At a high enough level, good scientists, mathematicians, and philosophers have many common traits. One trait is that these people are good at logical and critical thinking. They are very capable of following a train of thought, going through steps and avoiding logical flaws.

Good scientists, mathematicians and philosophers are also seekers of truth, so they will not allow themselves to stray from the path to the truth. In terms of historical records, Western philosophy as we understand it started in the 6th century (600 years) B.C., but Indian philosophy can be traced back to 10th century (1000 years) B.C. There has been evidence that complex mathematics was used as early as 3000 B.C. HOWEVER, there is a crucial caveat here that prevents us from concluding that math came before philosophy - historical records can be incomplete and biased. The truth is that we don't know, but I suspect that one cannot exist without the other, so it is likely that they came together from the needs of our ancestors to keep records and use reasoning to solve problems. If we were to strictly limit "philosophy" and "mathematics" to certain definitions, we may be able to pinpoint the dates better, but those definitions are not very likely to be complete or sufficient.

Most people use "science" to refer only to the natural sciences; in this context, neither philosophy nor mathematics is a science. However mathematics is a systematic and formulated knowledge. The idea behind science is that you observe reality and formulate ideas to explain it, and then test those ideas with more observations or experiments. Mathematics does not require you to observe reality, but for a mathematical statement to be accepted as a theorem, its conclusion must be known to always be true whenever its hypotheses are satisfied. In mathematics, however, the ultimate arbiter of correctness is proof rather than empirical evidence. On the other hand, science could make few advances without mathematics.

The requirement that you make observations in science is a philosophy, but many other philosophies do not require that you make observations, and so are not scientific. The usefulness of science is that you can know what reality consists of for a fact by applying it, but science also has the disadvantage that you can only use it to answer questions about things that you can observe; it is useless toward things that you can't.

During the Enlightenment period (late 1600s through early 1800s), educated men and women were exploring new fields of knowledge and considering many new ideas. Together, these ideas were called "philosophy", and many philosophers dabbled in multiple fields. Among these fields were science, mathematics, and politics, but back then they were lumped together.

As the amount of knowledge in each of these fields grew, it became such that it was no longer possible to learn it all in a single human's lifetime, forcing "philosophers" to specialize. This is when what we now know as modern science, mathematics, and what today is called philosophy became separate disciplines. Today's mathematicians are usually not also philosophers, and today's philosophers are even more rarely also mathematicians. Modern scientists treat mathematics as a tool: we use it, and will develop it if the branch of math we need for something doesn't exist, but are content to use existing math if we can.

This is a really interesting question because it really makes us think about the difference between math and philosophy. Back in early civilizations, most of the population didn’t worry about education. They were much too busy just trying to work enough to survive. The only people who had time to receive an education were the richest portion of the population. Those who received an education might begin to question how the world works. Why does an apple fall when I drop it? How far away are the stars? Why do I think? What makes me myself? At the time, there was no difference between science, math, and philosophy—the great thinkers were just that, thinkers.

It was these thinkers that slowly began to develop different schools of thought. Those that cared about our movement through space became physicists, those who questioned how the body worked became biologists, and those who questioned thought and existence itself became philosophers. This distinction was only possible because we learned enough about a particular type of information because before that, everything was just philosophy. For that reason, it is hard to say whether it is philosophy or math that is the mother to all sciences because for a long time, they were the same thing. Thank you for your question!