If I want to learn about astrophysics, should I study up on mathematics?

Question

I am currently reading A Brief History of Time and while the book itself does not contain much mathematics in it, I want to learn more about the concepts Prof. Hawkings talks about more in-depth.

Now I am aware that I will never get the expansive knowledge that a university tuition in the field would give me, but I have already branched off into something else that does not allow me to pursue that field even if I really wanted to so I want to make do. (I also understand that any knowledge I do get will be basically useless to me, but I love space that much that, in spirit, the knowledge would feel useful to me.)

My question is, before I read books more technical, should I brush up on my math? I am aware that a more applicable subject like physics has more correlation with what I am interested in, but I don't want to read about physics if I have little to no knowledge what the hell each equation means. (Also, how I will learn is through online courses/websites/books. I know it is not the ideal way to go about it, but again, I will do what I can.)

Of course, if you believe I should somehow go back a few years and try my hardest at physics and follow the most tried path, I am all ears. It is just that I am now going to a technical college for IT and if I want to leave, I would have to spend a lot more time in education than most - meaning (as I live in the UK) will probably have to pay extra when I pass a certain age.

I know this question is not exactly linked to astrophysics, but I do not know where else to ask it. If I had read A Brief History of Time earlier in my life, I would not be in this sticky situation. Thanks in advance.

(ADDITION: I have always had a love for space and I was interested in physics, but my teacher was uninspiring and I was going through a tough period in my life. I am willing to work towards it now, even if my teacher is the worse thing to ever exist.)

Answer 1

Yes, absolutely. At bare minimum, you'll need to study some geometry to understand how distances are calculated and how the shapes of orbits are related. Next, you'll want to study some algebra, so you can understand the likes of the inverse square law for how the intensity of light drops off as you move away from an object emitting light equally in all directions. Algebra also helps in understanding the magnitude system astronomers use to describe how bright objects are in the night sky.

After geometry and algebra comes trigonometry, especially spherical trigonometry, because of its use in dealing with how we describe the location of objects in the sky, and how to relate positions in one coordinate system to positions in another.

Finally, if you want the really deep understanding, you'll want to go for integral and differential calculus. As my high school physics teacher used to say, the difference between an ordinary formula and one that uses calculus is like the difference between prose and poetry - the calculus encodes deeper meaning and is applicable in more situations than any single formula that can be derived from it.

Answer 2

It would help quite a bit but not absolutely necessary. Don't get me wrong, astrophysics, like most types of physics, is highly mathematical. If you wanted to study it in depth you would need much math. But astrophysics is a broad field and much can be learned, at least at a beginners level, with only a little calculus. This is my opinion of course. As StephenG said, knowing basic physics would be more helpful. I agree with that statement.

Answer 3

I agree with the answers here suggesting that geometry, algebra, trigonometry, and calculus are all highly helpful.

However, if I were you, I would reframe your approach a bit. Instead of asking yourself "I want to read more advanced sources on astrophysics, what math should I read first", I'd instead try to move towards this kind of process:

• What particular subject do you want to start with (e.g. how stars form, or what is a black hole, etc.)
• Read a general resource about this (e.g. Wikipedia articles, popular science pages online - long form books like Hawking's are useful, but can be hard to probe for just one topic)
• Ask yourself how much deeper you want to go; what didn't you understand, what holes are left unfilled, etc.
• Now, go find something more technical (a textbook, that mathy section of the Wikipedia article, whatever you can find)
• If you start seeing math/physics you don't understand, you may have to dig around to find out what you are missing. You can ask questions on SE about this kind of "mathematics/physics orientation".
• Learn what you need to progress, and then keep going. Repeat the above steps as necessary.

The main difference in this approach is that you spend less time moving through your "prerequisites" list, and more time reading about what you want to learn.

Now, there won't be any skipping algebra, trig, or calculus if you want to dig much deeper than A Brief History of Time. You will have to learn a lot of that stuff to understand basically any textbooks on astrophysics. It could be worth your time to go through some of the math and physics exercises on Khan Academy or another online learning resource.

The route I am recommending is filled with plenty of frustration, and might be annoying at times. But speaking as someone who's been learning a lot on-the-side of undergrad and graduate school for the last five years, I think it works better than trying to systematically learn everything in order. And it has the advantage of whetting your apetite with the "good stuff" you're trying to learn more frequently. YMMV, however.

Answer 4

Yes, mathematics is essential for all branches of physics and critical for astrophysics. It is required that you improve your mathematical skills throughout school and university.

Answer 5

Learning about astrophysics does not require math. Sure, most textbooks, papers, etc. are generally very math heavy, but these are geared towards academics who are trying to go beyond and discover new things. There are plenty of sources that explain the concepts in non-mathematical terms. A Breif History of Time is one of the most popular. But Hawking has other books which are similar, and other authors like Brian Greene, and Neil deGrasse Tyson have even more. Alex Filippenko has a good course from The Great Courses, as well as books and other sources. Those are just a few. You might be better off asking "What are some good non-mathematical astrophysics resources?". There are a lot.