Joachim,

Many thanks or references. Arithmetic (numbers) is not seemed to me quite magic thing :). Monkeys could count, couldn't? A new batman-superman-ironman I think should possess more powerful ability - to create euclidean geometry. This is in fact the first physical theory of nature on which Newton based his mechanics. Could you present some research in this dark place of human brain?

Exactly which type of neuron involved in the mathematical abilities are not clear, but I am sharing some link which may useful to you. Most probably dopaminergic neuron with gabaergic neuron of TGN may be responsible for mathematical abilities.

Geometry is related with visual areas.

Article A case for neuroscience in mathematics education

http://www.sciencemag.org/neurons-do-math-distinguish-predictions-reality

http://healthland.time.com/2013/04/23/your-brain-on-math/

https://www.scientificamerican.com/article/how-does-a-mathematician-s-brain-differ-from-that-of-a-mere-mortal/

https://books.google.co.in/books?id=DbHWCwAAQBAJ&pg=PA342&lpg=PA342&dq=neurons+which+are+responsible+for+our+mathematical+abilities&source=bl&ots=v50ObHebU3&sig=lfQY13Vb23EvCuyUBWVnd_JwuD4&hl=en&sa=X&ved=0ahUKEwiH__C9_uHXAhXEtI8KHSBgAn4Q6AEIXzAI#v=onepage&q=neurons%20which%20are%20responsible%20for%20our%20mathematical%20abilities&f=false

Prof. Hawking's has seriously underestimated the current human brain/mind. We have just whetted our feet at the edge of an ocean which is the human brain. we do know that the left angular gyrus is involved in calculation and the left parietal association cortex is involved in logical thought. The same area on the right side is involved analyzes the world as a gestalt. these have been proven with corpus collectomies which completely separate the two hemispheres. Any creature that wholly depends on logic is actually inferior to us. Symbolic logic and the mathematics on which it is based upon is quite simple compared to the way the different parts of our brain interact with each other. We do not know what that "logic" is! It is unlikely to be symbolic logic. it is probably more closer to quantum mechanical logic where A and B can be same or opposites depending upon the state of the rest of the System (Brain). Let us take something like Time. It used to be thought that it was Universal, but now we know that it depends on the frame of reference. It is an abstract entity and is ultimately a creation of our temporal lobes to organize the events we experience. sometimes it falters and we have conditions like deja' vu and jamais' vu. We do not know if the other parts of the brain follow the same sequence as the temporal lobe. more than likely they do not and we may actually have to consider the possibility of different kinds of Times! Mathematics and Physics are not the greatest achievements of the human brain. The functioning of the human brain itself is it's greatest achievement. thanks.

If I am not mistaken, not all civilizations used the decimal number system only. the Babylonians, for example, used the heximal number system besides the decimal. we still use the heximal system in our lives, such as 12 months makes a year, 24 hours makes a day, we have 60 minutes and 60 seconds. even our work week, which comes from the Bible, is six days as G-D rested on the 7the day. the decimal system seems natural to us, but it is very likely that the heximal system is the natural number system for our brains. thanks.

I am again asking for "geometry" neurons. I heard that Finnish guys recorded fMRI activity of brain when a person solve math problems. It was about 20 years ago, maybe.

Did anybody record neuron activity when a volunteer solve simple school geometry problem? Maybe it would be interested to design a real life problem which is solved by geometry theorems? Here we would possibly see how our brain apply ideal math terms of "line", "infinite straight line" ,"point" "intercept", etc. for real nature objects. Some very simple examples below.

You are building a house by yourself outside a city. How many wood boards, plywood do you need to buy in a shop to safe money, the house sizes are known. Of course the problem should be as simple as possible to simplify the search this neuron population.

Of course it could be made for healthy humans in fMRI experiments but also for epileptic people with implanted electrodes.

In people who are talented in mathematics, it is the same area or neurons that are involved in all forms of mathematics, be it arithmetic, geometric or algebraic. this area is usually in the left parietal association cortex. this is different from people who are not mathematically inclined. in them the geometrical or visuo-spatial capacity is in the right parietal association cortex. A good example of the former is the brain of Einstein. It was noted that the number of neurons in the parietal lobes was not any significantly higher than normal people, but the number of glial cells per neuron was higher in the left parietal association cortex compared to the right and to the normal people. Einstein used to describe his thinking as being geometrical. On the other hand, in patients with Alzheimer's disease we find a correlation between the atrophy of the right parietal lobe and the degree of loss of visuo-spatial or geometrical ability. these patients cannot draw two intersecting pentagons or the face of a clock. Hawking has also described his mathematical thinking in geometrical terms. he would be an ideal candidate to test this hypothesis. thanks.

The prefrontal cortex is involved in executive functions. these include, planning, assessing the consequences of different plans, working memory, volitional activity and so on. the temporal lobe, especially the neocortical part is involved in language function such as syntax, semantics, nomia, phonetics. the occipital lobe is involved in putting together the scattered visual input but not in the recognition of the resultant object. it is the parietal association cortexes that are involved in the visuo-spatial, geometric, logic, mathematical and the gestalt view of the environment. these can be seen in parietal syndromes such as Gertsmann syndrome, Balint syndrome and others. the prefrontal cortex and the frontal association areas are involved also in volitional motor function. injuries to these areas produce, abulia, apathy, akinetic mutism, apraxias and others. thanks.