I need help to write an essay about: probabilistic method || Occam's razor || mathematics in the 21st

I am interested in one of the master's programs in Data Science. In the application process I need to submit an essay of 1,000 words about one of the following topics:

1. Drawbacks of the probabilistic method
2. A mathematical theory for Occam's razor
3. What drives mathematics in the 21st century?

I have a background in numerical analysis and I do not have any idea about how I can tackle these topics. I would like if someone familiar with one of these topics to give me pieces of advice, resources, or how the essay must be structured so can start writing the essay.

I appreciate your help, thank you in advance.