If you're serious enough into this that you really think a career change could happen down the line I'd first make sure you actually like what it is professional historians do. Researching and authoring an book based on original research is a pretty big goal.

One of the things to keep in mind is that there is a pretty big gap between what we often teach to high school students and lower level undergraduate students and what historians actually do at a professional level. Issues of rote fact, memorization and pure narrative get complicated by different modes of interpretation, different theories, and having a strong grounding in historiography (the history of history).

In other words, there's a big gulf between reading a pop history book that is on the shelf in the history section down at the Barnes and Noble and actually doing history. That isn't to say you aren't interested in doing history, but it might not be exactly what you think it is at the professional level.

An advanced degree in history is probably required to really get the training in theory and methodology required to do serious scholarly research and write a book length work on the topic.

If you are interested in getting a taste of what professional historians deal with beyond "the facts" as it were you might want to consider:

E.H. Carr - What is History - Carr talks about how history is an "unending dialog between the present and the past." Excellent read.

John Lewis Gaddis - The Landscape of History: How Historians Map the Past

William Sewell - Logics of History: Social theory and social transformation - This one is a bit more in depth, you might want to read the others first as a primer.

John Wiener - Historians in Trouble: Plagiarism, Fraud and Politics in the Ivory Tower - this is a pretty quick read that is worth your time lest your get too romanticized an idea of what professional history can look like.

If this isn't the kind of answer you were looking for, let me know and I'll try again.

First of all, I can totally sympathise with regards to your starting point. For me, history has become my main focus and it is other things that I later discovered a liking which I had to reconcile to that focus. But I know that this is often true regarding history for others.

Secondly, and more directly, you are not the first person that I have encountered who focused on maths/science and also liked history, and by that I am including professional historians. Dr Eleanor Robson began as a maths student, but during the course of her degree she did a project on Babylonian mathematics and that opened up ancient Babylonia as a subject for her. She currently teaches the history of the ancient Near East at UCL, and has an enormous list of publications and research behind her. You can never predict how, when, and why you begin to like a particular thing. But there are also ways to combine interests- there are those who specifically study the history of science, for example (and who frequently seem to get into hilarious arguments with scientists), which is quite a vital area of study. Likewise the history of mathematics is a fully fledged subject.

Thirdly, if you are seriously considering a career change, then you should seriously consider formal training. I would not go so far to say as history lacks common sense. However, the mindset of how to research, write about, and in some ways think about the past is something that one needs help with. When encountering an area for the very first time, it is very tempting to try to reinvent the wheel by accident, or to copy a bad wheel design because it was the easiest one to get hold of, or to not realise that we tend not to use wooden wheels any more. That metaphor sort of went places. But my genuine point is that understanding not only what historical methodology entails, but why it does that, can be opaque without a guide. And the best guides are those who have already had experience.

This is the great cheat of history, but it is almost impossible to get your head around current trends, methodology, and up to date research in any given field without a key. That usually requires somebody who has done it before. This subreddit partially exists to aid in this, but the most immersive way to go about doing this is to be properly taught. We can't set you work, and spend long hours of dedicated contact helping to train you (as much as I think a number of us wish that was a feasible possibility). There are books designed to play this role for a given area as well, but it isn't easy to spot them without already knowing what they look like. It is relatively easy to encounter a well-written, accessible book and think of it as being a key, but this is not always the case. Without having feedback from people who already know the area, how could you be expected to know how accurate any given historical work actually is?

The other advantages of being trained in a degree is that a) prior to a degree, all of us have misconceptions of both history generally and our area of interest, b) over the course of the degree it will expose you to areas that you had not encountered or considered before. Just as you can't predict how, when, and why you might find yourself enjoying history as a subject, you don't know when you might find the right things clicking and a whole new area of interest opens up for you. I didn't start in the ballpark of the Ancient Near East at all, or even by the end of my BA- this was an area I had an opportunity to get into during my MA, and I am extremely glad I did so.

In other words, by the time you finish a degree you almost certainly have a total different idea of what history as a subject is, and you may very well have a totally different area of interest. That's not something to be scared of, either- if there wasn't something appealing about almost every historical subject to someone, the field would be a whole lot smaller in scope.

You're flirting with history. That's a good thing. At first, keep it casual. You know, appetizers and drinks after work, coffee and a scone, stuff like that. Read some popular histories. Snag some Ambrose (Band of Brothers) for a WWII fix, grab some Kurlansky (Salt or Cod) for some culinary history. Read the little tidbits here. Have some fun with it. Skip around some and find the kind of thing you like.

When you're ready to kick it up a notch, think about taking a weekend road trip. Grab yourself a one volume history of something--maybe Beevor's Battle for Spain. Or if you're looking for something more intimate, try a biography like Robert Leckie's Helmet for My Pillow. Or maybe a close look at something interesting, or a trip to a museum.

Now, when you're starting to take things a bit more seriously, focus in on what you're really looking for. Find that subject (or subjects) that really fits. We're not talking a lifelong commitment here, but you're starting to not just flirt. You want something solid. So grab more than one book on the same subject. Along with Beevor's Spanish Civil War book, find Thomas. Then look at Orwell or Hemmingway, as well as Jose M. Sanchez's The Spanish Civil War as a Religious Tragedy. Just like several dates with the same person but at different locations will tell you more about them, looking at a number of books on the same subject will start to give you a depth of understanding.

Now you're ready to get really serious. You likely have enough knowledge to start posting here and get some flair. But there's some stuff that you want to do behind closed doors. You have to be careful about diving in too deeply, because you could get exposed to some really shocking stuff, but maybe check out a place like /r/badhistory. There is some really hardcore stuff going on in those kind of places, and it's not for everyone. If you're inexperienced, it could scar you for life, but maybe you'll find a niche there too. Just take it slow, and remember you can back out at any time if you're uncomfortable.

If you take away my relationship comparison, basically just read a ton about whatever strikes your fancy. Once you think you've found an area that you find interesting, dive in with every book you can find on the subject. That way you have some experience with the historiography of one subject. Only after that go looking for historiography in general (in my opinion), because otherwise it can be a bit confusing (again, in my opinion).

I suggest you use your skills and apply them to history. Too many people retreat to history because they aren't comfortable with math and science - and engineering, so you background is extremely valuable to history. Contact military historians in areas you like, explain your background and interest, and ask if there are some engineering questions in your shared field that need to be explained or better understood. It would be a valuable addition. I work a great deal in mining history, and it is always great to have a mining engineer who likes history explain implements or techniques.

I really like some of the answers here. I was in the same boat at one time and what really helped me bridge the gap between my love of science and history was looking at the French Revolution. Science and the salons of the time really played a huge role in the events of the Revolution. A personal favorite of mine in regards to researching into this time was how cholera, soap and the revolution were all tied together.