Currently, machine learning (ML) is applied for inferring some insights (quantitative and qualitative) from an empirical collection of various data obtained usually without preliminary planning (just because the data are available). ML is limited to exploring merely some empirical patterns, and associations/correlations of past data using various statistical methods, and then attempts to make a formal projection of these patterns to forecast some future data (assuming, of course, that the patterns are statistically stable).

Solving mathematical equations has nothing to do with the search for statistical patterns in data. Solving equations requires the application of calculus or numerical methods. No ML can improve the solution of the equation found using a solid mathematical technique.

Peter Breuer

Sorry for the late reply, to your first question

In my current project, I'm tackling equations that involve multiple variables. I've developed my method to crunch the numbers and find solutions, but I've noticed that as the number of variables increases, so does the time it takes to get the answers. It's becoming a bit cumbersome. That's got me thinking – what if we leverage the power of machine learning?

Imagine having a solid amount of data – enough to train a machine learning model- say, between 95% and 100% accuracy. I believe using machine learning could speed up the whole process and make it more efficient. Plus, it might demand less computer space compared to my current method. This potential efficiency boost could be a game-changer once the system is in action, making the whole solving process quicker and more resource-friendly.

Additionally, this approach might be handy for non-linear equations where the solution is a numerical value. I haven't explored symbolic solutions yet. Do you have any guidance on delving into symbolic solutions for equations?

The variables I'm dealing with are integers. For initial testing, the equation is quite straightforward, something like y = m*x + b. The data I'm working with is essentially a dataset, where each row contains values for x, y, m, and b. I've even published an example dataset for reference.

Peter Breuer

I'm in the process of learning machine learning, and I've generated a dataset where y is the dependent variable and x is the independent variable. My goal is to create a basic machine-learning model capable of predicting y when provided with new values for x, m, and b. It might sound simple, but I plan to gradually scale it up to linear equations with 2, 3, and 4 variables. Eventually, I want to delve into non-linear equations that produce numeric values as output.

My main objective is to understand how machine learning interacts with mathematics and whether we can harness ML principles for efficient space and time optimization in calculations. While I'm not sure about the real-world applications at this point, I'm driven by the curiosity to explore and gain insights from this intersection of machine learning and mathematics.

Peter Breuer

I appreciate your insights into the challenges with randomness and computational complexity in linear equations. Now, consider if we were dealing with more complex equations, say quadratic, cubic, or even higher powers like 5. In such cases, the computation resources needed would likely increase significantly. How would you approach or suggest tackling the computational demands of more intricate equations while still aiming for efficient solutions?

Rohit Agarwal If you are in the process of learning machine learning, I suggest you start with one of many books on the subject. The way you choose to start is a dead end, regardless of the type of relationship between y and x (linear or non-linear, one or multiple variables).

I suggest that you start instead with the use of the so-called Iris data set. It is a multivariate data set used and made famous by the British statistician and biologist Ronald Fisher. This set became a typical test case for many statistical classification techniques in machine learning such as support vector machines. The data set consists of 50 samples from each of the three species of Iris. The Iris data set is widely used as a beginner's dataset for machine learning purposes. Several other classic data sets have been used extensively, such as (among others):

• MNIST database – Images of handwritten digits commonly used to test classification, clustering, and image processing algorithms
• Time series – Data used in Chatfield's book, The Analysis of Time Series, are provided on-line by StatLib.
• "UCI Machine Learning Repository: Iris Data Set". Archived from the original on 2023-04-26.