"I tend to think that scientific papers (for scientific consumption, not necessarily for mainstream popularity) are warranted in using math..."

They're warranted using math only when it's necessary, Matt. Milton Glaser: "Less is not more. Just enough is more."

One of the most famous examples in energy is Mark Z. Jacobson et al's 132-page 2015 paper, in which authors purport to show the entire U.S. can be powered by wind, water, and sunlight:

100% clean and renewable wind, water, and sunlight (WWS) all-sector energy roadmaps for the 50 United States

and a response by 21 acclaimed international co-authors, published in the Proceedings of the National Academy of Sciences, which found the lengthy analysis

"...involves errors, inappropriate methods, and implausible assumptions. Their study does not provide credible evidence for rejecting the conclusions of previous analyses that point to the benefits of considering a broad portfolio of energy system options. A policy prescription that overpromises on the benefits of relying on a narrower portfolio of technologies options could be counterproductive, seriously impeding the move to a cost effective decarbonized energy system."

Evaluation of a proposal for reliable low-cost grid powered with 100% wind, water, and solar

In response Jacobson sued both the authors and the NAS, then dropped the suit after critics alleged it was an attempt to stifle legitimate academic discourse. He never reimbursed his critics for the legal fees they incurred.

To the point: size isn't everything (concealing them in a swamp of equations can't validate bad assumptions).

In the Jacobson paper that Bob mentions, one example that struck me as deliberate deception was that the PR announcement said that Jacobson and his team has analyzed the actual weather data for a year in hourly slices, in every region of the country he proposed siting renewable generation to confirm system adequacy without fossil fuel backup.  In the fine print of the paper, he admits that he took each hourly time slice, and averaged it over a 30 day period.

Of course there is no such thing as a battery or pumped hydro reservoir that holds 30 days of energy, so obviously this averages away every passing cloud or wind lull. 

The paper described the implausible 30-day averaging as a "subject for future study", again, hidden in the fine print.