It breaks my heart when I hear people say that interesting Maths is impossible to access as non-mathematicians. The whole point of high level maths is to synthesise your ideas into pure logic and reasoning; while I'm not suggesting your average English professor should be able to get differential calculus, I do think that to a certain level a lot of abstract maths is quite intuitive. Have you ever seen the geometric proof for how the series of 1 + 1/2 + 1/4 +1/8.... tends to 2? I think it's one of the many examples of how brilliant mathematicians are able to very clearly display and communicate topics. (I promise I have a point I promise I'll get onto it soon!)
Even if you don't actually want to learn any maths, the subject has had a fascinating life which is fun to read about, filled with drama, rivalries and huge embarrassments! First born in Sumeria at around 4,000 BC as a way of counting things once people began to trade livestocks and produce artisanal goods, it soon reached the Egyptians and became a unit of measurement (hence beautifully regular pyramids with sides of lengths divisible by pi due to the circles used to measure them!). Under the guidance of Pythagorus and, more importantly, Archimedes, maths slowly began to move into the theoretical. So blossomed the field of mathematics as we know it today!
What was the point of that rant? Everyone can enjoy reading a maths book, as a Drama student (there used to be mathematical duels!), a history student (mathematicians are everywhere throughout history) or a even philosophy student (I won't even START on how useful learning propositional logic is).
Here are a few to get you started
Fermat's Last Theorem: This is a wonderful retelling of the series of events that followed from Pierre de Fermat proposing the following proof: that there are no solutions a,b,c to the equation a^n +b^n =c^n for any values of n except 2. Even though its a very simple idea, even the most brilliant mathematicians have tried and failed to solve it (with much embarrassment ).
The Millennial Problems: A summary of the 7 "Millennial Problems" that were proposed at the start of the 19th century by David Hilbert, which have a 1 million dollar prize for their solutions! Each one has it's own flavour, and fascinating history.
The Music of the Primes: focusing on one of the millennial problems, this book explores how important prime numbers are in our modern history. I know: a book about prime numbers, must be terribly boring!! But if you take a moment, you might find yourself noticing prime numbers everywhere in your life; they have a huge multitude of applications in technology, and even appear in nature.
The Art of Statistics: what would any mathematics book list be without at least one stats book? This is a WONDERFUL place to start for anyone looking for real maths in action. We use statistics everywhere, and in very novel and perhaps non-intuitive ways. This is an incredible book to read if you want to understand what news releases quoting COVID infection rates really mean. I'll pose to you the following (completely true fact): the accuracy of a covid test (the ability to correctly a patient with covid) increases with the number of people who have covid! How is this possible? I suppose you might have to read and find out.
Please write in the forum via a comment section if you have any more recommendations!!