Next great mathematical invention

In summary, the conversation discusses the possibility of a revolutionary mathematical principle or tool that is yet to be discovered or developed. This could potentially have implications for computer technology and could simplify complex problem-solving processes. However, it is difficult to predict what this new mathematical concept could be and if it will ever be discovered. Some believe that mathematics as we know it may be replaced by purely computational methods, while others argue that mathematics will always have a role in explaining natural phenomena. The conversation also mentions the use of calculus as a systematic way of solving tasks that would otherwise be difficult and the potential for future advancements in mathematics through interdisciplinary approaches.
  • #1
mryoussef2012
6
0
Hi , I was thinking about this , as you know calculus was used many years before the explicit work of both Newton and Leibniz , it was used the hard way , unrecognized , scattered and buried among unrelated formulas and topics.
The golden question is ; what if there is another revolutionary mathematical "principle" "tool" "method" (call it what you want) lurking on the orizon and living incognito inside the works of mathematicians ?!
Do you have some insights on what would it be like ?
Everyone who works with math , experiences sometimes the "aha" feeling when meeting with some beautiful pattern or similarity or a connection between unrelated stuffs , that would be a great hint for this subject.
 
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  • #2
Maybe it is there, just yet to be discovered
 
  • #3
Research from the P vs NP problem if its determined that P = NP will revolutionize computer technology since so much depends on search algorithms.
 
  • #4
jedishrfu said:
Research from the P vs NP problem if its determined that P = NP will revolutionize computer technology since so much depends on search algorithms.

It won't really revolutionize anything; knowing that P = NP doesn't give you any useful tools or algorithms. The truth or falsity of the statement has severe implications, but knowing the truth or falsity doesn't really do anything for you.
 
  • #5
P=/=NP probably. It's hard to prove but most of the computer scientist have a lot of reasons to think that.

It's hard to tell if there is some area of mathematics that will get very important in the future. If we knew we would probably concentrate mostly on it.
 
  • #6
Number Nine said:
It won't really revolutionize anything; knowing that P = NP doesn't give you any useful tools or algorithms. The truth or falsity of the statement has severe implications, but knowing the truth or falsity doesn't really do anything for you.

Sometimes the mechanics of the proof lead to new methods of computation.
 
  • #7
While doing physics problems, I wonder if we're doing it the hard way, when in reality there's some mathematics that we haven't developed or discovered that is much simpler and perfectly suited for all problems we encounter.
 
  • #8
leroyjenkens said:
While doing physics problems, I wonder if we're doing it the hard way, when in reality there's some mathematics that we haven't developed or discovered that is much simpler and perfectly suited for all problems we encounter.

It corresponds well with my line of thinking.
 
  • #9
Guess and check... Works every time, eventually.
 
  • #10
leroyjenkens said:
While doing physics problems, I wonder if we're doing it the hard way, when in reality there's some mathematics that we haven't developed or discovered that is much simpler and perfectly suited for all problems we encounter.

Yeah, I ran into that when I learned Lagrangian mechanics wondering why didn't they teach us this instead of Newtons way. The funny thing now is that I still remember Newton but nothing of Lagrange. the things you learn last are the things you forget first.
 
  • #11
Aero51 said:
Guess and check... Works every time, eventually.

If you think about it , calculus gives us a systematic way of doing some tasks that otherwise would be as painful as guess and check , so if we revise our current methods for resolving certain problems we may get insights about a new systematic way ...
 
  • #12
mryoussef2012 said:
If you think about it , calculus gives us a systematic way of doing some tasks that otherwise would be as painful as guess and check , so if we revise our current methods for resolving certain problems we may get insights about a new systematic way ...

That is exactly the job of mathematics. To abstract things and find systematic ways to solve different but related by something problems. In the future there might be some easy way find solution of the things that seem impossibly hard to us but it would probably require a massive amount of knowlege.

If you think about proving the formulas for area of circles volume of spheres, cones, pyramids without knowing calculus ( like ancient coltures did it and in school) it's really painful because you just try different aproaches for every case and they don't aways work. Sometimes they require a lot more effort. With calculus this is very easy job. You can do it in less than a minute with very small efforts.
But if you think about it in order to get there you need to prove many other theorems and statements about derivatives, integrals, limits... You are not actualy gaining all this for free.
 
  • #13
About ten years ago, I looked at Stephen Wolfram's "A New Kind of Science." It's a huge tome with thousands of computer generated patterns based on a limited number of simple rules for combining cells of cellular automata (either white or black or 0,1). The idea is that complex patterns seen in nature might be explained by a tractable set of simple rules of combination. His work is not original and his claims are controversial. A review by mathematician Rudy Rucker seems to give balanced view of his work. I'm not qualified to say whether mathematics as we know it will be replaced by purely computational methods for the hard problems of present and future science.

www.rudyrucker.com/pdf/wolfram_review.pdf
 
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  • #14
I am pretty sure that natural scientists (vs math guys) would be the first to find something when facing an out-of-place phenomenon ; just as Newton and Leibniz were Multidisciplinary men of science.
 

1. What is the "Next great mathematical invention"?

The "Next great mathematical invention" refers to a groundbreaking mathematical concept or theory that has the potential to revolutionize the field of mathematics and its applications.

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There is no set timeline for the discovery of a "Next great mathematical invention". It can take years, decades, or even centuries for a groundbreaking concept to be developed and recognized by the mathematical community.

5. Can anyone understand and utilize the "Next great mathematical invention"?

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