I firmly believe that dialogue is an undervalued and underexplored form for didactic writings, but I don't think The Little Schemer's two-column version with its short snippets of text is as good as it could be, or indeed very good at all. I would be in favor of something less catechismic and more discursive. And having more than two characters lets you illuminate questions and answers from many different angles. An example closer to my vision is Lakatos's Proofs and Refutations, which is half philosophy and half mathematics: the philosophy of mathematics as grounded in actual mathematical practice. That book is perhaps needlessly digressive, owing to its ultimately philosophical purpose, but it demonstrates an effective adaptation of classical philosophical dialogue to more mathematical matters.

Incidentally, Proofs and Refutations is the only book on the philosophy of mathematics that I'd recommend without hesitation or reservation to a fellow mathematician. You should all check it out. The excerpt on Amazon gives a pretty faithful impression.

If any of you know of any, I'd be very interested in other books that put dialogue to effective use outside its usual philosophical domain.

These three sent me to grad school.

ET Bell, Men of Mathematics
http://www.amazon.com/Mathematics-Touchstone-Book-E-T-Bell/dp/0671628186/

Davis and Hersh, The Mathematical Experience
http://www.amazon.com/Mathematical-Experience-Phillip-J-Davis/dp/0395929687/

Lakatos, Proofs and Refutations
http://www.amazon.com/Proofs-Refutations-Logic-Mathematical-Discovery/dp/0521290384/

If you want to read about how reliable a proof is, I highly recommend Imre Lakatos' Proofs and Refutations book. The best book about proof that I have ever read. It also doesn't require you to have a mathematical background, because the proofs are mostly geometrical.

Imre Lakatos' Proofs and Refutations helps make a little bit of the magic less magic.

Entrepreneur Reading List

1. Disrupted: My Misadventure in the Start-Up Bubble
   
2. The Phoenix Project: A Novel about IT, DevOps, and Helping Your Business Win
   
3. The E-Myth Revisited: Why Most Small Businesses Don't Work and What to Do About It
   
4. The Art of the Start: The Time-Tested, Battle-Hardened Guide for Anyone Starting Anything
   
5. The Four Steps to the Epiphany: Successful Strategies for Products that Win
   
6. Permission Marketing: Turning Strangers into Friends and Friends into Customers
   
7. Ikigai
   
8. Reality Check: The Irreverent Guide to Outsmarting, Outmanaging, and Outmarketing Your Competition
   
9. Bootstrap: Lessons Learned Building a Successful Company from Scratch
   
10. The Marketing Gurus: Lessons from the Best Marketing Books of All Time
    
11. Content Rich: Writing Your Way to Wealth on the Web
    
12. The Web Startup Success Guide
    
13. The Best of Guerrilla Marketing: Guerrilla Marketing Remix
    
14. From Program to Product: Turning Your Code into a Saleable Product
    
15. This Little Program Went to Market: Create, Deploy, Distribute, Market, and Sell Software and More on the Internet at Little or No Cost to You
    
16. The Secrets of Consulting: A Guide to Giving and Getting Advice Successfully
    
17. The Innovator's Solution: Creating and Sustaining Successful Growth
    
18. Startups Open Sourced: Stories to Inspire and Educate
    
19. In Search of Stupidity: Over Twenty Years of High Tech Marketing Disasters
    
20. Do More Faster: TechStars Lessons to Accelerate Your Startup
    
21. Content Rules: How to Create Killer Blogs, Podcasts, Videos, Ebooks, Webinars (and More) That Engage Customers and Ignite Your Business
    
22. Maximum Achievement: Strategies and Skills That Will Unlock Your Hidden Powers to Succeed
    
23. Founders at Work: Stories of Startups' Early Days
    
24. Blue Ocean Strategy: How to Create Uncontested Market Space and Make Competition Irrelevant
    
25. Eric Sink on the Business of Software
    
26. Words that Sell: More than 6000 Entries to Help You Promote Your Products, Services, and Ideas
    
27. Anything You Want
    
28. Crossing the Chasm: Marketing and Selling High-Tech Products to Mainstream Customers
    
29. The Innovator's Dilemma: The Revolutionary Book that Will Change the Way You Do Business
    
30. Tao Te Ching
    
31. Philip & Alex's Guide to Web Publishing
    
32. The Tao of Programming
    
33. Zen and the Art of Motorcycle Maintenance: An Inquiry into Values
    
34. The Inmates Are Running the Asylum: Why High Tech Products Drive Us Crazy and How to Restore the Sanity
    
    

    Computer Science Grad School Reading List
    

    
    

35. All the Mathematics You Missed: But Need to Know for Graduate School
    
36. Introductory Linear Algebra: An Applied First Course
    
37. Introduction to Probability
    
38. The Structure of Scientific Revolutions
    
39. Science in Action: How to Follow Scientists and Engineers Through Society
    
40. Proofs and Refutations: The Logic of Mathematical Discovery
    
41. What Is This Thing Called Science?
    
42. The Art of Computer Programming
    
43. The Little Schemer
    
44. The Seasoned Schemer
    
45. Data Structures Using C and C++
    
46. Algorithms + Data Structures = Programs
    
47. Structure and Interpretation of Computer Programs
    
48. Concepts, Techniques, and Models of Computer Programming
    
49. How to Design Programs: An Introduction to Programming and Computing
    
50. A Science of Operations: Machines, Logic and the Invention of Programming
    
51. Algorithms on Strings, Trees, and Sequences: Computer Science and Computational Biology
    
52. The Computational Beauty of Nature: Computer Explorations of Fractals, Chaos, Complex Systems, and Adaptation
    
53. The Annotated Turing: A Guided Tour Through Alan Turing's Historic Paper on Computability and the Turing Machine
    
54. Computability: An Introduction to Recursive Function Theory
    
55. How To Solve It: A New Aspect of Mathematical Method
    
56. Types and Programming Languages
    
57. Computer Algebra and Symbolic Computation: Elementary Algorithms
    
58. Computer Algebra and Symbolic Computation: Mathematical Methods
    
59. Commonsense Reasoning
    
60. Using Language
    
61. Computer Vision
    
62. Alice's Adventures in Wonderland
    
63. Gödel, Escher, Bach: An Eternal Golden Braid
    
    

    Video Game Development Reading List
    

    
    

64. Game Programming Gems - 1 2 3 4 5 6 7
    
65. AI Game Programming Wisdom - 1 2 3 4
    
66. Making Games with Python and Pygame
    
67. Invent Your Own Computer Games With Python
    
68. Bit by Bit

You're right: the amount of texts out there is daunting, so it can be hard to find the right area that appeals to you. Maybe a little more about the issues and questions you're interested in would help narrowing the options down a bit.

Two books that might be worth looking at: Proofs and Refutations by Lakatos. It looks at math and advances a thesis about what "proving" in math is really about.

And, Structure of Scientific Revolutions by Kuhn. It looks at the development of science through history and puts forth a provocative thesis about how science develops.

Take a glance at those, and see if they are up your alley. They are not too difficult, but they aren't really intro texts.

Try Proofs and Refutations by Lakatos
http://www.amazon.com/Proofs-Refutations-Logic-Mathematical-Discovery/dp/0521290384