Comment on Small and Large Gaps Between the Primes
https://www.youtube.com/watch?v=pp06oGD4m00
All this wonderful insight and technique, and most is lost because he does not store anything in the computer in a form that can be readily verified and improved upon. Yes, you can use symbolic math tools, rather than chalk. Human memory has carried us so far, but more people will benefit from communicating in forms where the process steps run independent of a human. Guide it, create it, use it, find new applications and insights. But then let it be in a form that others can use the parts that work.
Highlight problem areas and good pathways. Leave it in good form, and future generations can pick it up as though no time had passed. With the proper tools, ALL the existing tools and results for primes can be gathered and checked. NOT by forcing a few humans to memorize things for years. But by putting the whole outside our human limitations. People build motors and machines, processes and procedures – so it can exist and run outside a human memory and lifetime and strength and ability.
Hi George.
The problem, for the Internet, is that the universities charge a lot for access to simple summaries. The tools and data needed are not in a form for immediate use for problem solving. Try searching anything related to “primes” on the internet. And what you find on the EDU and AC site is old HTML and PDF and PS stuff that is not properly documented, and often incorrect. And only accessible by a human reader (it is all the same as though it were printed on paper) with infinite memory and experience. Putting the information in usable forms would allow all the people interested in these topics to access living models and tools of all that is known. Not spend a decade in university reading and writing on “paper”. In my tired moments I would say the sharing is no better than if everyone was still writing with a stylus on papyrus or sheep skin.
I count the cost in time and money and opportunity cost for every topic on the Internet. For a new person to cover all of “primes” could take a hundred lifetimes of reading paper, but might be absorbed and usable it all the knowledge were in tools – NOT ones that some company hoards, but available to anyone. I could work on some of these problems in grade school and certainly in high school. I had to invent my own tools and methods for some things, but the basics had to be read from paper and manipulated on paper. It takes weeks to check even one “paper” sometimes. And who has time to check all the new “paper”s to see if they are correct or usable? But it might be possible if all of mathematics were in computable form.
The world is content to send people through years or decades of university, when the unsolved problems now often need tens of thousands or sometimes hundreds of millions of people all working on the same game-board to solve. There are just that many variations and possibilities. We don’t even have a real time check on what has been done for every problem in mathematics, because it is still all on paper. PDF and HTML are “paper”. They require a human reader and human memory – because there are no tools and methods for sharing the living models, results and open issues.
When I read what you said, my first response was, “He wants to force every person who has an interest in mathematics (of primes) to spend years reading paper and paying for expensive materials only accessible through universities that make more money if they take longer to give someone the tools and information. And there are billions of people now being trained in math skills. The cost to society is very high, too high when there is so much to be done.”
Richard Collins, Director, The Internet Foundation
