**Missed Opportunities**" for the Gibbs Lectures.

The purpose of the Gibbs lectures is officially defined as "

to enable the public and the academic community to become aware of the contribution that mathematics is making to present-day thinking and to modern civilization." This puts me in a difficult position. I happen to be a physicist who started life as a mathematician. As a working physicist, I am acutely aware of the fact that the marriage between mathematics and physics, which was so enormously fruitful in past centuries, has recently ended in divorce. I shall examine in detail some examples of missed opportunities, occasions on which mathematicians and physicists lost chances of making discoveries by neglecting to talk to each other.

**Freeman Dyson**didn't mention

**Emmy Noether**, a German mathematician, and her contribution to the conceptual structures of the mathematics in modern physics in his paper.

**Nina Byers**goes into this in detail in her paper "

**E. Noether’s Discovery of the Deep Connection Between Symmetries and Conservation Laws**" in 1998.

Though the general theory of relativity was completed in 1915, there remained unresolved problems. In particular, the principle of local energy conservation was a vexing issue.

In the general theory, energy is not conserved locally as it is in classical field theories- Newtonian gravity, electromagnetism, hydrodynamics, etc.. Energy conservation in the general theory has been perplexing many people for decades. In the early days,Hilbertwrote about this problem as ‘the failure of the energy theorem’. In a correspondence withKlein[3], he asserted that this ‘failure’ is a characteristic feature of the general theory, and that instead of ‘proper energy theorems’ one had ‘improper energy theorems’ in such a theory. Thisconjecture was clarified, quantified andproved correct by Emmy Noether.

**mathematical differences**between

**Improper Integrals**,

**Proper Integrals**and also

**Indefinite Integrals**are in

**Calculus?**This is what this thread is about so please give your examples from the link below.

**Elementary Calculus an Infinitessimal Approach**" PDF link: https://www.math.wis...lc-03-07-17.pdf