Physics Lournal

Why Mathematics?

Historically, it has not always been that Mathematics was respected, or even trusted. In fact, some of the people responsible for laying the foundations of Christian doctrine were known to have said "bewareMathematicians", and the Roman legal authorities labeled Geometry and Mathematics in general damned, and forbidden.

Even renowned practitioners of the field, such as Blaise Pascal, referred to the study as useless (though having praised it in the same breath), and considered it to be akin to carpentry.

Arthur Schopenhauer, a respected philosopher, considered arithmetic to be "...the lowest activity of the spirit, as is shown by the fact that it can be performed by a machine."

What's key to note here is that, these individuals tended to be peculiar in these opinions, with Mathematics being an accepted set of knowledge for one to be acquainted with, especially in educated society.

**From here, we face the question of why would one then, choose to study Mathematics?**

The answer could stem from taking a look at what Mathematics is, but this is a tedious endeavor, because it is a vast, and convoluted, interwoven field of study.

One can gain a much clearer understanding by asking the question, What is Mathematics intended to do?

Mathematics largely focuses on what can and can't be known through the faculties of reason.

Reason however, is also required to earn its keep. From the realms of business, art and sex, we see clearly that success in life certainly doesn't require the use of reason (in fact, these things can be downright unreasonable).

Generally, people are quite comfortable to rely on sensory perception as their method of gaining knowledge about the external world.

The benefit of the application of reason as a method of gaining knowledge of the external world can be seen in the fallibility of sensory perception: the size of the sun, or the imperceptible forces of gravity and wind, would lead us to draw incorrect conclusions about the physical world.

The sun is generally below the vanishing point of the horizon during sunsets, but due to the curvature of the earth and it's atmosphere, the sun becomes visible at a point in space that it doesn't actually occupy.

Because our senses are unreliable, and we encounter situations where correctness and accuracy are life and death matters (medicine, architecture), reason is how we account for the inaccuracy of sensory perception.

Another question of importance is: what does Mathematics hope to accomplish?

The overarching goal of Mathematics, can be seen to be the understanding of Nature.

If anything, the sheer economic and civilizational utility derived from the study of Mathematics can be championed as evidence of it being worthy of study.

However, the intellectual value and satisfaction gained from the study as well, should be kept in mind, when assessing the value of the field.

Furthermore, from these accurate observations, and the resulting understanding, we can elevate ourselves above the terror of being solely subject to Nature's whims, or those of angry Gods, and spirits, and the effect of curses.

Not only has Mathematics illuminated the Nature of the external world, but it has allowed us to derive key insights about the internal world: via information theory, understanding of the X-Ray section of the electromagnetic spectrum, and other things, probability, we've been able to glean knowledge about how we, observers of nature work ourselves.

Why Mathematics?

Physics Lournal

Why Mathematics?

Even renowned practitioners of the field, such as Blaise Pascal, referred to the study as useless (though having praised it in the same breath), and considered it to be akin to carpentry.

Arthur Schopenhauer, a respected philosopher, considered arithmetic to be "...the lowest activity of the spirit, as is shown by the fact that it can be performed by a machine."

What's key to note here is that, these individuals tended to be peculiar in these opinions, with Mathematics being an accepted set of knowledge for one to be acquainted with, especially in educated society.

**From here, we face the question of why would one then, choose to study Mathematics?**

The answer could stem from taking a look at what Mathematics is, but this is a tedious endeavor, because it is a vast, and convoluted, interwoven field of study.

One can gain a much clearer understanding by asking the question, What is Mathematics intended to do?

Mathematics largely focuses on what can and can't be known through the faculties of reason.

Reason however, is also required to earn its keep. From the realms of business, art and sex, we see clearly that success in life certainly doesn't require the use of reason (in fact, these things can be downright unreasonable).

The benefit of the application of reason as a method of gaining knowledge of the external world can be seen in the fallibility of sensory perception: the size of the sun, or the imperceptible forces of gravity and wind, would lead us to draw incorrect conclusions about the physical world.

Because our senses are unreliable, and we encounter situations where correctness and accuracy are life and death matters (medicine, architecture), reason is how we account for the inaccuracy of sensory perception.

Another question of importance is: what does Mathematics hope to accomplish?

The overarching goal of Mathematics, can be seen to be the understanding of Nature.

If anything, the sheer economic and civilizational utility derived from the study of Mathematics can be championed as evidence of it being worthy of study.

However, the intellectual value and satisfaction gained from the study as well, should be kept in mind, when assessing the value of the field.

Furthermore, from these accurate observations, and the resulting understanding, we can elevate ourselves above the terror of being solely subject to Nature's whims, or those of angry Gods, and spirits, and the effect of curses.

Recommended Readings: [The Study of Mathematics], by Bertrand Russell, The Mathematical Curriculum from The Aims of Education, and Chapters 2 & 3 of Science and The Modern World by Alfred Whitehead.

Referenced in

Mathematics For The Non-Mathematician

Why Mathematics?