What is the importance of mathematics in today's world?

I would say that there are practical, pragmatic, and poetic reasons to study mathematics.
Practical reasons: You will need to be able to compute areas for paint, carpet, sod etc..., compute interest payments and charges, keep a bank account including budgeting and investments, track changes such as your car's mpg, the rate of electric/water/data usage, etc... Statistical knowledge is absolutely necessary to vote for your best interests, to understand when a person or company might be giving you the wrong impression, to understand how to interpret scientific results outside of your field of expertise, etc...
Pragmatic reasons: For better or worse mathematics is used as a gatekeeper. Universities and colleges use math scores to determine who to accept as well as placement. Popular programs use mathematics to screen applicants. In large cities you would take a basic skills test in order to get into a trade union or be trained as a fireman, etc... In today's world math is used determine where you can live, what kind of things you can buy, the most efficient way to move stuff, and many applications of maximizing profits/ minimize costs.
Poetic reasons: Mathematics is a creative activity closely related to poetry and musical expression. There are rules but there are times/places to bend or break the rules. Understanding the beauty of a logical argument, a proof without words, or an organizational construct uplifts the human spirit.