Recently, I wrote a tweet declaring how astounded I was by the magnitude of climate-change deniers' ignorance combined with their arrogance.

I compared them to the flat-Earthers who condemned Copernicus and Galileo in a bygone era.

"The sheer idiocy of those who ignore the math of climate change is stunning," I declared.

What's worse, I pointed out, is that they don't even feel any shame about that.

https://twitter.com/charliesmithvcr/status/1166526094737997825

Naturally, this elicited a bunch of criticism from people who don't accept the scientific consensus that human-induced climate change is a serious problem.

One of them has sent tweets asking me to show him the math.

It's as though the carbon dioxide measurements at Hawaii's Mauna Loa Observatory, which exceed 415 parts per million, weren't enough to convince anyone.

"You want some math?" I thought to myself.

I'll show you some math—and it won't only be those compelling charts from Al Gore's 2006 documentary, An Inconvenient Truth.

Instead, I've decided to post a video of a lecture last November by Chris Budd. He's a professor of geometry at Gresham College in the U.K. and a popular speaker about mathematics.

I highly recommend it for climate geeks and policymakers forced to respond to moronic criticism by conspiracy theorists who think scientists are on a Marxist-inspired mission to wreck the world economy.

Budd begins by pointing out that modern weather forecasting and officially recorded weather data is 150 years old.

So he says it's necessary to use "proxy data" to determine what took place before that.

It can be derived in a number of ways, including by measuring oxygen in ice, the width of tree rings, and even the quality of wines from a bygone era.

This proxy data shows that the temperature was low in Roman times, then warmed up, before cooling down in the Little Ice Age, and then increasing significantly since the beginning of the Industrial Revolution. 

Certain natural phenomena, like El Niño in the oceans or volcanic eruptions, can cause temperatures to rise or fall in individual years. 

But over the past two centuries, average temperatures have risen quite a lot, as the chart above indicates.

"That's our first indicator that the climate is changing," Budd says in the video.

The second indicator is the reduction in Arctic sea ice. It's measurable—43 percent thinner over the past 25 years, according to NASA.

The late summer extent of Arctic ice is down by nearly half.

That, in turn, leads to the runoff of more fresh water in the Atlantic Ocean.

"Then that changes the circulation patterns in the Atlantic," Budd says.

Sea ice is actually increasing in the waters around Antarctica. According to Budd, that's because land ice is melting and flowing into the sea. 

The third indicator of climate change, according to Budd, is more extreme storms. This week, we're seeing one of those extreme storms, Category 5 Hurricane Dorian, pounding the Bahamas and heading toward the United States.

The number of extreme heat events is increasing—and that's more dangerous over the long run to humanity than any rise hurricanes and cyclones.

"Storm, flooding devastate property and kill a few people," Budd says. "Heat events kill people in the tens of thousands."

Moreover, the math indicates that "a small change in the mean value [of temperature] means a large change in extreme events."

A fourth indicator of climate change is the rise in sea levels. They're up about 80 millimetres in the last 20 years, according to Budd.

That's because as water warms up, it expands. Also, as ice melts from land, it raises the amount of water in oceans.

It's worth noting that sea level does not change due to Arctic ice melting because this ice is already in the ocean. Land-based ice, like that on Greenland and Antarctica, however, will increase sea levels if there's runoff into the oceans.

The final indicator of climate change is the sharp rise in atmospheric carbon dioxide.

"We're not sure whether the Earth's systems can cope with that rapid rise," Budd says.

There's a clear correlation between carbon dioxide rise and temperature rise.

Budd also points out in the video that climate change is difficult to research because of the use of proxy data that has statistical variation, as well as the challenge of extracting trends.

Then there's the natural unpredictability associated with complicated systems. Moreover, it's difficult to create computerized climate models.

Then there's the issue of how much climate change can be associated to human activity and how much to natural variability.

"When you have nonlinear systems with lots of interacting things, they are not always predictable," Budd acknowledges.

Yet in one convincing section of the video, Budd points out that the solar data indicates that the Earth should be cooling, not heating up.

Despite this data, the planet is clearly warming. That offers a strong indication that human activity is responsible, not sun-related activity.

If that's not enough to convince the skeptics, nothing probably will.