Spiritually speaking, what happens to a person who only believes what science can prove?

One doesn't "believe" what one can "prove", unless you realize that "scientific proof" is like believing in the Ninja Turtles, in which case you'd be rather foolish. One believes in what one can't "prove" by the wondrous "scientific" method, which even "scientists" rarely use. One believes in a "TRUTH" which is far above such lowly matters as "science" and "proof" or "logic". When one can finally, truly believe in God, as in Jesus our Christ, then that person has exercised the ultimate mental functioning. And then there's the one step beyond that, which is acting on that belief. That is the ultimate, followed only by Heaven and spending eternity with our Lord and Saviour, Jesus Christ. God Bless you.