On the necessity of importing neurobiology into mathematics

Synaptic integration mainly includes the summation of graded potentials. Graded potentials, regardless of their type, cause subtle alterations in membrane voltage, resulting in either depolarization or hyperpolarization. These incremental changes, when combined or summed, can propel the neuron toward its threshold. Consider, for example, a membrane experiencing a +15 mV shift, causing it to depolarize from -70 mV to -55 mV. In this scenario, graded potentials govern the membrane's ability to...

Neuroplasticity reflects the brain's remarkable capacity to adapt and evolve, responding dynamically to learning, experiences, or injury by reorganizing its neural circuitry. This reorganization involves creating new neural connections and refining old ones through a series of biological processes that contribute to the brain's lifelong development and adaptability.

Neurons, the fundamental units of the brain and nervous system, communicate through complex electrochemical signals that underpin all cognitive and bodily functions. This communication is primarily facilitated by a process involving the generation and propagation of an action potential along the axon of the neuron. When the internal electrical charge of a neuron surpasses a certain threshold, an action potential is triggered. This rapid change in voltage travels swiftly along the axon to the...

Biopsychology serves as a vital bridge connecting the intricate domains of biology and psychology, shedding light on how biological systems influence psychological phenomena. This field scrutinizes the biological substrates of behavior and mental processes, emphasizing the nervous system along with the roles of neurotransmitters, hormones, and genetics. It also incorporates evolutionary perspectives to explain the adaptive nature of mental functions.
The nervous system, the cornerstone of...

A postsynaptic neuron usually receives numerous impulses from several other presynaptic neurons. The axon hillock of the postsynaptic neuron integrates all these signals and determines the likelihood of firing an action potential.
Sometimes a single EPSP is strong enough to induce an action potential in the postsynaptic neuron. However, multiple presynaptic inputs must often create EPSPs around the same time for the postsynaptic neuron to be sufficiently depolarized to fire an action potential....

Neurons, the fundamental units of the brain and nervous system, function as the primary transmitters of information throughout the body. Their ability to communicate through electrical and chemical signals is vital for every bodily function, from regulating the heartbeat to processing complex thoughts. Each neuron has three main components: the cell body (soma), dendrites, and an axon, each specialized to facilitate swift and efficient neural communication.
Cell Body
The cell body, also known...