Mathematics Limited to Finite Numbers Hinders Physics --- Professionals and academics struggle in their attempt to reverse engineer alien technology, which they must, to counter aliens exterminating life on Earth. Young students put their focus on math, because applied-mathematics limited to finite numbers excludes infinity, and if math, which is the language of physics, is to expand, then that expansion is out to infinity. State-of-the-art applied-mathematics only pertains to numbers that are finite, that can be counted-to, because to be finite is to be logical, rational, solvable, and knowable. But because sqrt(2) is proven not rational, meaning its numerator and denominator are not finite, the students understand that numbers can be larger than finite, what is called infinity, and their mission is to expose and explain infinity. The students find that state-of-the-art axiomatic deductive logic of pure-mathematics includes actual infinity as a quantity of a set, but there are holes-in-logic which suggest that version of infinity is wrong. But what alternative is there? Frustrated and desperate, some of the students go where logical minds should not, wondering if contemplative artsy or philosophic / religious speculations hold a clue for what infinity really is. Half the chapters develop properties for a useful infinity in the context of geometry, irrational numbers, quantum mechanics, special relativity, and the reciprocal of zero. Other chapters have the students reviewing historical revelations that contrast rational with irrational, and logical with paradoxical. The students fight misdirection and find hope in unexpected clues. Failures provide lessons. And they are under pressure. If you love math and don't mind a book full of equations, you'll enjoy this story of discovery. Paul C Daiber is an engineer who wants his readers to learn exciting new technical concepts and have fun while doing so. --- Before reading what is the needed new math, the reader is given a chance to solve the mathematical clues. The story carries a reader unfamiliar with math. To follow the math, be familiar with f(x) and df/dx, at least. --- In its first draft, storybook Alien Invasion Math Story was a collection of the essays and calculations written during the hunt for a useful infinity, but which were not included in the completed project's final textbook Special Algebra for Special Relativity. The added storyline that united the essays and calculations to create Alien Invasion Math Story, with its exaggerated emotional extremes, portrayed the confusion, frustration, misdirection, and stress felt in the hunt. Inspiration for a storybook came from the movie The Race for the Double Helix (BBC Horizon), in which Crick and Watson mixed incomplete bits of data (mostly from Franklin) with staggered inspiration. They persevered past criticism and little failures to win the race. Their moment of success came with a revelation. Me sitting at a desk or standing in a store watching my wife shop while thinking through proofs is not nearly as exciting as Crick and Watson in their quaint apartments and labs, so my storyline is fiction. But at least the math and the essays on human will are real. And, for the revelation at the climax, well, you'll just have to read it. Please do. I tried to make it fun.