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"Mathematicians pride themselves on being useless"-Michio Kaku

I was recently watching a video by Dr.Michio Kaku who said the above thing in a video titled "Is God a Mathematician".Please comment below about your views as I'll be eager to know.

My personal experience quite agrees with the fact that mathematicians pride themselves for being useless.Also there are popular beliefs by laypeople and internet memes that a PhD is maths is useless and stuff.In fact,when I read "A mathematician's apology" by G.H.Hardy I was quite shocked to see that my views about mathematicians was not even close to his philosophy.He claimed that "number theory" is a pure and gentle science and he was proud of this uselessness. The role that this "pure and gent;e" science played in the development of public key cryptography may serve as a reply to Hardy.

To be honest with you ever since I was a kid I looked upon mathematics as a means to explore the world around me ...not for mere recreational purposes.I was inspired by the people who did the same.If mathematics is useless then:
What about Issac Newton discovering Calculus to understand the nature of falling bodies and hence giving birth to Classical mechanics??
What about C.F.Gauss's work on the movement of Asteroids and electrostatics?
What about Leonhard Euler's work in mechanics??
Sophie Germain's work on elasticity which deeply influenced civil engineering(Though some people deny her credit)??
What about differential geometry being used as the basis of Einstein's special relativity??
What about Sir Roger Penrose's and Stephen Hawking's contribution to theoretical physics?
What about Alan Turing and his team breaking the Nazi Enigma code and saving countless lives??
What about Alan Turing's published paper "On Computable numbers...."giving birth to theoretical Computer Science??
What about Donald Erwin Knuth's definitive work on Algorithmic Analysis?
Or John Nash's equilibrium revolutionising modern Economics??

Note by Eddie The Head
2 years, 4 months ago

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Mathematics is no more useless than music, painting, rock-climbing or writing a good book. Are these things useless? Of course not!

You may have noticed this. There is a double standard going on against mathematics. You have never seen questions like “What are the real life applications of music?” or “What are the real life applications of reading good books?” But questions like “Why would anyone learn math? What are the real world applications of it?” are readily available everywhere. Why the double standards?

I view mathematics as an art form. It is not useless. I also do not believe that mathematics is important only because of its “practical applications”. Mathematics is not useful just because Gauss used it locate asteroids, or people now use it to encrypt stuff. The original appeal of mathematics does not lie there. Mathematics is useful in its own right and merit. Like I said, it’s an art form. And I shouldn't have to justify why I do mathematics. Mursalin Habib · 2 years, 4 months ago

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@Mursalin Habib People don't say these things about music and books because the audience for mathematics is infinitesimally small compared to music.... Eddie The Head · 2 years, 4 months ago

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Mathematicians aren't useless, and I thoroughly disagree with Kaku here. The humorous analogy I use for students about the relationship between physicists and mathematicians is that there's a line of mathematicians, all bent over and carefully looking at the ground, so that they know that when they take a step, the ground is solid beneath them. Hence they move slowly. On their backs leaps a physicist, not looking down, hopping without a care from back to back, and thereby making much faster progress than each of the mathematicians. Until, of course, the physicist reaches the end of the line of mathematicians, still doesn't look down, and falls flat on their face.

On a more serious note, even pure mathematics provides structure. We use these structures as physicists to make progress and without such structures we'd be fairly hopeless. When physicists do generate new mathematical concepts, we often don't prove them - we just say "looks plausible". Quite often we employ mathematical techniques which, if push came to shove, are not even completely and rigorously well defined. We make progress with these techniques because at the end of the day we need to just spit out some real numbers - and if those real numbers match what we experimentally measure, then we are pretty happy. However, I don't think any physicist would be completely content with a physical theory that could not eventually be made mathematically rigorous. Hence there is a role in physics for "pure" mathematicians in terms of filling in the blanks and fixing all the physicists mistakes. Many of those pure mathematicians (at least the ones I have met) do take pride in improving the discipline of physics. And, of course, outside of physics there is a whole host of problems mathematicians are involved in as well.

Finally, I've met some Fields medalists who are killer mathematical physicists too, so one shouldn't make too broad judgements... David Mattingly Staff · 2 years, 4 months ago

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@David Mattingly These days, one almost has to be a top mathematician in order to be a top theoretical physicist. The level of mathematics involved in theoretical physics is daunting. But physicists take more chances, they leap on unproven intuition where mathematicians would pause or stall. One of the best examples of this that I know of is the way physicist Paul Dirac pulled a rabbit out of a hat, in coming up with the famous Dirac Equation, which predicted, among other things, anti-matter It was well known at the time that the Klein-Gordon equation, which is the more general relativistic form of the Schrodinger equation, wasn't easily yielding any useful solutions, so Dirac simply forced the issue by devising an equation which would. A mathematician would have shuddered at his audacity, but Dirac had accidentally uncovered a truth about physics, which is that physical reality doesn't need mathematical perfection in order to exist, or to have the properties it has. Michael Mendrin · 2 years, 4 months ago

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@David Mattingly Sir, Are you a physicist? In which field? Swapnil Das · 1 year, 7 months ago

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You know, I came from a time when knowledge of mathematics was a highly regarded thing. Of course that was during the height of the Cold War, and it ultimately led us to things like the space program. Today, it's true, these days I keep hearing people ask, "what good is mathematics anyway, why do we have to learn this stuff?" Habib has made the excellent point that you don't hear people asking about what music or painting is good for. Mathematics is art too, which is why many mathematicians talk about taking pride in the fact their work is "useless". What they are really saying is, "I follow mathematics where it takes me, not where someone else tells me where I have to." That's pretty much the same attitude that many of the early explorers had, didn't they? It's the pure excitement of walking on ground no man ever has before. Michael Mendrin · 2 years, 4 months ago

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@Michael Mendrin

What they are really saying is, "I follow mathematics where it takes me, not where someone else tells me where I have to."

This is exactly the point I was going for. Mursalin Habib · 2 years, 4 months ago

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Dude, you have misinterpreted the whole implication of the video. What michio was doing was making a contrast between a mathematician and a physicist. A mathematician deals with abstract concepts of maths, while a physicist deals with a more practical application of math.

Supposed a mathematician solves the Riemann hypothesis or any of the millennium problems , in all honesty how useful will it be, while a physicists( as michio pointed out) in an attempt to solve the mysteries of the world, are spewing out incredible, mathematical concepts. This is what has lead him to conclude mathematicians are useless.

Think of it this way, Suppose you give a mathematician and a physicist the following equation \(F=ma\). To a mathematician this is simply an equation nothing more, they could come up with different ways of solving the equation, but they are pretty much clueless on what to do with it, On the other hand a physicist can use this equation beyond its mathematical expression. You can check this video, where richard feynman explains it excellently.

But of course being a mathematician, is something that goes beyond being respectable Beakal Tiliksew · 2 years, 4 months ago

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@Beakal Tiliksew No no....I am not disrespecting Dr.kaku's thoughts....the video was really good but what I wanted to discuss in this post is totally tangential to that video content... Eddie The Head · 2 years, 4 months ago

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@Eddie The Head i never said you disrespecting kaku, i was saying u misinterpreted what he said, of course newton and gauss law where significant. Beakal Tiliksew · 2 years, 4 months ago

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I was captured by Robin Williams in Dead Poets Society when he says, "We don't write poetry because we think it's cute. We write poetry because we are members of the human race, and the human race is filled with passion." When I start doing maths in the morning, I don't worry about completing coursework, or living up to expectations, or ridding the world of AIDS. I do it because I like the challenge, the mystery, the investigation, the thrill of being on the right path on a problem playing "hard-to-get". Art and music offer the rewards for passion, too, but Math offers additional benefits: theorems and formulae come up in practical uses and mathematicians are "rewarded" for their work by being "useful" to society. Is a mathematician worried more about the application of her theorem than actually, rigorously, proving it? I hope not.

I come from a bourgeois society where people celebrate art yet measure achievements in life materialistically. So when I say I am an undergrad majoring in Math, and that I want to have a PhD in Math, they frown at me. I think the rift comes from lack of foresight and conventional values: doing a B Tech and an MBA will get me a job quickly and earn me a handsome cheque every month while, frankly, nobody knows what a PhD in Math will earn me. What they do not see is that some people are ambitious and want to make their footprints last in the sand, and not merely eke out an existence and then die aimlessly. "...the powerful play goes on and you may contribute a verse", as says Williams, to the wonder-filled eyes of boys sadly trapped in routine. Siladitya Basu · 2 years, 3 months ago

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@Siladitya Basu A PhD in math can earn quite a bit...not doing pure math usually, but working in finance or other technical field as a fall back position. You just need to make sure you study something on the side that is suitable for such a position. David Mattingly Staff · 2 years, 3 months ago

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@Calvin Lin Please share your views..... Eddie The Head · 2 years, 4 months ago

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Who said that Physicists and Mathematicians have contradicting relationships? In fact, they are interdependent and good friends! Swapnil Das · 1 year, 7 months ago

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It seems Mathematics is the only independent subject.Everything in this universe has its major part made use of both Science and Mathematics.In the present era,one can be a scientist if he has knowledge about Mathematics.

A Mathematician is also a great philosopher. Mathematicians dont pride for being useless but they pride for showing themselves as useless which they are actually not.

The argument is like "God made a man and a woman but those two are fighting for their existence being unknown of the fact that both are made for a reason for which both are equally important." Vinay Sipani · 2 years, 4 months ago

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Mathematics isn't useless. However, as a mathematician, I'd be very happy if it was so. Agnishom Chattopadhyay · 2 years, 4 months ago

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@Agnishom Chattopadhyay You mean, you want it to be useless if you were dealing with it , right? Krishna Ar · 2 years, 4 months ago

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@Krishna Ar Yeah! Who wants to risk messing with working things? Agnishom Chattopadhyay · 2 years, 4 months ago

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@Agnishom Chattopadhyay LOL XD. Krishna Ar · 2 years, 4 months ago

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Well, Mathematics is generally divided into two parts- Pure & Applied Mathematics. And unlike Applied Mathematics, Pure Mathematics is not expected to deal with application in the 'real' world. And as far as I know, many Mathematicians didn't like to deal with real world application. If I am not mistaken, Gauss wasn't a fan of applied side of science or Mathemstics. Most of those Mathematicians liked Mathematics for 'mere recreational purpose'.

But in practice, applied scientists and mathematicians found out uses of most of those 'useless' mathematical findings.Because ,in the end, Mathematics IS the most useful branch of knowledge.

So, the conclusion of my view is - Mathematics is in no way useless.But its not the usefulness of a law/rule/theory/formula of Mathematics that attracts those mathematicians,rather its the beauty of it, or the joy of thinking about it that attracts them. Adeeb Zaman · 2 years, 4 months ago

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@Adeeb Zaman I appreciate your thought but gauss was immensely interested in the applied part of mathematics during and afterhis thirties due to which he repeatedly kept turning down sophie germain's letters containing her work on fermat's last theorem which did not interest him at that time.....he gave the same reason when he was asked why he refused to work seriously on the last theorem.... Eddie The Head · 2 years, 4 months ago

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@Eddie The Head Oh I must have made a mistake.I thought I was misguided by a quotation once I came across, which read like -

"....the greatest thing is purely mathematical thinking: this is worth much more than the application of Mathematics."

I thought I read that he said this a few days before his death.But I don't have any reference for this.

And of course thanks for clearing me out.I always thought that Gauss was not a fan of applied Mathematics! Adeeb Zaman · 2 years, 4 months ago

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@Adeeb Zaman There is a point in Gauss' life where he got more interested in astronomy than mathematics. He even considered becoming a philologist once. That was right before he solved a problem that had been unsolved for a millennium - constructing a regular 17-gon with an unmarked straightedge and a compass. Mursalin Habib · 2 years, 4 months ago

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