Hi, I am a student of secondary school. I have to prepare a homework about " the positive effects of mathematics on human's thought". If you help me I'll be pleased. thank you...
Yucel Tucker

I can read this question in two different ways:

1. historically - the positive effects on 'human thought' as a collective development (philosophy, science, etc.);
2. individually - the positive effect on a the thought and thinking of an individual student of mathematics.

There might, of course, be a connection.

For example, historically, philosophers describe geometry as playing a critical role in the developlement of 'proof' and 'logic' as a form of thought which is very precise and comes with a strong guarantee that there is reliability and 'truth' in the connections.

Pedagogically, many people believe that the learning of geometry (if taught in an appropriate fashion) gives the individual a strong model of what truly reliable reasoning (proof) is all about. Some even believe that practicing such exact reasoning will have an impact on how one reasons and solves problems in other areas.

A second example would be the necessity of mathematics for the quantitative reasoning and the study of patterns in science. While, in principle, there is no guarantee that these precise games played in mathematics will actually 'fit' the objects and relationships studied in science, there is an 'unreasonably' good fit of these patterns (appropriately chosen) with the patterns found in science. Simply put, much of engineering, physics, etc. would not be possible without the way that parts of mathematics allow us to take one set of measurements and predict other events (measurements) with amazing accuracy.

Again, this is a model for all kinds of problem solving - thinking.

If you are willing to identify 'thought' with activities in the brain, or cognition, then it is important to realize that our brains are actually WIRED to do certain mathematical tasks. Lots of visual-geometric tasks (seeing what is connected to what in a diagram or a live scene, detecting that lines are at least roughly straight, interpreting a 2-d picture as a 3-d scene etc.) as well as simple arithmetic with numbers 1,2,3 (pehaps 4) is wired into our brains and, in part, into the brains of many animals.

It would be a very strange, and damaged, brain, that would think without some aspects of mathematics. However, there ARE people who can think very logically, and do problem solving at a high level, but cannot do arithmetic. (The condition is called Dyscalcula.)

There are also people who can do high level problem solving, but are very poor at 'language' and 'formal reasoning' (they reason visually and by association).

There are both types of people who have PhDs, for example, in fairly technical fields (like Psychology or engineering design of facilities for handling animals)

In some situations, perhaps in the context of this assignment, mathematics is identified with logic and proof. If that is the context then there is an analogy I learned from my advisor (Gian-Carlo Rota) Logic is to thinking like medicine is to food. It is NOT a good idea as your entire diet. However, there are situations where you will be a lot better off by pausing, clearing up the situation, and making sure things are healthy and reliable.

Walter Whiteley