No so long ago mathematics mathematics was very popular and allowed for the computer and Internet revolution, and progress in engineering sciences. Then statistics started to gain even more popularity (general linear model) until computers became much more powerfull. We now have fewer statistic jobs, and many are related to clinical trials (small data). Designing probabilistic model is not so popular anymore - although the term has been replaced by predictive modeling.
Then came data mining, then data science.
What will be next?
I believe statistics could experience a come back, possibly in the context of energy, environmental protection, climate and insurance. By the way statistics are also heavily used by actuaries (survival model, insurance pricing).
But where's the border between data science and statistics?
Some people think that advanced decision trees belong to mathematics, while others thing it is either a statistical, data mining or data science tool...
Based on my experience by attending University of Minnesota's Financial Mathematics program, I found it very interesting to see people who excel at Mathematics struggle with either computer science or database. I think people tend to think those who are mathematically bright should be good at any quantitative discipline. However, I have seen a great mathematician struggle with probability theory. I think it is similar to those who are not athletic at all think a baseball player should be good at basket ball too.
I think advanced decision tree belongs to any depending on how you apply it. I learned to apply my actuarial skills and the database skills in investment management. It gives me a lot of satisfaction to know that my approach is a new application and I have not seen so called "quantitative investing" out there really impressive. Here are some examples...
I use a very simple mathematical formulas that work in investing. The ultimate sophistication is simplicity. I see way too complicated mathematical formulas out there in finance just to impress others.
I will also admit that simple tax accounting really wears me out when I do it all day long. So my English literature teacher asked me to help him with his tax and I told him that tax prep drives me crazy. He didn't seem to understand. In his mind, I should feast on a lot of numbers.
Anyways, I am very happy that I found my passion. Please check out if you are interested at UAK Diversified
Well statistics is typically though of as under the body of or a branch of mathematics, so in essence, mathematics is still strong and alive. While needs change over time, mathematics will still be needed. It might be possible to say that the framework of data science has been formed, it is entirely incorrect to say that there are no more discoveries to be made in the area. As far as the question of the next big thing...well lets see if some predictive modeling will help answer that one haha. Stat's will definitely make a big amount of activity since there is so much being done in data creation, we are approaching this point where we are not able to analyze all of it, so there is much room for improvement in model refinement and model creation.
In my view, tying data to a geospatial location might be next. This would mean mapping the result of the analysis.
For example, where are our Cardiac Surgery patients comming from? In what parts of our market are we gaining share? In what parts are we loosing share?
Being able to geolocate data and trends would be highly desirabel to marketers, and could propel the discussion forward.
Tying data to geo is always en-vogue, but to me, its scary as hell. Why on earth would I want some money hungry marketer following me around town so to speak, even though they pretty much already do. Of course getting the who, what, when we have, getting the where I can see the importance, but getting the why I think is more important.
This is a well-developed branch of data science/statistics/mathematics - geostatistics and GIS. Since 1960ies at least. https://www.esri.com/en-us/what-is-gis/history-of-gis ESRI was a foundation, but now there a lot of open-source. Also most of geo-software is Python-based, so many modules can be incorporated. GIS encompasses big data, remote sensing data, spatial and temporal series. basically, GIS is a relational database where tables (layers) can also be linked by location.
Do we not already get the data for why I think? Steven you typed; but getting the why I think is more important.
Then I have a key to that gold mind, what you do is work with "how we think" translate that into a mechanism, then transfer that over virtual networks, then we begin to get access to why I think.
Artificial Intelligence (AI). Intelligent agents need lots of data.
Reasoning, knowledge, planning, learning, communication, perception and ability to move and manipulate objects requires data.
One next big thing will be closer interrogation of virtual data acting with the human consciousness and possibly the sub-conscious.
Statistics was initially called as "Biometrics', as it had to cater to the needs of natural sciences, especially biology related; this continued until 1925 when Prof.R.A.Fisher wrote his great paper "The Fundamentals of Mathematical Statistics". Again, statistics turned to data crunching when computers came. Now it is really difficult to see where it is going. One possibility will be the development of techniques to analyse BIG DATA, especially those under Resampling Framework.