What is this equation called and why is it regarded as beautiful?

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SUMMARY

The equation discussed is identified as the fundamental theorem of calculus, represented as $$\int_S dw = \int_{dS}w$$. This theorem illustrates that understanding the behavior within a region can be achieved by analyzing its boundary. The conversation highlights the historical context of the holographic principle, noting that mathematician James Gregory conceptualized it in 1667, predating physicist Leonard Susskind's work in 1997. For further study, Robert Ghrist's "CalcBLUE" is recommended, specifically chapters 18.1 to 18.5.

PREREQUISITES
  • Understanding of calculus concepts, particularly integrals
  • Familiarity with the fundamental theorem of calculus
  • Basic knowledge of mathematical notation and terminology
  • Awareness of the historical context of mathematical principles
NEXT STEPS
  • Study Robert Ghrist's "CalcBLUE" chapters 18.1 to 18.5 for in-depth understanding
  • Research the Generalized Stokes' theorem for broader applications
  • Explore the historical development of the holographic principle
  • Examine the implications of the fundamental theorem of calculus in various mathematical fields
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Mathematics students, educators, and enthusiasts interested in calculus, historical mathematical concepts, and the beauty of mathematical equations.

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$$\int_S dw = \int_{dS}w$$
Saw a few seniors talking about this equation, I don't know what it is called hence I can't google it, It doesn't look very correct as the RHS integral doesn't have a differential and both the limits look incomplete.
(they looked like they knew what they were talking about)

where can I study this equation and see its beauty?

also it didn't show up when searching for the most elegant/beautiful math equations, so maybe it isn't that significant?
 
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It is the fundamental theorem of calculus: In order to know what is going on inside a region, it is sufficient to know what's going on at the boundary.

Personal remark: It Seems mathematicians found the holographic principle 328 years prior to physicists (James Gregory 1667 vs. Leonard Susskind 1997), :-p .
 
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FWIW, it is less beautiful once you add all the terms, conditions and definitions to it in fine print (smoothness, continuity, domain of permissible values, etc.), like a great sale on a new car with a half a page of fine print attached.
 
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