy domains). Having qualities such as an extensive general knowledge is for me far more important than being good at math in Economics.

By “how far,” do you mean as a mathematician or phycisist, or do you mean in terms of education? If you want to do any sort of research, you will need a graduate degree. Most degree programs have a specific concentration for those who want to pursue academia. Typically, applied physics is not the degree one pursues for this, but rather those who major in applied physics do more engineering-esque work. Although programs vary, applied physics programs generally have less physics than a typical physics degree (obviously) and instead also focus on engineering principles.

In terms of education, the math requirements are similar. You will probably have to take a calculus series and linear algebra for both. The physics degree will require more upper level physics courses (such as statistical mechanics) while applied physics will substitute those courses with ones in fields such as engineering and computer science. To summarize, applied physics is for students who want to work in engineering-related positions and can often do so with an undergraduate degree whereas those who major in physics often continue to graduate school and work in academia (although not necessarily – an undergraduate degree in physics has plenty of viable options, just not in physics) Compare the Bachelor of Science in physics with the Bachelor of Science in applied physics from Georgia Tech.