Bousso and Zukowski performed a mathematical analysis of multiverses that start out in one of two different initial states: an older model first suggested by Stephen Hawking and his colleague James Hartle, and a newer model that has come out of
mathematical treatments of the string multiverse.
may give cause for some to question the wider role of climate change and not solely global warming, that are induced by anthropogenic emissions, changes in land use, water quality etc for which there is direct empirical data in the form of images, and not
in mathematical treatments of theory and simulated models.
That's why I noted that Jones had let poor
mathematical treatment go to the IPCC record, despite the documented probability of knowing that it was poor.
His current area of research is non-commutative geometry, a branch of mathematics which is likely to provide solutions in
the mathematical treatment of «singularities» such as in the physics of the «Big Bang» beginning of the universe.
A key challenge for educators is in how we can support students to grapple with unusual but realistic problems that may be buried, ill - formulated or complex and that require the student to transform the problem into a form amenable to
mathematical treatment.
I know from my own experience that until a concept is conceptually grasped,
a mathematical treatment is often not really helpful.
The raw database is a mess and
any mathematical treatment to resolve problems (e.g. discontinuities, station moves, stations missing, TOBS, etc.) introduces other problems (e.g. estimating, correct adjustment to use, etc.).
Also
the mathematical treatment relying on reduced or effective degrees of freedom based on a «red» assumption is not sound even if the noise is red.