Using the 'Gapminder' dataset, filter the data for the year $2007$ and create a new variable $\text{'}$gdp$\_$category' based on GDP per capita. Classify countries into three categories: 'Low,$\text{'}$ 'Medium,$\text{'}$ and 'High' based on the following criteria:

$$ 'Low' if GDP per capita is less than $10000.$

$$ 'Medium' if GDP per capita is between $10000($inclusive$)$ and $20000($exclusive$).$

$$CM$2024$

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$$ 'High' if GDP per capita is $20000$ or more.

Write a script to perform these operations and provide a brief explanation of your approach.