History of Math & Machine Learning
Tags: datascience, machinelearning, ai, math
Published: 2024-05-03 16:48:40

With the increase in popularity of Ai and machine learning, more and more people are looking to break into the field.

A quick look at the Google Trends stats for the keyword “machine learning” shows the interest in the term has quadrupled since March of 2016 (from a popularity score of 20 to a peak of 93 in March of 2024, at the time of writing).

With this, there has been a recent discourse amongst people wanting to get into Ai/ML. With the tools necessary to build your own neural networks being so easily accessible and the multitude of premade models already out for use, do you even need to still learn the math to get into Machine Learning?

## **Background**

Before we dive into the arguments on both sides and I give my opinion on the topic, it’s important that we first get a background on what led us here.

The creation of Artificial Intelligence is usually dated back to 1950. This was the year **Alan Turing** published his paper “***Computing Machinery and Intelligence***”, all about the theory of building intelligent machines and how we could measure or test said intelligence. However at the time theory was far ahead of technology, so although **Turing helped popularize the thought process**, his impact was stunted there.

A few years later in 1956, a man named **John McCarthy** would be the next to propel the field forward. McCarthy, **who is also credited with actually coining the term “Artificial Intelligence”**, hosted a conference with Marvin Minsky at Dartmouth College in 1956 called “***Dartmouth Summer Research Project on Artificial Intelligence*** (DSRPAI)”. McCarthy brought together researchers from multiple different fields to discuss the possibility and techniques necessary to make Artificial Intelligence happen. Although the conference didn’t exactly go to plan (it was reported that only six people there, including McCarthy and Minsky, stayed consistently present), **it was integral in starting the field as we know it today**. However, like with Turing, the technology still wasn’t fast, accessible, or capable enough of turning theory into practice at that time. That would not stay the case for long.

Nine years later in 1965, **Gordon Moore**, co-founder of Intel, had noticed that the number of transistors on an integrated circuit they were manufacturing had increased by a factor of two in the previous 5 years. He later posited that at the rate they were at, the number of components on a single chip would double every two years. This came to be known as **Moore’s Law** and would have massive effects on computing and society as a whole; but Ai especially. The exponential growth in computing power helped push the ML boom that occurred around the time. By 1970, Marvin Minsky was quoted as telling TIME Magazine “**from three to eight years we will have a machine with the general intelligence of an average human being.**”

There were several setbacks and rollercoasters the field has went on since which helped prove Minsky wrong: Ai winters, defunding of projects, lack of access to data, etc. However all of those events laid the foundation for the modern space of Ai/ML today. Skipping over multiple years and achievements later, we come to the surge in 2016 mentioned earlier. Google’s DeepMind team had created an Ai that successfully beat some of the best human players at Go, a feat so difficult people still questioned if it would be possible even with the release of Siri in iPhones 5 years earlier. This helped push the idea that **not only were intelligent Ai models possible, they were here**.

## **What’s Math Got to Do With It?**

So we know what led us to where we are now, and it sounds like a lot to do with computers. So where does math come in? **It had been there from the beginning**. Computer Science itself wasn’t it’s own discipline until the early 1960s. Even when it was created, it was considered the intersection between math and electrical engineering. **Many of the important names we mentioned earlier were all mathematicians by degree**. McCarthy was a mathematics professor at Dartmouth when he organized the summer conference with Minsky, who had received his PhD in mathematics from Princeton 2 years prior. Alan Turing graduated from King’s College with a mathematics degree in 1934 before publishing “***Computing Machinery and Intelligence***” 2 years later. Math has always been an integral part in the study of computing and ML as an extension. In fact, the majority of what happens in Machine learning is all about a computer being fed data and using math to optimize that data around a certain metric. Just like with the rest of computer science, when you peel back the curtain of programming it’s all math.

## **The Current Discourse**

So if it all started with math, and still consists of math, where’s the discourse come in? Well Ai has come a long way since it’s inception. Back in the early days of Ai, and even up until recently as Ai isn’t that old, it was assumed **you needed a PhD to do anything regarding the field**. The complex nature of the science and the fact that many of the biggest names in it were all PhDs helped push that narrative. Due to this, many stayed away from studying or pursuing ML unless they were already in a highly quantitative degree like computer science, math, or physics. Due to the nature of having a higher level of math requirements for these degrees, math was just accepted as a necessity to get into ML. **All that changed with this most recent boom in Ai.**

With chatGPT helping bring Ai to the mainstream and Tesla showing it’s applications on self-driving cars, **Ai has become the biggest buzzword** again and **everybody wants in**. This, along with the advancements being made helping make ML more accessible for the common man, caused people to see Ai as a hugely lucrative opportunity. However, with this influx of people from different and less quantitative fields, those who may not have had to take Calculus II or Statistics in college, or perhaps just don’t remember or don’t care to. And these people had a good question: **If there’s multiple different types of models already made, polished, and available on the internet for whatever I may need, why learn the math behind them?**

To their credit, there is a case to be made there. The math behind Ai is used to make the algorithms, right? So **if the algorithm is already premade then hasn’t the necessity for math been abstracted away?** And these aren’t just people from outside the field saying this either. Many data analysts and even ML engineers are saying that tough math is no longer needed to break into the field, citing the fact that **the majority of the models used in production are premade models** and that focusing on data cleaning and prepping would be a better use of time.

## **The Case for Math**

So I just solved the problem right there, most the models are premade so the math is a thing of the past. Right?

So here’s where I state my stance as well as make the case for learning the math first. As previously stated, **math has always been a huge part in all of computer science, *especially Ai***. The math is necessary in understanding what the algorithm for the model you’re using is, what it does, and how it does it. Now, it is 100% true that nowadays you can pickup a model online or load a GitHub repository and have an algorithm up and running without having to so much as know how it works. And oftentimes you can get by with most tasks doing just that. However, what happens when you want to change the algorithm to better fit your use? Or if it seems to break under certain use cases?

**Understanding the math is important to knowing what is going on behind the scenes in an algorithm.** Taking the time out to get at least a good foundation in the math behind ML can make a huge difference in your ability to use Ai, when to use it, and how to use it. It will give you a better intuition on which models work best in which conditions, and how to tune and track your model accurately. **Overall, the math is a crucial part in actually knowing what’s going on in Machine Learning.**

## **So Where Do I Start?**

So now that we’ve established why math is crucial for Machine Learning, how do you learn the math necessary? **Most of the math necessary you can pick up in an average college degree**. It’s pretty much all just linear algebra, calculus, and statistics. What if you didn’t go to college, or don’t remember? **Luckily, the internet is full of resources, both free and paid, to help you catch up and fill the gaps in your knowledge.**

[Abhishek (Adam) Divekar](https://medium.com/u/2df6dfeb5a48?source=post_page-----935f3a3929ee--------------------------------)

wrote an article with recommendations that I advocate you take a look at [*here*](https://medium.com/@ardivekar/high-quality-math-resources-that-helped-me-become-an-amazon-ml-scientist-82f7164500b2).

I also recommend the [***Mathematics for Machine Learning and Data Science***](https://www.coursera.org/specializations/mathematics-for-machine-learning-and-data-science?utm_campaign=websitecourses-m4ml-navbutton&utm_medium=institutions&utm_source=deeplearning-ai) specialization by Andrew Ng hosted on Coursera. The course breaks the math up into 3 categories: Linear Algebra, Calculus, and Probability & Statistics. I will also be doing a summary/review of each section in the course separately here on Medium for if you want to see what each section is about or just want a reference guide to freshen up or come back to.

Now that you know all about the history of math and Machine Learning, you know about the discourse, and have the resources to fill in the blanks, the only thing left is to get started studying. **Enjoy the process.**

*Reference List*

[https://trends.google.com/trends/explore?date=all&geo=US&q=%2Fm%2F01hyh\_&hl=en](https://trends.google.com/trends/explore?date=all&geo=US&q=%2Fm%2F01hyh_&hl=en)

[https://www.britannica.com/science/computer-science](https://www.britannica.com/science/computer-science)

[https://www.alumni.cam.ac.uk/news/cambridge-alumnus-alan-turing-to-be-the-face-of-new-%C2%A350-note-1#:~:text=Turing%20studied%20mathematics%20at%20King's,a%20first%2Dclass%20honours%20degree](https://www.alumni.cam.ac.uk/news/cambridge-alumnus-alan-turing-to-be-the-face-of-new-%C2%A350-note-1#:~:text=Turing%20studied%20mathematics%20at%20King's,a%20first%2Dclass%20honours%20degree).

[https://home.dartmouth.edu/about/artificial-intelligence-ai-coined-dartmouth?source=post\_page-----935f3a3929ee--------------------------------](https://home.dartmouth.edu/about/artificial-intelligence-ai-coined-dartmouth?source=post_page-----935f3a3929ee--------------------------------)

[https://ai100.stanford.edu/2016-report](https://ai100.stanford.edu/2016-report)

[https://www.investopedia.com/terms/m/mooreslaw.asp](https://www.investopedia.com/terms/m/mooreslaw.asp)

[https://bjc.edc.org/bjc-r/cur/programming/6-computers/2-history-impact/2-moore.html?topic=nyc\_bjc%2F6-how-computers-work.topic&course=bjc4nyc.html&source=post\_page-----935f3a3929ee--------------------------------](https://bjc.edc.org/bjc-r/cur/programming/6-computers/2-history-impact/2-moore.html?topic=nyc_bjc%2F6-how-computers-work.topic&course=bjc4nyc.html&source=post_page-----935f3a3929ee--------------------------------)

[https://www.theguardian.com/technology/2016/dec/28/2016-the-year-ai-came-of-age?source=post\_page-----935f3a3929ee--------------------------------](https://www.theguardian.com/technology/2016/dec/28/2016-the-year-ai-came-of-age?source=post_page-----935f3a3929ee--------------------------------)

[https://en.wikipedia.org/wiki/AlphaGo?source=post\_page-----935f3a3929ee--------------------------------](https://en.wikipedia.org/wiki/AlphaGo?source=post_page-----935f3a3929ee--------------------------------)