What do you enjoy/like about mathematics?

[ISamson]

What do you enjoy/like about mathematics?

Let me start:
I enjoy the beauty of mathematics and how beautifully it describes the World.
You?
Feel free to post equations.
Thanks.

 

[lekh2003]

I think of Math as a language. I like that Physics can easily be accessible by people from all over the world through mathematics. It simplifies everything and eliminates all confusion through logic and perfect statements.

 

[jedishrfu]

I like the hidden connections that are discovered in mathematics like when $\pi$ pops up in the strangest of circumstances.

 

[fresh_42]

https://www.physicsforums.com/threads/how-is-new-math-researched.935167/#post-5907666

I like to compare mathematics with model railroading: Usually male persons flee into their basements and start playing in an idealized copy of the real world for hours without recognizing anything outside of it. Mathematics can be a playground where fantasy and imagination is far more important than physical problems. The latter often come afterwards to justify their achievements to the rest of the world, which don't understand the childish part of their motivation (which I find is mainly responsible for the gender gap). Mathematical concepts frequently are used later on outside their original context: Grothendiek, Fock etc. As there will be no experiments, there won't be any restrictions beside the requirement to have no logical contradictions. Therefore we can invent whatever we want and play with it. I regularly read Terence's blog (T. Tao) and he's a master in finding interesting problems where others never look at. He also demonstrates, how important a mathematical background is. His solutions are very often a crossover of various mathematical disciplines.

 

[hyunxu]

If I solve a problem or question in physics or other science, I will be happy for sometime.If it is in the case of maths, my happiness will be like unlimited package.

My 8th grade maths teacher too say the same.

 

[anorlunda]

I was amazed to hear the story of Noether's Theorum. Emmy Noether was a mathematician. Yet her work proved to be immensely important to physics. That is serendipity on steroids.

 

[fresh_42]

That is serendipity on steroids.

I don't think so. Calculus of variations wasn't new in physics and at the end of chapter one in her second paper from 7/26/1918 "Invariant Variation Problems" she even wrote:

Theorem II gives the relative invariance of the left sides of the dependencies, which are combined by means of the arbitrary functions; and, as a consequence, another function whose divergence disappears identically and allows the group - which, in the relativity theory of physicists, mediates the relationship between dependencies and the law of energy. Finally, theorem II gives the proof, in a group-theoretical version, of a related Hilbertian claim about the failure of actual energy laws in "general relativity". With these additional comments, theorem I contains all in mechanics and so on known theorems about first integrals, while theorem II can be called the largest possible group theoretic generalization of the "general theory of relativity".

I did Google translate do the job, so it might not be the best English, whereas her German was perfectly written.

Für Satz II ergibt sich die relative Invarianz der mittelst der willkürlichen Funktionen zusammengefaßten linken Seiten der Abhängigkeiten; und als Folge davon noch eine Funktion, deren Divergenz identisch verschwindet und die Gruppe gestattet - die in der Relativitätstheorie der Physiker den Zusammenhang zwischen Abhängigkeiten und Energiesatz vermittelt. Satz II gibt schließlich noch in gruppentheoretischer Fassung den Beweis einer hiermit zusammenhängenden Hilbertschen Behauptung über
das Versagen eigentlicher Energiesätze bei "allgemeiner Relativität". Mit diesen Zusatz-Bemerkungen enthält Satz I alle in Mechanik u.s.w. bekannten Sätze über erste Integrale, während Satz II als größtmögliche gruppentheoretische Verallgemeinerung der "allgemeinen Relativitätstheorie" bezeichnet werden kann.

This shows, that she was well aware of the implications her results have for physics.

 

[anorlunda]

This shows, that she was well aware of the implications her results have for physics.

Thanks! Every day on PF, I learn something new.

 

[QuantumQuest]

What I enjoy / like most about math is the most obvious but also essential thing: abstractness. While there are already tons of established results in various sciences owing their existence to math, nobody can tell in advance where and to what extent math can also be useful. Math reveal their beauty in a perpetual manner with not so obvious repeats every so often. So I think that they are called very rightly "the mother of sciences".

 

[ISamson]

I like that it brings different people from different countries together towards one goal.

 

[Mark44]

One thing that I liked about mathematics early on was that it could produce an answer that was objectively verifiable. This was much less so in classes such as English, in which many of the criteria being used were more subjective.

 

[fresh_42]

I like that it brings different people from different countries together towards one goal.

Yep. That's one of the amazing things nowadays and part of the charm of PF. You talk with people literally around the world and use the same logic and language, and observe the same difficulties. I often have to think about my Grandma. She would have called me nuts, if I told her I talked to someone in Australia without leaving Europe at any time of day and people from America chime in their views. It hasn't been so long ago as nowadays normal was future's vision.

 

[Stephen Tashi]

I enjoy the clarifying nature of mathematics. I can't rave about the Beauty of math - in fact some of it is downright ugly. As to its Power, there are many cases where math is Powerful, but there are also cases where it is powerless. However, be it beautiful or ugly or powerful to powerless, a good mathematical analysis clarifies the issues.