Weather is the atmosphere's behavior right now - the temperature, humidity, visibility, wind, brightness, cloudiness, precipitation and atmospheric pressure changes.
Climate means a long-term (30 years) average pattern of weather in a particular area, including temperature, humidity, sunshine, wind, precipitation, fog, frost, storms, etc.
I was amused by this description, which I found on the NASA website - Climate is what you expect, but Weather is what you get. Like it or not.
Math is a tool we use to measure the weather and calculate the climate.
I searched for weather and math on Google Web. I got 46 million hits in .15 seconds. I read ten of those and got depressed.
I searched again in Google News. This time I had 484 results. The first hit was professor Cliff Mass in Seattle, talking about weather and math and the need for better math education. Read it if you wish.
My third search was weather and math on Google Images. This provided 11.6 million hits in .33 seconds. Here's the first image that came up, from Mr. Taylor's Science Website (now "inactive"). It shows the water cycle through the earth and atmosphere. [click image for a larger view]
Moving along, a Video search turned up 1830 videos in .15 seconds. That doesn't mean there are 1830 videos on mathematicians doing weather predictions - one of the links led to Weather After Math (a nice thought) but the author meant to say Weather Aftermath (an entirely different thing).
A search for weather math in Shopping located 7,340 products that I could buy, ranging from $1 to $350 (I discarded 2 outliers).
Did you know you can search the full text of books on Google? I found 95,400 occurrences of weather and math in books that Google has indexed, including the NY Times bestseller Kiss My Math by Danica McKellar.
Moving along to YouTube, I located 934 videos on weather and math.
I went to Patent Search and dug up 335 patent citations. One patent described a grid of satellites to control the weather. The claimant says his invention can generate energy, reclaim wasteland, and improve the environment. Satellites with big sun vanes would orbit the planet, reflecting the sun's rays back out into space and/or generating solar energy. The combination of this shade and "free" energy would enable us to selectively adjust global weather. However, the last page of the paper says:
Should we do the math on the price and risk of implementing this invention? Whether he means one million or one billion satellites, I'm not expecting implementation in my lifetime ...