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Pi-is-3

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In summary, the conversation discusses the potential use of streams of mathematics that are not commonly used by physicists, particularly projective geometry. However, it is noted that there are limitations and uncertainties in applying new mathematics to physics, as well as a reliance on measurements and known methods. The conversation ends with a realization that the initial question was not well thought out and is ultimately closed.

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Pi-is-3

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Physics news on Phys.org

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String theory which is based on graded Lie algebras are an open problem, but it has known methods, whereas the physical significance is missing.

The cosmological investigations of de Sitter and anti-de Sitter spaces can be seen in the context of algebraic topology, but it is again known methods with open questions in physics.

So how should an answer look like? As soon as we can accurately describe a problem in physics, as soon do we have methods at hand, namely those the problem is described by. Whether such a problem can be dealt with new mathematics is per definition unknown, so cannot be answered.

There are some fundamental limitations and it is unclear whether they are necessary or only the usual way. Physics is done in frames, that is we have coordinates and we can measure quantities. These are strong restrictions since many mathematical objects have neither a coordinate system nor a metric, and I'm not aware of a physical question which doesn't expect them.

I remember that I once asked on PF why the Lie groups and Lie algebras in physics are always (I know, Heisenberg and Poincaré are exceptions here) the semisimple ones? Why don't their big solvable subalgebras play a role? Why do we always need to consider operators which walk the ladder up

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Vanadium 50

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fresh_42 said:. 'Unknown' and 'which methods' cannot be answered simultaneously.

I was once asked "...and how many more unanticipated problems do you expect to have?"

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martinbn

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It would be hard enough to list areas/techniques of mathematics that haven't been used in physics.

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Pi-is-3

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Sorry, I have realized my question is very stupid. I'll flag it to the moderator.

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Mark44

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Closed at OP's request.

Some examples of unknown mathematical methods used in Physics include fractional calculus, non-commutative geometry, and category theory.

These methods are applied in Physics to solve complex problems, explain phenomena that cannot be explained by traditional methods, and to bridge the gap between different theories.

The benefits of using unknown mathematical methods in Physics include a deeper understanding of complex systems, the ability to explain phenomena that cannot be explained by traditional methods, and the potential to discover new laws and principles.

Yes, there are challenges and limitations to using unknown mathematical methods in Physics. These methods may be difficult to understand and apply, and they may not always yield accurate results. Additionally, there may be a lack of experimental evidence to support these methods.

Scientists can ensure the validity and reliability of using unknown mathematical methods in Physics by thoroughly testing and verifying their results, conducting experiments to gather evidence, and collaborating with other experts in the field.

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