I am a PhD student in physics studying high energy theoretical physics at UCLA. I am back in LA (where I’m originally from) after 4 years in New York studying math and physics at Columbia University and 2 years in England getting a masters in mathematics by researching twistor theory (a proposed theory of quantum gravity) at Oxford University.
Being a graduate student, I am not that far removed from the math education system, and I therefore have a crisp memory of having gone through it. In my opinion, the state of our math education system is terrifyingly bad (at least in some respects). Why do I believe this? Amongst other things, because most students never see the good stuff, i.e., what’s on this site. Most of us had to wait until the first or second year of an undergraduate mathematics curriculum before seeing this kind of math (i.e., real math), despite the fact that we could have been exposed to it much earlier on. In other words, by the time most people can see the cool stuff, they’re already so passionately turned off from mathematics that they don’t want to touch the subject with a 10-foot pole. I discuss more about this throughout the site, so I’ll spare the reader for now.
Second only to my love for math itself is my passion for teaching it. Thus, this site is in a large respect a selfish endeavor. I love learning new math and finding new results, and I also love explaining how I think about those findings to others. Seeing as it is my way of thinking about things that makes me enjoy the subject (after all, I have no way of thinking about things other than my own way (by definition)), I figure that explaining to others how to think of these things also inspires the same awe in their minds. The way I see it, there is a mathematical world “out there” and we’re fortunate enough to have the ability to experience parts of it. Moreover, the way that we experience this world is by communicating it to others. For if this world just sits in our own heads in just the same way that it sits “out there”, then it still does no one any good. I therefore feel that a large part of the responsibility of being someone who studies and loves this subject is to explain it to others. And that’s why I’m here now. The rest isn’t too important.
The True Beauty of Math 
So awesome. Thank you for embarking on this “selfish endeavor” as I think many others will benefit from it.
Thanks! I’l try to stay “selfish” 🙂
Excellent, thoughtful, profound and superbly communicated. Thank you for sharing this great passion. For the first time in my life, I am able to consider that mathematics is both beautiful and accessible. Please continue with your secondary ‘selfish endeavour’….
Thanks! That’s the goal!
i need to site you in my math essay but dont know your name. what is your name?
Hi, I’m flattered that you’d want to cite TBOM. I’m sure you can just cite the website itself, depending on your needs. Would that be sufficient?
Thank you for doing this. I have always maintained that everyone can “get math” (if not “do math”) with the right approach (that is, by following a step-by-step process). It is truly sad that so many people give up on mathematics in school, without ever finding out what it really is – I almost did myself and am so glad I didn’t.
This is a powerful resource for learning what mathematics is really about, from square one. You succeed in communicating profound concepts in simple terms; indeed the goal of mathematics. I hope you continue to do so and wish you success in your endeavour.
Hi Ezekiel,
Thank YOU for the comment. It’s comments like yours that keep me going 😉
I obviously totally agree about how unfortunate it is that so many people give up on such a great topic, before ever seeing what it’s all about. I’m glad you’ve found this site to communicate those ideas well, as I hope others have. I definitely plan on continuing, perhaps indefinitely. There are endless amounts of topics to cover, and with infinite time there could be infinite lessons. I’ve slowed down recently because I’m working on another project, and this project will end up finding its way to the site. It’s a high school course covering all of the topics the site has covered, plus all of the things the site will hopefully cover in the near-ish future. It goes at a much faster pace, though, with less “fluff”, but will be posted on here in the next couple weeks (barring any contractual obligations that say I can’t) so that the particularly keen readers can plow forward.
Anyway, I digress. Thanks for the comment and thanks for reading the site!
Cheers
really-amazing&beautiful-work-you-are-doing-for-students.i-m-aftar-hussain-from-pakistan
Your explanations are really very clear, accessible, and enjoyable.
You might be interested to know that I am not your average student; I am a 71 year old retiree
who craves the type of mental stimulation and intellectual challenge that can only come from
studying mathematics.- I discovered this when I picked up a precalculus text and decided to
see how much I remembered. I am now up to Linear Algebra and Differential Equations and
only regret that I did not discover all this forty years ago.
I scour the web for new material, which is how I discovered you. Have you written anything else?
Are there any books that you would recommend?
Regards,
Larry Shapoff .
Dear Larry,
I’m glad to hear you’re enjoying the site so much, and indeed I was very interested to hear that you’re not the “average student”! Learning to love math is definitely a “better late than never” endeavour—it is one of mankind’s oldest intellectual art forms and therefore lets you communicate with minds from centuries/millennia ago, and also holds some of the most beautiful secrets that our minds have the ability to grasp.
As for other things that I’ve written, the only thing that comes to mind is my “textbook” The Language of Nature, which is found in pdf form at the bottom of the “Lessons” page. This is still a work in progress (particularly the solutions) and hopefully I’ll be able to continue that progress again in the next couple of months. One genuinely heavy (but accordingly gorgeous) textbook on abstract algebra (which is what most of the lessons so far have been about) is Artin’s “Algebra”. This is a slow go, and the exercises are not easy, but it is a great way to learn how to think abstractly and like a mathematician, once my site becomes too easy for you.
The last few months and the next couple of months have been/will be insane for me, so progress on the site has been/will be minimal, but I do plan on continuing to add lessons (many more, in fact, and on drastically different material). I therefore hope you continue to enjoy!
Cheers
Hi Larry! I just happened to be looking through my comments and re-stumbled across your comment and thought I’d let you know (if you don’t already) that I have no elaborated on this site and turned it into a book, titled after the site, which you can get to over in the “books” tab up above. I’d love to know what you think! 🙂
Best,
Michael
It was great to hear back from you. Once I began to understand Calculus I found myself hopelessly addicted to mathematics so that now I can’t stop even if I wanted to. There is
no joy like mathematical discoveries you make on your own even if they are trivial. They
are still yours.
t
You know, I was once a little girl so deeply in love with Math. Then I became a victim of adolescence and a truly poor educational system. Reading this rekindled aspects of myself that had been dormant for years and will hopefully, with some hard work and passion, now blossom. What a gift you have for teaching and what an open person you are for sharing. Thank you from the bottom of my heart.
Wow, thanks! I’m so happy to hear that this site is helping you rekindle a love for math — that’s exactly what I do this for 🙂 I hope you keep enjoying the site!
Thank you for doing this and thank you for this plain english.
My pleasure! I’m glad you enjoy it 🙂
Hello!
I was looking on google “how beautiful math is” and i ened up here on your blog. I really like it as I’m a math lover. The next year i have to choose the university and I’m a little confused about it.. i love economy and math at the same level and i don’t know how to choose between them. Could you tell me your experience in the uni studying math? Do you suggest it to me? I’m worried to choose math because i don’t know what type of job i could do. Sorry for my bad english, i’m italian. Thank you so much x
Hi! I’m so sorry for my late reply, the last several weeks have been absolutely nuts for me but now I’m back in action! I’m glad to hear you’re liking the site and I certainly hope that continues 🙂 As for your future plans with math, I would never let worries of future jobs deter you. If you know how to think mathematically and abstractly, then you’ll be able to find jobs (even if not in academic math). You’ll be able to learn to program quickly and analyze data efficiently. So for now, if I were you, I’d just study what interests me most and devote myself fully to it. The jobs and everything will work out 🙂 If you want to talk more feel free to send me an email! 🙂
Love this site. Too bad I don’t have enough time to really dive into it. Soon tho…
Glad you like it! 🙂 There’ll be more lessons soon I hope (probably in about a month) as well as some other exciting things. Stay tuned! (Whenever you find the time, of course)
Thank you such much for embarking on such a “selfish” journey😁. I’m going into university next year and olan on majoring in physics, which i absolutely love (especially the quantum world). However, since highschool math I have consistently been told by my math teachers that my questions (I would always question given concepts like why 1+1=2 or what imaginary and comlex numbers really mean) will be answered in a higher math class.. For the time being i should just do my homework and solve my equations. This led me to a hatred of this rote memorization of sensless equations and numbers.
Luckily, my love for physics brought me to the realization that math and physics are like a peanut butter and jelly sandwhich. You really cant2have one without the other. For almost 6 months i searched for information that would devulge the abstract information of the language of the universe, and i have finally found it.
I’m almost dine with your first volume of “The true beauty of mathematics” and will then move on to the language of nature and then the website lessons!
Basically, I just wanted to say thank you for sharing this beautiful information with the world and allowing me to get a few steps closer to my goals in life.
– Cheers brother and thanks again
Hi Alex, thanks so much for your awesome comment! It’s comments like these that keep me going and I really appreciate you reaching out. I’m so glad to hear that the things I talk about here have helped you even in the slightest in your mathematical journey 🙂 Thanks for reading Volume 1! I’m currently putting the finishing touches on Volume 2 and it should absolutely be ready within a month so hopefully you check that out too 🙂
I wish you all the success in the world in your quest to explore math and physics. The relationship between these two fields is truly amazing, perhaps even approaching divine. There are many incredible secrets that the Universe has in store for us, many (perhaps all?) of which are mathematical. It’s a never-ending process, so please do find joy in the journey! And feel free to email/comment whenever and I’ll do my best to respond asap!
My entire school district on the central coast of California is working on ‘upping’ our math game. Your site mentions many of the visual conceptual models supported by Jo Boaler…have you hesrd of her work? Thank you for creating & sharing this richer, more approachable viw of mathematics. It is in dire need for all learners & thinkers & citizens!
Hi Jay, glad you like the site! And thanks for the reference to Jo Boaler, I looked her up and she’s great, we can definitely all learn a lot from her. It’s very exciting to hear about your district focusing on math so much, I think we’re really on the verge of some big changes in math education. If you want, I have some extra copies of my book lying around (leftover from a recent talk) and would be happy to send them your way if you think you/your students/your colleagues would be interested. Shoot me an email (see “contact me” tab) if so and we can work out the details!
Hi, thank you so much for all the courses you have provided for free on your website!!! i was just wondering if you were going to release Lessons 37 to 41 anytime soon? And are you currently working on a volume three of your book?
Thank you so much again
Hi, thanks for your nice comment and sorry for the lateness on my response! Technically I am still working on more volumes and more lessons, but unfortunately other commitments have made it extremely hard to keep creating content. One day (hopefully in the not-too-distant future) I hope to be able to really get back to it though. In a perfect world there’d be hundreds of lessons and dozens of volumes, and that’s indeed my long-term goal, I just unfortunately can’t give any solid time frames on it
But comments from readers like you are what keep me going! 🙂