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I have learned through studying theoretical physics that the ultimate goal of physics is to unify all the fundamental forces and build a theory of everything . Almost all the physicists are working to do that ; to derive an equation that is able to describe everything of fundamental physics . But my question is , what is the ultimate goal of modern mathematics ? What are the mathematicians up to ? Aren't they trying to build a mathematical theory that unifies the fundamental distinct branches of mathematics in very deep way ? Is Robert Langlands is the only mathematician to make an attempt to it ? Where is MODERN MATHEMATICS heading to ???

Laptop
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In a certain sense the ultimate goal of mathematics is to understand everything. Other sciences use mathematics to help formalise and develop their understanding of what goes on, and if you accept a (slightly naive) formalism that biology arises from chemistry, which arises from physics, which in turn is highly applied mathematics, then you have to conclude that mathematics is at the base of everything. (Although then you should really consider the argument that philosophy sits below mathematics.)

But: mathematics is beautiful, elegant, complex, dynamic, balanced and immersive. After a while, the ultimate goal of mathematics is... more mathematics, because it becomes addictive.

postmortes
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  • I find that formalism more than slightly naive. Also, even if you accept it, if you still say that physics, chemistry and biology are different from mathematics, you would say the goal of all those disciplines together is to understand everything, and you have not said what mathematics is about, as opposed to the others. – Torsten Schoeneberg Aug 31 '18 at 07:00
  • @TorstenSchoeneberg It is more than slightly naive (I'm British, understatement is a way of life). The very first sentence of my answer says what mathematics is about :) – postmortes Aug 31 '18 at 07:13
  • OK on the first point, but the second sentence of my comment says why I think the first sentence of your post does not match its second sentence. – Torsten Schoeneberg Aug 31 '18 at 07:16
  • What serious argument is there that philosophy as a discipline should be considered below mathematics? Mathematicians do not use philosophy in most areas of mainstream research. – KCd Aug 31 '18 at 07:21
  • if you say that all the other sciences together are trying to understand everything then I think you put mathematics in the role of providing the tools to enable them to do that. I have no problem with that either, as it happens, you can make beautiful tools and let other people use them :) – postmortes Aug 31 '18 at 07:22
  • @KCd in mainstream research maybe not (Zorn's Lemma comes to mind as inescapable). But the question "what is number" sits at the base of mathematics and is philosophical. – postmortes Aug 31 '18 at 07:22
  • I would disagree that Zorn's lemma is from philosophy. Zorn was very much a mathematician. – KCd Aug 31 '18 at 07:28
  • @KCd Being a mathematician doesn't exclude you from thinking about philosophy :) Zorn's Lemma is a statement about the ability to choose from an infinite set in a meaningful way. Since it's non-constructible you can argue that it's philosophical in nature. I think you see a dichotomy between mathematics and philosophy that not everyone would agree with, perhaps? – postmortes Aug 31 '18 at 07:31
  • I don't understand. Are you taking this question as a philosophical one? – Laptop Aug 31 '18 at 09:32