Abstract Maths

These days someone shared an interesting article with me on Facebook (When Even Mathematicians Don’t Understand the Math) and I was impressed and it made me consider a lot of things. It is an article from 2004, but still I consider it to be even more true now than then.

I have a question for all of you: How abstract can mathematics be? To answer this question would be really hard (at least it seemed like this for me). I know that at university I have done some abstract things, not that many, but things that I find hard to explain to someone that is doing mathematics, but I find impossible to explain to people that never heard about it. And the most shocking is that if I go deeper and deeper I get to things so abstract that I cannot imagine. At first I thought that this is just myself, that something is going in a wrong direction, but seeing great people and mathematicians thinking the same makes me more unconformable about the whole situation.

”It is a bit like trying to explain football to people who not only have no understanding of the word ‘ball,’ but are also rather hazy about the concept of the game, let alone the prestige attached to winning the Super Bowl,” wrote Dr. Ian Stewart.

How hard is to explain a maths concept to the wide audience? Just a couple of days ago, I was thinking that there are not that many books, magazines, or booklets that talk about innovations in mathematics. There are some non-fictional books that present some mathematical fact to everyone, but they don’t touch deep things, they don’t touch hard things. And I always thought that it is not fair, that I would like to read about them more. I felt strange that there is so much physics, chemistry, geography or biology in all the science magazines, and not enough maths. But what if mathematics is indeed so hard to explain it to the general public?

Asked if there exist mathematical concepts that defy explanation to a popular audience, Dr. Stewart replied: ”Oh, yes — possibly most of them. I have never even dared to try to explain noncommutative geometry or the cohomology of sheaves, even though both are at least as important as, say, chaos theory or fractals.”

What can be done? Is there anything that we could do to change the situation? Right now, I don’t see anything, but I still believe that giving mathematics a little more credit will still change the whole ‘MATH = Mental Abuse to Humans’ concept. I understand that some concepts are so abstract that are incredibly hard to imagine, so almost impossible to explain to the general public, but what about the other things? What about emphasizing the importance of this subject to other disciplines? Can we find a way to make it more interesting the not so abstract concepts?


Let me know what you think about the article in the comment box bellow. I would love to find out your opinions. Hope you had a great day. Thank you for reading and enjoy your week. You can find me on Facebook,  Tumblr,  Google+,   Twitter  and  Instagram. Don’t forget that maths is everywhere!


5 thoughts on “Abstract Maths

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  1. Since my high school years I aspired to work within the universe of subatomic structure, but found it was not to be when I nearly failed my first Algebra course. Today as an avid amateur radio operator I can find I dread opening a book on antennas because after the first paragraph it is all about the math! I agree with you there should be some way to convey the inter-workings of the beauty that exists in mathematics to people in general… I know I would appreciate a radio reference book explaining in plane english what the math is about. Thanks for the great article.

    Liked by 1 person

  2. I’ve thought about how to make mathematics understandable to a general audience. The key seems to be finding good metaphors or images, but those are so hard to find. I recall a moment in Carl Sagan’s Comet where he mentioned that around the Oort Cloud a planetoid might orbit the sun at about the speed of a biplane puttering over a field, and that gives only the vaguest idea how fast it actually is — I couldn’t swear to whether it would speed along at 40, 80, 120, or 240 miles per hour — but it feels incredibly close to hand.

    Liked by 1 person

    1. sometimes, the way to explain them is to find an easy representation, but it is not easy. But I feel a little optimistic: things that were hard in the past, that were impossible and extremely abstract in that period are now easy to understand and we can explain them easily. So I am hopping that if we all do our best this thing will be possible, we will evolve


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