Short answer
Although the brain is indeed ‘split in half’, meaning there is a right and a left hemisphere, the idea that the two halves are fully split in their functions, such as logical and creative ones, is unfounded. This idea most likely comes from the fact that a few brain functions, such as language and attention can be performed more by one half then the other. However, the two halves are connected with an information ‘highway’, namely the corpus callosum, that ensures that there is a lot of communication between the left and right hemispheres.
Longer answer
Two hemispheres
If you have ever seen a photo or a drawing of a brain, you probably noticed it seems to be split, like a walnut, down the middle. It seems to be intuitive to some people that each half of the brain might be responsible for different tasks. For example, it is often heard that the left half is more logical, whereas the right half is more creative and emotional. Some people go even further saying that depending on what half is more dominant in your brain, makes you a more logical or creative person. In reality however, people do not have a dominant half of their brain, and halves of the brain do not correspond to personality types.
This myth partially stems from a true fact about the brain – a few brain functions are performed more by one half of the brain than the other. Parts of the brain responsible for language are mostly, though not fully, found in the left half. And there are other processes related to attention that tend to use slightly more of the right half. However, these examples are exceptions, and not as split in half as they seem at first.
Thousands of brains have been scanned specifically to observe the connections of brain cells in each half. No evidence for this general separation of brain functions into two halves has been found. Even with the few exceptions we mentioned above, involvement of brain cells from both halves of the brain can be seen, just one half slightly more or differently than the other. More importantly, such studies consistently find no evidence that individual people differ based on how their brains are connected. In other words, they find no so-called left- nor right-brained individuals.
The information highway
Our brain halves are actually densely connected to each other. The brain appears split from the outside, but if you look inside the split in the middle, you find that they are actually connected with the brain’s busiest ‘highway’ of information. This part of the brain, richest with connections, makes the two halves cooperate in all typical and healthy people in every single brain function.
Interestingly, in an extremely rare medical procedure, this highway has to be cut. The two halves are left completely separated with no direct way of communicating with each other. In such patients we can test whether language is completely processed by the left half of the brain. If that were true, then if we show a written question only to the right side of their brain, they would not be able to understand nor answer. Yet, they are able to understand and answer correctly! The patient cannot say the answer out loud. In order to speak it, their left half (where most speech is processed) would need access to the question that the right half received, which is impossible since the communication highway has been severed. But they can write the answer out on paper, showing us that the right half can still understand and process language on its own.
In an even rarer medical procedure, some patients have a whole half of their brain removed! Such extreme procedures are expected to seriously impact several cognitive functions. Scientists studied patients that underwent this procedure and in one study found that 70% of children who had one half of their brain removed still developed adequate language skills and finished mandatory education. And 21% of adults that had the same procedure were gainfully employed.
Conclusion
These examples show us that the brain is organized in much more complex ways than simply in two halves. In conclusion, even when we do find differences between the two halves, they are much smaller than what is commonly believed. In addition, modern neuroscience research repeatedly highlights that what makes the brain such a successful and powerful system is the efficiently interconnected and flexible organization which helps it constantly adapt to changes. This is useful not only for survival in extreme medical cases, but is a fundamental feature of our brain called brain plasticity.
Useful sources:
https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0071275
https://www.nature.com/articles/483260a
https://www.sciencedirect.com/topics/medicine-and-dentistry/hemispherectomy