Our mathematics will never advance to the next level unless we become rigorous and precise in our concepts.
Much like mathematics achieved new heights in ancient Greece once the strict standards of proof were introduced and abided by, triumphing over experimental and fanciful proof-less mathematics of other cultures. One could imagine past mathematicians protesting the standards of proof: "But proving things is hard!", "What good is proving that which I already know is true?", but after some time, the use of those standards was recognized. Today we hear mathematicians much in the same way protesting the finitist standard of proof and mathematical concept as unrealistic, too hard, and not in sync with current developments of mathematics. But, despite the fierce ideologues of the 20th century like Dedekind, the 21st century will see the vindication of the finitist standard, and as a result, we will see mathematics prosper like it never has before. People will be amazed at the backwards, schizophrenic thought of Dedekind-style infinitists.
