Mathematics: The Highest Truth
Mathematics is the highest truth because all its theorems and conclusions are absolutely true without qualification, true regardless of altitude or air temperature. The boiling point of water, as a counter-example, depends on air pressure, which depends on altitude. Physics is possibly in second place, although chemistry contends. Both physics and chemistry have the problem that at the atomic level, probability is involved. The life sciences have bigger problems because no two creatures are exactly the same. If the creatures happen to be human beings, their free will forgoes precision.
Ranking disciplines by the reliability of their truths is an idle pastime, except to highlight the least reliable: That would be economics. It is a subject of tendencies, not truths, because an economic time period cannot be duplicated. We can't rerun the economy at a different tax rate. To say that this tax cut caused that increase in gross domestic product is fatuous. Here is the answer to your middle-schooler who asks: What is the value of mathematics? Once you have experienced the highest truth ideally from proving your own theorem. - you can see the feebleness of lesser truths.
St. Augustine cited mathematics, specifically the natural numbers, as truth that was independent of sensory experience. That in his mind was preparatory to proving the existence of God.My hero, Aquinas, held that all knowledge comes from the senses. Hence I am hung up on this point, albeit possibly a minor one. Mathematical truth does not depend on physical experiments, the sine qua non of sensory experience. However, we do learn about mathematics through our senses. We read it in a book or we hear it from a teacher or a parent. What then about a genius like Leonard Euler who continued creating mathematics after he was blind? When he discovered that the sum of the squares of the naturals' reciprocals equals Pi squared divided by 6, was he not relying on known relationships that entered his mind through his senses?
Some mathematicians prefer physical representations while others are more comfortable in the totally abstract. The former enthuse over Euclidean geometry and representing integrals as area calculations. The latter like number theory and algebraic structures. All agree that infinity has no real world existence. Even perfect geometric figures like triangles and circles are only approximated in reality, although approximated quite well for the senses.
My next step on this journey will be to read Science and Hypothesis by Poincare.